2-whole-digital data processing in radio astronomy

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Page 1: 2-Whole-digital Data Processing in Radio Astronomy

http://researchspace.auckland.ac.nz

ResearchSpace@Auckland

Copyright Statement The digital copy of this thesis is protected by the Copyright Act 1994 (New Zealand). This thesis may be consulted by you, provided you comply with the provisions of the Act and the following conditions of use:

• Any use you make of these documents or images must be for research or private study purposes only, and you may not make them available to any other person.

• Authors control the copyright of their thesis. You will recognise the author's right to be identified as the author of this thesis, and due acknowledgement will be made to the author where appropriate.

• You will obtain the author's permission before publishing any material from their thesis.

To request permissions please use the Feedback form on our webpage. http://researchspace.auckland.ac.nz/feedback

General copyright and disclaimer In addition to the above conditions, authors give their consent for the digital copy of their work to be used subject to the conditions specified on the Library Thesis Consent Form.

Page 2: 2-Whole-digital Data Processing in Radio Astronomy

,.DIGiTAL DATA PROCESSING I N RADIO ASTRONOMY"

Trlesis subniitied to the

Universiiy of Auckland

for the ciegree of

Doctor oi" Phi'losophy

by

Mark David Apperley

Department of Ejectrical Engineering August 1971.

Page 3: 2-Whole-digital Data Processing in Radio Astronomy

ACKNOl^JLEDGEI{ENTS

The work desc'ribed in this thesis was carried out at the School ofEngineering, University of Auck'land, under the superv'ision of Mr B. Egan,

Senior Lecturer, Department of Electrical Eng'ineering. Technical assistance

was provided by Mr P. E. Do'ig. The project was financially supported by the

Uni versi ty Grants Cor,lmi ttee.

Page 4: 2-Whole-digital Data Processing in Radio Astronomy

CONTENTS

PageNo.

INTRODUCTION

CHAPTER 1:

1.1

1.2

1.3

t.4

1..5

1.6

L.7

1.8

1.9

1.10

CHAPTER 2:

2.r2.22.3

2.4

2.5

2.6

2.7

2.8

2.92.L0

CHAPTER 3:

3.1

3.23.3

3.4

3.5

3.6

3.7

\

THE II'ITERFEROMETER AS A RADIO TELESCOPE

Correlation or l4ultiplying InterferometersThe Incident Radiation and the Analytic SignalThe Spatial Frequency Concept

The Mutual Coherence Function and the Theory ofPartial Coherence

Properties of the Receiving SystemThe General Response RelationshipThe Special Case of an Incoherent SourceSource Position l,leasurement with the Co*elation

Interferometersource Diameter Measurement and Aperture synthesisConfusion in Interferometry

THE SENSITIVITY OF CORRELATION INTERFEROMETERS

Antenna Noise TenperatureEquiva'lent Noise Bandwidth

The Response of a square Law Detector to a l,loise InputCharacteristics of a Synchronous DetectorCharacteristics of an Ana'logue MultiplierThe sensitivity of a phase-Switched InterferometerThe Sensitivity of a Direct Multiplication InterferometerLfmitations and Assumptions

Comparison With 0ther ResultsThe Effect of Repeated Observations

THE INTERFEROI,IETER IN AN EQUATORIAL SYSTEM OFCOORDINATES

The Equatorial Coordinate System

The Measurement of Time

Solar and Sidereal Time IntervalsRight Ascension and Sidereal Time

The Right Ascens.ion of the Sun

The Output of an Interferometer in Terms of theEquatoria'l Coordinates of a Source

Coordinates of the Interferometer pole

I

6

7

9

11

L2

15

t719

24

25

29

31

31

32

34

37

39

42

47

48

50

52

56

56

57

58

59

61

61

66

Page 5: 2-Whole-digital Data Processing in Radio Astronomy

PageNo.

CHAPTER

4.L

4.2

4.3

4.4

CHAPTER

5.1

5.2

5.3

5.4

5.5

5.6

5.7

4: THE SPECIFICATION OF A DATA PROCESSING SYSTEM

The University of Auckland Radio TelescopeThe Function of a Data processing SystemThe specific Requirements of the 200MHz InterferometerA General Description of the Data Acquisition system

68

6B

79

BO

B4

5: FILTERING AND SAMPLING THE INTERFEROMETER OUTPUT 89

The 0utput Spectrum of a correlation InterferometerAnalogue Fi ltering TechniquesSampl i ng and Frequency A'l i as i ngDi gi ta1 Fi I teri ng Techni ques

General Fi'lteri ng ConsiderationsThe Dynamic Range rf a QuantizerThe Effect of Aperture Time on the Dynamic Rangeof a Quantizer

B9

93

98

L02

110

111

113

CHAPTER 6: THE DESIGN AND DEVELOPMENT OF ANCONVERTER

ANALOGUE-TO-DIGITAL 116

116

120

L25

130

133

14s

150

152

155

157

1s8

159

168

169

t72174

180

184

1BB

6.1

6.2

6.3

6.4

6.5

6.6

6.7

6.8

6.9

CHAPTER 7:

7.r

7.2

7.3

7.4

7.5

7.6

7.7

7.8

7.9

7 .70

t,

The specification of an Anarogue-to-Digitai converterA survey of Analogue-to-Digital convension l4ethodsThe Digital-to-Analogue Decodersign Determination and vortage comparison circuitsThe Programming LogicThe Input AmplifierThe Digftal Output and DisplayMechanical Details of the Analogue-to-Digital converterThe Performance of the Analogue-to-Digita] converter

THE GENEMTION OF SOLAR AND SIDEREAL TIME COORDINATES 157

Resolution, Stability and Accuracy Requirements of theCoordi nates

The Generation of Solar and sidereal Time IntervalsThe Development of a Standard Frequency OscilratorThe Solar/Sidereal Digital ClockThe Solar and Sidereal Frequency DividersTime Keeping and Dispiay CircuitsClock Control CircuitsControl of the Agquisition process

Physical Characterist.ics of the Solar/Sidereal CtockThe Performance of the Solar/Sidereal Digital Clock

Page 6: 2-Whole-digital Data Processing in Radio Astronomy

PageNo.

CHAPTER

8.1

8.2

8.3

8.48.5

8.68.78.8

CHAPTER

9.1

9.2

9.3

CHAPTER

10.1

L0.2

10.3

10.4

B: THE PAPER TAPE RECORDING sYsTEM

Requirements of the Multiplexing SystemGrouping of the Data into Eight_Bit BytesThe Development of the Digital MultiplexerPhys'ical characteristics of the Digita'l MultiplexerThe Requirements of the Tape punch UnitThe Development of a punch Control UnitThe Tape punch power SupplyTape Punch Mechanical Details

190

190

192

194

202

205

207

21,L

2L4

10:

9: A GENERAL DESCRIPTION OF THE DATA ACQUISITION SYSTEM ?Tg

The Complete Acquisjtion SystemThe Operation of the Acquisition SystemPhysical characteristics of the Acquisition system

THE DATA ANALYSIS SYSTEM

Storage Requirements

Analysis Requirements

0utput Requirements

A General Description of the Analysis System

THE ANALYSIS SYSTEM INPUT/OUTPUT

The Paper Tape Storage process

The Numerical Data 0utputThe Storage of Data from punched CardsThe Graphical 0utput program

L2: THE COMPUTER ANALYSiS OF THE INTERFEROMETER DATA

Rejection of Data Marred by Extraordinary Noise(a) By Consideration of-Collateral Daia FointsRejection of Data Marred by Extraordfnary Noise(b) By Consideration oisequential Data pointsAveraging of Several Collateral Sets of DataDigital Filter

SOME OBSERVATIONAL RESULTS

The Acquisition and Storage of the DataThe Analysis of the Data

Concl usi ons

2t9

221

22s

228

228

233

235

237

239

239

25L

254

254

259

259

CHAPTER 11:

11.1

7L.2

11.3

11.4

CHAPTER

L2.L

L2.2

t2.312.4

CHAPTER

13 .1

13.2

13 .3

The

The

The

The

265

268

27L

275

275

276

289

Page 7: 2-Whole-digital Data Processing in Radio Astronomy

APPENDIX

41. 1

.4L,2

A1.3

4i,.4

APPENDIX

. A2,L

42.2

42,3

PageNo.

?9t

291

2s2

293

294

3t7

317

32A

323

327

336

34V

6:

1: DATA A.CQUISITI0N SysTEM spEclFICATT0N

The Analogue-to-Digital ConverterThe Solarlsidereal Digital ClockThe Paper Tape Punch

Con,trol

2z DATA PROOESSING sysrEM 0PERATI0N INsrRUcrIONs

Stanting the Data Acquisition System

Recorrding Data w,ith the Acquisition Sy.stem .

Processing the Recorded,Data

THE DESIGN 0F A 200MHz PHASE REVERSING SI,JITCHUSING GERMANIUM SI.IITCHING DIODES

THE EACKFIRE ANTENNA

THE ANALYSIS OF SOME LOI,I-PASS FILTERS

The Ideal Low-Poss FilterThe Ideal Integrating Low-pass FilterThe Simple (first Order) nC FitterThe General Second 0rder FitterN Isolated RC Filters

THE OALCULATION OF LOCAL SIDEREAL TIME

APPENDIX 3:

APPENDIX 4:

AFPENDIX 5:

45.1

45.2

45.3

45.4

45.5

APPENDIX

ags

295

300

302

306

311

381

AFPENDIX 7: DATA PR0cEssINrG sysrEN cOMpurER PROGRAM LISTINGS

APPENDIX 8: LOGIC CIRCUIT SYMB0LS

AFPENDIX 9: SOME ADDITIONAL CIRCUIT DETAILS

Page 8: 2-Whole-digital Data Processing in Radio Astronomy

1.

IiITRODUCTIOiI

Research in raciio astronomy at ihe University of Aucklanci School ofEngineering has been in progress for a nerioC of six years. The program tvas

init'iated prinrarily to provide a variety of topics for posi-graduate research'in the Departrnent of ilecirical Eng'ineering, and at the same tinre to develop a

useful radio te'lescope installation. In'itial vrork tvas concentraied on thedevelopment of antenna arrays (Ljnt,1968) and low noise receivers at, a frequencyof 42l1Hz, ut'i1is'ing both phase-switched and correlation interferomerer prin-ciples (Irving, L966; Yamall, i968; Saunders, 1968).

At the beginning of 1969, the Department moved from its former cc*iriry sireinto the centre of.Auckland city. As no alternative field site was available,the te1escope was also moved, but space limitations meant that the city site was

inadequate for any usefu'l observations at 42F1Hz. It became clear that toutilise the site more ful'ly a higher observation frequency would be necessary,and a frequency of 200t'1Hz rrlas clrosen, as this was the upper linit of most ofthe ava'ilable'laboratory equipment, y€i stj'11 rvithin the range of semiconducrorcievices. In view of the inadequacies of the site, it lvas obvious tirat the per-fonnance of the system could be s1gnificantly improved by process'ing the outputin a digita'l computer.

The concept of digital data processing in radio astronomy is by no means

novel; since ear'ly in the development of radio telescopes d'igital data reductiorrtechn'iques have been used extensjvely in this field (Heeschen, 1961; Kraus et al,1966; Hobbs and Haddock,1967). It is on'ly through the use of such processingthat the powerful technique of aperture synthesis (Ryle et al, 1965) has beendevel oped.

The most obvious use of a digital computer in a sirnpie observation programis in the combination of a number of observations, a task vrhich can be perfornredmanually but is both tedious and time consuming. Holever the availabi'lity ofdigital computing facilities opens possibilit'ies for other forms of processing,such as filtering the data digitally (Cooper, 1970) and the complex mathematicalmanipulations of source extractfon (Kraus et al,1966; von Hoerner, 1967).

Radio telescope digital data systems have genera'l1y been designed to repiaceanalogue recording equipment (l4cLaughiin, 1962; Drake, 1960) although for largetelescopes, modern trends are towards on-line computers integrated with the

Page 9: 2-Whole-digital Data Processing in Radio Astronomy

2.

telescope to perform both data acquisition and pointing contro'|. (Cole and

Shimmins, 1971; Beard et al, 1967). A recent review of data processing in radioastronomy (Clark,1970) states that the design of a data processing system for a

radio te'lescope is 'a matter of simp'ly deciding what you want, and sitting down

and building the system to produce it'. Because the design of such systems hasgeneraliy been directed along these lines, the small quantity of literatureavailable on the subject tends to be descriptive, and no general methods ofapproach have been established.

This thesis describes the design and development of a general data process-ing system for the University of Auckland radio telescope. The present te'lescopeoperates at a frequency of 200MHz in a phase-swi:tched interferometer configura-tion, but the design of the data system has been kept sufficiently f'lexible tocope with most future alterations and extensions proposed for the telescope.

Any system for the digita] processing of experimental data can be dividedinto three stages: reduction, storage, and analysis. In a radio telescope thereduction is performed by the antenna-receiver system, which usually produces a

slow1y fluctuating output. The time variation of this output contains inform-ation concerning the position, shape and brightness of radio sources in theantenna beam. This output is digitised and stored in a computer for analysis.In the combination of a number of observations from different days, it is mostconvenient to record the data on a machine-readable medium, a temporary storageprocess, to be later stored in a digital computer for analysis. The systemdeveloped uses punched paper tape for this intermediate storage medium because

it is compatible with the available computer.

The unique feature of the system described is the recording of local siderealtime as a coordinate to the interferometer data. Because the bulk of the inform-ation contained fn the interferometer output is in its time variation, much ofthis information is lost if a time reference is not avai'lable. For a constantdec'lination angle, a radio source which is fixed with respect to the stars willbe observed once every siderea'l day, and hence sidereal time is the most usefulcoordinate to use.

The contents of the thesis may be convenient'ly divided into three sections.

(a) The development of the generai theory of interferometric radio tele-scopes and the establishment of the requirements of the dataprocessing system.

Page 10: 2-Whole-digital Data Processing in Radio Astronomy

J.

(b) The design arrd developmeni of tlie acqu'is'ition portion of the system,

that part of ihe system rvhich records tire output of the interferometer

on compuier readable punched paper tape.

(c) A discuss'ion of the computer programs developed to perform the basic

processing operations required of the system.

In Chapters 1-4 the relationship betr,reen the output of a radio'interferometerand the radiation inciCent on its antennas is developed, anci it is shown hovt the

output can be used to produce an innge of the radio sources present in the

antenna beanr. The sensitivity I irilitations of such an instrument are d'iscussed

and it is demonstrated that the sensitiv'ity can be inrproved by conbining the

results of several independent observa'ujons of a source. The input-outpu'u

relationships are appl ied to a source 'in the nornral astronornical coord'inate

system, and the relationship betvreen the time variation of the interferome'uer

output and the coordinates of a source is establjshed. In the light of t,hese

relationshjps, the Univers'ity of Auckland telescope is examined and tlte require-ments of a digitai data processing sysiem are cieveloped.

The design of the acquisition portion of the system is covered in detail inChapters 5-8. The effect on the performance of the system of d'igitising the

interferometer output is examined, together with the filtering required of the

data. The results of this investigation are applied to the design of the

analogue-to-d'igital converter for the system. A digital clock, described inChapter 7, produces coord'inates in both solar and sidereal time, and can be pro-

grammed to automaticaliy control the operation of the acquisition system. A

digital mult'iplexer is described which controls the format and punching of botlt

the coordinates and the digitised data on to paper tape. An overall descript'ion

of the acquisition system and its operation is given'in Chapter 9.

The computer programs, l.rhich form an integral part of the system, and theirdevelopment, are described in Chapters 10-12. The University of Auckland com-

puting system is described and the requirements of the softl.Jare established.

Chapter 11 gives details of the programs developed to control the storage ofthe data from the paper tape, a process which is essential'ly automatic and selfchecking. Details of some ana'lysis programs developed to combine and filter the

Cata, are given in Chapter 12.

Some observational resu'lts obtained with the systenr are discussed in

Chapter 13, and these are evaluated in lighr of the performance expected of ihe

system.

Page 11: 2-Whole-digital Data Processing in Radio Astronomy

4.

REFERENCES

3EARD, i-4.,1'10Ri140T0, lvl., and HEDGES, P. (tg0Z): "The Computer". Proc. LR.E.E.Aust. on the Culgoora Radio tleiiograph, ?8 pp. 345-352.

CLARK, 8.G., (1970): "Infornration-Processing Systems in Rad'io Astronomy and

Astronomy". Ann. Rev. Astron. Ap., B pp. i15-138.

C0LE, D.J., and SHIMllIilS, A.J. (197i): "A Tirne and Frequency System for Use atthe Aus-ura]ian f,lational Radio Astronomy 0bservatory". Proc. I.R.E.E.Aust., 31 pp. t2-t6

COOPER, B.F.C. (tgZO): "Post Detector Filtering in Radiometry". Proc. I.R.E.E.Aust.,31 pp.41-48

DRAKE, F.D. (1960): "Radio-Astronomy Radiometers and Their Calibration". In"Te1escopes", Kuiper, G.P., and Middlehurst, B.M. eds., (Un'iversityof Chicago Press, Chicago).

HEESCHEN, D.S. (1961): "Observations of radio sources at four frequencies".Ap. J. 133 pp. 322-334.

H0BBS, R.l^J., and HADDOCK, F.T. (tg0Z): "Measurements of the Lineariy PolarisedComponents of Radio Sources at a Wave'length of 3.75 cm". Ap. J., 147

pp. 908-911.

IRVillG, J.R. (1966): "A Total Power Radiometer". M.E. Thesis, University ofAuckl and .

KMUS, J.D. , DIXON, R.S. , and FISHER, R.0. (1966): "A New High-SensitivityStudy of the M31 Region at 1415 l4c/s". Ap. J., I44 pp. 559-567.

LIM, ,1.C. (1968): "Non-Uniformiy Spaced Arrays of Directional E'lements".

Ph.D. Thesis, University of Auckland.

McLAUGHLIT'I, J.C. (1962): "A Data Digitising and Processing System for a Radio

Tel escope" . M. Sc . Thesi s , 0hi o State Un'iversi ty.

RYLE, M., ELSMoRE, 8., and NEVILLE, A.C. (1965): "observations of Radio

Galaxies with the One Mile Telescope at Cambridge". Nature,207pp. I0?4-L027.

SAUNDERS, A.l'1. (i968): "A Design Study of the Correlation Radioneter".14.E. Thesis, University of Auckland.

Page 12: 2-Whole-digital Data Processing in Radio Astronomy

5.

VOi\i HOERNEF., S. (1967) : "Least Squares Fit of a Gaussian to Radio Sources".Ap. J., 147 pp. 467-470.

YARRALL, J.l'.l. (196S): "A 12i,1lz Rad jonrerer Using Metal 0xide Fielcj-EffecrTransistors and Integrated Circu'its,'. M.E. Thesis, University ofAuckl and.

Page 13: 2-Whole-digital Data Processing in Radio Astronomy

6.

CIIAPT:R

The Interferorileter as a Raciio Telescope

The output of a corelatibn interferorneter is a conrplex function of thepropert'ies of ilte jncident r aCiaijon anC the receiv'ing systen. This cirapterdevelops a relationshjp betleen this ourput anC the inc'ideni field'in ierms

of tlte properties of the receiving system. A general relationship is esta-bl'ished for the response of a tlo elenrent correlation jnterfenometer to an

incident part'ia'l1y coherent fie1d, rnrith no restrictions on the bandr.ridth ofthe receiving systern or the antenna propert'ies. It is shorvn hol^l a'knowledgeof this relationship can be used to determine the position, size and f1uxciensity of a source in the more particular case of an incoherent field, and

how it can be used to develop the princip'les of aperture synthesis.

The function of a radio telescope is to measure the intensity and distri-bution of rad'iatlon received fronr various parts of the sky. The basic radjoteiescope consists of three principal elernents - an antenna system, a receiver,and a measuring dev'ice. The antenna systen collects radio waves incicient upon

it from a particular direction, having a particular polarisation, and within a

particular frequency range. The energy collected by the antenna is deliveredto the input of the rece'iven, l.rhich amp'lifies and detects those components

within its pass-band, and the resultant fluctuat'ion of the measuring device isan indication of the power incldent on the antenna.

The two limiting factors of any radio ielescope are its sensitiv'ity and

its resolution. Most celestial radio sources are relat'ive1y weal< (flux density-10-2u V!/nt/Hz) and of smal'l anguiar size (.10 diameter). The sensitivity of a

teiescope is limited by the fact that the rad'iation received from celestialobjects is incoherent and thus 'indistinguishab'le from the background radiationreceived by the antenna, and noise originating in the receiver itself. The

resolution is'limited in that a telescope cannot resolve a profile which isnaffower than its beamrvidth. As.the beamvlidth of an antenna in any plane isrelated to its aperture dimension in that p'lane, and'independent of its collect-ing area, resolution can be increased by spacing two antennas some distanceapart in an interferometer.

Page 14: 2-Whole-digital Data Processing in Radio Astronomy

7.

1 .1 Correl at j on or I'lul t'iplyi ng i n-uerfero,rreiers

The basic additive radio interferometer consists of -urvo antennas at theends of a long transmission 1ine, r.''ith a receiver connecied io the midpo'int insuch a llunner that jts input voltage is proportional to the sum of the voltagesat the tt'ro aniennas. For a source moving jn the plane of the baseline, iherecepiion pat'uern contajns a "fringe" co;:rnonent caused by the interference ofwaves arrivjng at the tws ends of the baseline, modulated by a cornponent varyingmore slotvly r,'tith position, anci corresponding to the radiation pattern of a singleantenna.

The phase-switched interferometer (Ryle, 1952) has the advantage that it,discriminates against background radiat'ion received by tlre antennas. The tlvo

antenna vo'itages are effective'ly nrultiplied together, so that the output of thereceiver is proportjona'l to the product of the two antenna voltages. A b'lockdiagram of this system 'is shown in Figure 1.1.

FiSrure 1.1: The phase-slitched interferometer

Multiplication is achieved by alternately adding the turo antenna voltagesin phase and in antiphase, measuring the poh,er in each case, and averaging thispower. If the instantaneous voltage at antenna 1 is vr and that at antenna 2

is vz, then when these voltages are added in phase, the available power from thecombination, and the output from the square law detector is proportional to(vr+vz)2. Sim'ilanly in the antiphase case the ouiput from the square law detectoris proportional to (vr -vr)'. The output of the synchronous detector-1ow pass

fi'lter combination is the time average of the difference of these two voltages*

PHASE

yt.r j ILOW-PAS5I FtLl i.n

*Yhi,s is established in C?npter 2.

Page 15: 2-Whole-digital Data Processing in Radio Astronomy

'1 a

where

Vo0

=

the angular brackets

((ur+vz)2

( urt*urt*2v1v2-vf-v2

Cenote the

-1v,-v,))2+2v

1v z)

(+v'v) ,

Later versions of this system use

n'ique and have been ca1'led correlationblock d'iagram of such a system is shown

average:

c/+\ .l+| \ L,' .ut

a direct analogue multipf ic.ation tech-

interferometers (Saunders, i968). A

in Figure 1.2.

(tttl) =

l'i ma

r+T1lLII

lri-r

OUTPUT

Figure 1.2: The correlation interferometer

It can be seen that the output of this system is also the time average of

the product of the instantaneous antenna voltages. Both of these systems ni11

hereafter be referred to as correlation'interferometers, of the phase switched

and direct multiplication types

Assuming that the output voltages of the two antennas contain a correiated

component vsr cduSed by radiation from a celestial source, and an uncorrelated

component vu caused by the diffuse background radiation, then the output of a

correlation interferometer will.be given by

Voo

=

(ur.ur)

(vq1+vur ) . (vcz+vu'))

(u., vcz+vc r vu r*vu, v. r+vu, vu.)

(.,u.') + (.,uu')* (u,v..)* (uu,urr)

MULTIPLIER

Page 16: 2-Whole-digital Data Processing in Radio Astronomy

, .9.

It t'he time averoge is taken over a sufficiently long period, the productssf the uncsrrelated conrponents wi'll average to zero i.e.,

rlll- u, = (il.ro"r) (1.1)

The averaging period 2T wil'l a'lways be finite (fo'r jnstance sbservatisns ofvt and v2 are lirnited to a finite intenval), and t,he unco,rrelated produ,ct termswill intnoduce a noise fluctuation superir,nposed on v6 which will llimit thes€Itsitivt'W of the telesco,pe. The' sensitivity of a direct mult{ptrieation inter-ferorneter will be greater than that of the phase-strttched varierty, a.s the noisevoltage anisin9 ln the receiver of the latter will gtve csrrelate.d. voltaEes whenrefert^ed; back to the antennas. In addition, ':ln the phase-sl+{'tched interferometer,obs,ervatlons of (vr+vr) and (vr-vz) ane made alternately, so that the observationtime is effectively ha'lved.

1,2

.The electric field of the r.adiatisn'incident on the earth at tirne t can bel^e"presented by E(g"rn,,[rt], where {,0 fi and n are the cosines of direction withrespect to,a Cartesiansystem of eoor^drinates, (see,Fi,gure 1.3) and whel.e E is i:n,general complex.

1 ; colorm: cos/3n: CoEf

The followlngradiating sourcgs:

Figyre, f .S: The coor.dinete syste.nr

ass.umBtions can be rnade ahout the dis,trnibu,tion of the

Page 17: 2-Whole-digital Data Processing in Radio Astronomy

1ntu.

1. The scurces are isolated froin the receiving antennas ('i .e., the vJave-

fronts are pianar).

2. The sources are stat'isti cal j n naiure and are stati stical 1y stationaryin time.

3. The spatial distribution of the sources is one dinensjonal and thefielcjs tltemselves are scalar. The angular djstribution of the electricfield of the incident radiation can thus be represenied by E(.0,t)-

4. The s'ignals from any one direction are not necessarily independent ofthe s i gnal s f rom a ny other d'i recti on .

If E(L,t)'is to be considered as a stationary random process in iinre, then'its temporai Fourier transform does not exist.* As the temporal transform is

' necessary to the follorving analysis, -ulris difficulty is circumvented by defininga truncated function associated yrith E(t,t) as follows.

. -?,. _ FLet E'([,t) be the real field quantity, then define EI(g,t), its truncatedversion as

rf(l,t)=Er(g,t) , ltlsT II tt'21

=Q , ltltt )

The analytic signal Er(g,t) associated with the truncated function is then

rrtu,rl=rf{t,t)+irri(s,t) (1.3)

where the imaginary part,Ei(g,t) is the Hi'lbert transform** of the realpart (Beran and Parrent, 1964;'D.un. and parrent, Lg6Z).

* The known sufficient condition for the existence of the Fourier transform?(t) or r(t) is that f(t) be square integrable (Beran and parrent, 1964).

** The Hilbert transform i(t) or a time function x(t) is defined by

*rtl = * o{-gp-.o.J_6

I

where pf Oenotes the Cauchy principal value (Beran and Parrent,1964; Drane and

Parrent, 1962; Wozencraft, 1961).

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11.

The Fourier transfo* Ertl,f) ot E(.q,,t) can then be defined as

^'f*Er{r,,r) = f- rr(r,t1E-jznft61J_o

(1,4)

be writtel as ..

plane) thdnpoint dis-

1.3 The Spatial Freguency ConceBt

In the case of monoehromatjc radlation tlre lncldent field can

E(&,t) '= E(t)ei:?rft '

Considering a wave po:lari,sed in the plane of inc,idence (th,e

from Figure 1,.4 the hori,zontal ,compsnent sf the eleetrie field attance x from the origin is

AIE'(x) = E(1,)cost"j2nft.j?n

-')t .

XZ;I

a

Fiqure 1.4: Arr incident wave in the xz olane

Not'ing tha,t d = *.sing.e x.0 and cos = ,ffi,

th€n E'(x) = r(r,).Jznft trc "ihrn'xl

x

= E(e-,t) , ,E:6E'..j2rlx/f

The total e'lectriE field at x (horizontal component) is this quantityE'(x) integrated over all e. If the radiation is. restricted to a snall areaof sky near th,e zentth, as in the case of a hfghly directiona'l antenna, theh4,2<{1 and the,'horizontal conponeht.,of the ,electric field on the grou,n'd is

E(k)

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L2.

e(x/r,t) uilnnx/xo!, (1.5a)

.f@

+ | Er(er ,i)Ei(g.,t-t) .dt

J

r-= lE('q"t)

)

r+T1lTl)-T

f*= | E([,t)

)

But this has the fornr of the Fourier transform of E(L,t)

e(u,t)

and the superscript * denotes the

If 1,1= Lz=L, then f (.(,,r) isthe radiation from direction .Q,.

comp'lex conjugate.

identica] to the autocorrelation function of

"iZruLdL , (1.sb)

vthich is known as the spatial frequency spectrum of E(g,t). Comparing equations1.5a and 1.5b it can be seen that if the spat'ial frequency u is interpreted.aswl^i,1,, then the spatial frequency spectrum is the horizontal component of theelectric field on the ground. By nreasuring this quantity for ait values of x,then E(.e,,t), the angular source distribution over a small monochromatic source

can be obtained by Fourier transformation.

I.4 The Mutual Coherence Function and the Theory of Partia'l Coherence

Radiation fields encountered in radio astronomy are statjstical in nature

and can usual'ly be descrjbed in terms of Gaussian random processes. The

statistical description of these fields forms the theory of partial coherence(Beran and Parrent, 1964; Ko, 1.967; Hagfors and Moran, L970).

The mutua'l coherence funct'ion can be defined in terms of the time average

of the product of the compiex analytic signals from two different directions attwo different times (Beran and Parrent, 1964)

tIo a -\ - LimL\I,Lr/ezrLl - T * _

(1.6)

nhere the angular brackets novr denote the infinite time average

= <r(tr,t)E*(.sr,t-r))

(r'D _ Liml'+@

f (t).dt

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'l3.

(1.7a)

This has been named the temporal coherence function by some authors (Kon

1967; Hagfors and Moran, 1970) because it is related to coherence in the timedomain only. Beran and Parrent (i964) call jt the self-coherence funct,ion.The tempora'l power spectrum can be obtained from this temporal coherence functionusing the hliener-[.,hinchin theorem (Helstron, 1960)

P(.t,,f; =

l*I rt.q',t)e-J tTtr'tdr

J

(t.zu)

(1.e)

Keepi ng,

l,Jhen t=0, the temporal coherence funct'ion is proportional to the incidentpower from direction .Q, i.e., I([,0) is the brightness distribution of a source,

r(r,o) = (t(t,t) .r*(l,t))

= (lE(r,t) l) (t.41

The compiex degree of coherence f*(Lr,L",r) is defined as the normalisedmutual coherence function

f*(.cr,,tz,t)

and it can be seen direct'ly1963) that

= f([r,Lz,r)/

from the Schwarz inequa'lity (Kenney and

0 s I r, (f.r ,1,2, r) l-<1

The extreme values of 1 and 0 correspond to the cases of complete coherenceand complete 'incoherence respectively. In all other cases the radiation fromthe two directions.Q,l and 9a is said to be partial'ly coherent.

It has been shown (Beran and Parrent,1964) that a non nuli field forvrhich lfN gt,Lz,r)l = O for al1 pa'irs of directions and all tinre delays cannotexist in free space i.e., if ltf,f l = 0 for all pairs of points on a continuous

surface, then the surface does not radiate. Holever a completely incoherentsource can be dfined in a manner consistent with this resu'lt. An incoherentsource is a source for which the mutual coherence function is given by

(1. io)I(.cr,0z,r) = f(Ll,r).d(!,r-.q,2)

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14.

Defining

i1en,nr,f) = rllrn- *r[+t*-,rl,iftnr,rl] (1 .11 )

then it,cdn be sholvn that r(f"l,[z,f] is the ternporal frerqr.l,e,r,rcy spectrum off (0r ,0z rr) .

Refenring to the definritionr of the, nrutua:l coheren,ce filnction (equation 1.6)dnd subslituting the For,rrier transform relationships for E, (eQuation l.4) then

r(,.er,ra,r) = rtl** *r[r.[.0r, [rr..f;r{rn,f, 1oiznr,t.Eftcr,f")e-Jz*rz(t-t}J ) J

'trT\&zttzt= lrrr\-d, r@ -p^. (r.ra)

ltl

lim |^iZnt(fro\T'*'- | ."-"-\'r-'2tdt = 6(fr-fz))rl

where 6(x)'ts the Di'rac de'lta fu,nction at x ='0, then tlre ti:nrc integrationyields a delta fu'nction, and one of the frequency integrrations can be pe,rfo'rnnred

to give

r(sr n&a,r) = ,tlt- *rfarr*, ,f)ai(r,, ,11eJznf"df .

J

Combining thls with eQU,dtion 1'Xl yields

26l^r(x1 ,sa,r) = | itrr,ge,f)ei2trf.df. (r.ts)

L.

If $1=g2=g then i(g,f) is the brightness distribution or temporal power"

speet!'um of the source as shown by equation 1.7'b

,trf the s:patlal frequeney spec:trum of t-he mutua1 csherence fu,nctiony(ur,uzrr) is defined as the mutual cohere,nce f,unction, expressed in ter.ms o the

spatial f'requency spectrum of the incident radiation i.€.,

As

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15.

f*

rtlt* hl er(ur , t)ef (uz ,t-r)dtl

ro9I

= |'r(.0r n3r,r)ei2rn(91u1-&2u2)dgr,dgzI

1-

u=Ll1 -us , the,n fronr equati on 1 . 10 n for

|'*rro,"tdznur'6*JrOO

Y(ur nuzrt) =

= (e(u1,t)e*(u2,t-n))

transfonn re1 ationships between e(u,t) and

(1. t+)

E(s,t),then usirrg the Fourierequation 1.14 becomes

Af*^ v(,so,f) = | r(*,r).G(t-r,o,f)dt

J

(1.rr)*

ana f;(x,,'t)

the visi b'l ,

Noting that this integrral differs from the convolution of E(g,f)*This integnal can.be evaluated as finct'ions of .[, arie defirpd only in

range lsl.t

.y(u1 ,ua,r) = Tll** h[r. [on, [ou..E([r,r)e.jz?rurc, .E*({,0,r-t)e-jzn vz;z'

iJ ) '.+6, -S

(1.1s)

Letting a compiletely incoherent source

Y(u,t) = (t..10tr

i'e., fon a cornpletely incohenent source the se'lf-cohe,rence function and itsspatial frequenry spectrnum are a Fourierr transforrn pair.

1.5 Properties qf the Receiving S.vstem

A cot'nelation int.erferometer system can be represented by two antennas

Ar and As, the outputs of whlch are passed through fi'lters into a multipiier,whicln produces the cross-col"relation product of the tvlo antenna voltages.

The antennas can be def"ined in terms sf their vroltage radiatisn p-atternse(g,t) which are the Forur:ier trarrcfonns of their aperture field illuminationsg(x,f), (Bracewell, 1965), For an- an enna pointed in direction &o, the responseto an input angular spectrum tCg,tl is

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16.

only in the siEn of (r,={,o), define

G0,,t) = 6(-s,r)

so that equat'io,n 1.1,7 can be l:dwritten as

wltere *^ representsL.

is defined by

^r@*Av(fl,o,f), = I E(s,f).G(&o-{,,t}asIr6

AAA

V(so'f) = E([o,f)*e!l(e0,fl (1,tr9)

convolution in the g-domain. Fn Bracewell (1g6s) convolutionL.

f(x)*s(xy = [*t,",.s,(x-u] aulIJ'-*

or

(t. tg)

(1.20)

( 1 .21)

For the p:urposes of this- analysisn the R.F. and I.F. amplifiers of thersceitving systern can be considered to merely define the fr equency resplnse ofthe sJstem. They can be pepresented by a tilter of tl"ansfer function [(f).The outpurof these stages, ilott) is retated to rlle input fi(f), ny

fro(t) = ili{r).fi(f}

Vs(t) = R(t)*rVi(t)6r

}

the time averageAs sliown in section 1,.1 the output of the, system ist-he pnoduct of the tuo filter outputs, or in generall

of,

fR(r) = r'l.t* hl vrr(t).vrf (t-r).at

)

where the tnrncated analytic signal has bee,n,fntroducedof the convolution integral tn the t-domain. Equation

R[r) =' (v. tt).vf(t-t])wlthin the previous definiffon of the angular brrackets.

A time delay r has been l'ntroduced into the pro'duct of equation l.2L because

Irlr(t) and Vry anise f,rom an incident fleXd Er(*,t). Different path lengthsfnom the source to the rnultiplier' (geometrlc and instrumental) will shift the

to ensure t-he exisrtence

1..21, can alss be written

' (1.21a)

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L7"

time reference of one in,put voltage with respec't to the other

1.6 T.he Qe re,[-a] F{esponse Relationship

If the two a:ntennars are polnted in directions ca, a.nd 4ss, then fr:om

equat't'on 1.19r the antenrna output voltages for an inc'ident field ET(l,,t) willbe*

and V21(soe,f) = Er(goe,f)*uS(tsz,f)

3*(ou, ,f) =

i,or,,f).r^A

(ru,,f)

Frorn equation 1.2!, 1,69 output fronr the multiplier is g,iven by-

R'(t) = Ttl** hl'irrr&s1,t)'vrr1($oa,t-r)dtJ,

where ,t/g1(*n"t) = A(t)*rVr(*,u,t)

and Vt(,co,t) ls gtivern by equation !;.22. Thus from equationd 1,?0 and 1.?2

ilcr{su,r) = nrfl fircr,f) .G(cn-.r,,f)dg

'--

and by Fourier trans-for^mation

r^r" vrr(lo,t) = | itul I rrCl,rl.6(uo-u,f).d!,.ei,2nft.dr

LJ*Nroting tlrat fr(t) is a function of f,r"equency onrly,, this equat:ion may be

written as

} (r.aey

ff^,\^.:D-j&vrr(lo,t) = l.otl..al.n1r1.er(l,t).6(r,o-*lgjzntt (1.23)

J J-*

*Although the tlruncated analytie function is not necessary for the validity ofequotion 1.,22) the tru:ncated version of V(["f) is requined when it ls considered

as the i'nput to the multiplier.

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18.

obtained

tem.

frorn which Va* and Vg2+ can be obtained

fr*AAurrr(&o*r) =

J

.or,.| .ou,.A-, (rr1 .ir{lr,f, ),L (ror-&r1."i2nfrt,-6 rd

r* r*vr'f (eou nt-t) =l .or,

| .orr.frltt").i;{nu,rn).Af Lc oz-tuzl.u-jZri'fz(t-t)

JI*..o

Substitu ing these vo;ltages into equation tr.Zl the orutput R(t) isin terr'ns of the incident radiation E(.g,t) and the paRameters of the syg

R(r) = rll*- lrf "rl"r, [ir,lilou, [r,.,''l* L i"" l- l*

.fi, (f, ) .fi!(r,1 .ir{*, ,r, } -tf ({.2 ,ra)

'6, k"r-&r ,fr ) .Gj(r.or- f.z,f t)'.jzrrfrt.*-iZr'rfa(t-t) [l.eq)

As the on,ly time f,uncti;ons in equation 1.24 afe the two exponentiall terms, I

the time integration san be perfonned to yie:Id

(1.25)

ie

I'n additi,on, as

(t.ao)

then equatign 1,24 can be reduoed to

1-'* ','f- f fR(r) = ttl% *tl .otl .oo, | .ou..i, (t).i*(t)-'l* 1* l*

.1{r, ,r) ,Ef trr,f .A (&oe-4r,t) .Gi(gog-&s,f}ei2nft $.a7}

where integrati'on, wilh pgs:p€ct to ttrne has hee,n car"ried out as i,n (t.ZS),

. integration with respect to f1 cnrried out as in (1.26) and fz replaced by f.

f*uturttt1 -fe)ujzn f zr dt= 6.(fr -f 21slznf zr

)

rqt

I Fr (xr ) .d(x, -xc)dxr = Fr (xz)It-q

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.10LJ.

^ The only terms concerned in the I imit (T-l-) are the analytic functionsET(.q,,f), so that equation 1.27 can be rervritten as

t6r@e@F-f f f . l-r.,* 1t-^ L. tlR(r) = l .arl .ot, l .a.c..Ar (f).Ai(f). lrl*'_ iifrrtt,,f).Ei(12,t)l

I) ) ) L 'rLr- r- -Jo-@

:

.d, (so, -!,,r) .Gj(% r-t,f ) . sj2rft

and from equation 1.li the term insjde the outer brackets may be replaced by

r(gr,92,f) i.e.,e@ ,6 o6

Itl^ . ^'4t*€-R(t) = l.dfl.d&1 l.d.q,2.Ar(f) .AI(f) .r(er,e,z,f).G,(ror-r,f) .etru.rr-e.,f).sJanrt))) _6 ( I .28)

Equation 1.28 is the general equation relating the output of a correlationinterferometer to the mutual coherence function of a polychromatic partia'llycoherent source, in terms of the antenna patterns and filter responses. Thisrelationship is now examined in the particular case of a completely incoherents0urce.

L.7 The Special Case of an Incoherent Source

In radio astronomy sources are general'ly assumed to be incoherent, implyingthat the radiation from one point is statistical1y independent of the radiationfrom any other point. The mutual coherence function of an incoherent source isgiven by equation 1.10

equation L.?8, one of the

(1.2e)

following assumptions can be made about the receiving system.

The power patterns of the two antennas are identical (with respect totheir own phase centres) and the antennas are pointed in the same

direction ([el,ot=[oz) .

(Loz-L,f) . ei 2nft

l(It,9,z,r) = f (gr,t).6(l,r-.gz)

Substituting this mutual coherence function into.Q, integrations can be performed as (1.26) to yield

r- f@| | _ A

R(t) = | .url .od, (r) .iii(r) .i(s,t) .9., ({,o, -s,r) .qi))

The

1.

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2A,

?. The fi'lter respons:es are identica'l (this is implicit in the casephase-switched intenferometer) and are non-zero oinly f€r a smallof frequeRcies Af centred on fo"

tlith these assumptions equatrron L.Zg becornes

R(t) = (1.30)

At this stage-it is ne:cessary to examine he time de:lay r in equati,on 1,.30

and to relate it to tJre f,actors frorn which it arises. The delay can be dttri-buted to two cdus€s (f) tne geometric delay caused by t-he dif,fer.ence in pathr

Iengths from the source to the two antennas, and (2) the instrunrcntal del'ay

caused b.y differ^ent cable:lengths to the receriver, Bhd phase differences in thetwo ch,annels.

If the base]fne'is defined so that D is the length in met-res measured f,rom

A,r to Ae 0n the x axis, then referring to Figurr"e 1.5,'it c-an be Seen that thegeometric delay tg is given by

ofarange

t* ffo+aq

J.rrl .at.i(r,,rl. lorr"-*,r)l:lntrl l?"izf.'-@ ?o-*f1,

T,g =

whene e is the veloci'ty of light..

dc

D:g

c

- $ s'ino

Figure 1.5: The cause of the geometric delay ts.

Page 28: 2-Whole-digital Data Processing in Radio Astronomy

f,i is then the direction for whicJr the geometric delay andare equal and opposite.

. (1.31)

instrumenta'! del ays

trf the fi'tter passband Af ls sufficiently srnall ffrat i(*,f) and 0{*o-o,f)do not vary slgni:ficantly over its range, then equati.on 1.30 can be rewritten

r. Af

n(t(.si-sl,ro) = ft,u,ro,.lG(uo-r,ro) l'lli(r.+r)l'..jen1ro*r)BLet-&).dr.dgL4whi,ch can

The instrumental

Letting:

then

and

delay ri s.an be attributed

ri = B sinoi

.0,i = sin01

,i = $ni

T = Tg*ri

' E Sq-r)

?T,

to an additional angle 0i, where

(x,le1

(1.33)

expnessed

t@

R(D,ri,eorfu) = | i(s,t.) .Fqn,..e,i-r,[o-s,fo),dt,J-!(t

F(0,.r,,i-s,&6-$,fg,) = l6tt-c,ro)

.affT-

'*iz'ft.t*r-o) l' ', ^ re iznfli1-*).,

J orlA(r*ro) 1' 'e

b.e

il{0,*i -!,,ils-L",fo) is ca,lled the conrplex power pattern and is gtven by

where )tn = "/fn. The complex power pattern- can be expressed as the product ofthree tenns

A l^ 12F(0,&i-g,,te-.s,f6) = le (no-t,fo)

| .r10,*1-r,rfo).ts(D,Bi-t,fe,af) (l.ssa)t-.--l

where these are the antenna power pattern, the interfe-rence or fringe patternand the bandwidth pattern pespeeti$ely. The'clllaracteristics of these three

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22..

terms al'e shown in Figure 1.6,

(a) The antenna potler pattel-n

aperture of length L.

^2lo(n-.eu, fo)l is shown for

-j2nu.C6ug(s,fo) =

r*l.J;T

(b,) T,he, fr-inge pattern

F{0'&1-.9,,fsi = *i z"tltt -r')

l:s sh.own for a rectangu:lar passband

t+iI it"&J e *'dfJaf-

has a real cornfonent "orfz,ofout-o{,

(c) The bandwldth pa,ttern B(0,$,i-l',fs,af)of width Af i.e.,

B,(Drs,fo,Af) =

The'antenna power pattern (,Figune 1.6a) 'liLmfts the field sf view to that

s,f the antennas sf th,er system. Fsr a uniforntly illulninated apertlre of length

L it has nulls at &. rtro/1, The fnlr'rge pattern (Eigure,1.6b) deter,mines the

nesolution of the instrument, and as.the bas,eline is usually longer than the

aperture sf one of the antennas, the fringe funetion varies more rapidly with

4, t,han the pog1er pattern (D>L) . The bandwtdth pattern ('Ftgur€ 1.6c) al's,o

limiu's the field s:f view but usually lt is much wi:der than the power pattern

and can be a:ssumed constant over its extent, i,e.1 L.fs>)D.Af,. This assumPtion

a uniformly i1'luminatedL

Page 30: 2-Whole-digital Data Processing in Radio Astronomy

l6t l-ro, rol;2

l-to(q)

F( D,1;-1, fe)

B( D. ti-1, fo,a,f )

1 = ti(c)

The components of the complex power pattern.Figure 1.6:

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24.

reduces to af<<fo for short base'lines, and on'ly in the case of very-long-baseline interferometry is the bandwidth pattern usuaily significant.

1,8 Source position lrleasureine,nt w.ith the. g:o,t"relatipn Ihterf€ro{ne,tgr

The brlEhtness distribution of, a point source in direction t, can be- represented by a delta function 'i.e.

.

t(&,r) = d(s-osrfs) (1.34) i

Subst:ittlting this into equatio,n 1.32,

= P(Dr,Si-&g,CI6-[5 rfg)

PR(D,si'r,6,fo) = [ e(l-rs,to)i(0"!,i-[,.co-.c,fo)dr.

)

= [6tuo-ur)

.af

, -ztfuri-rs') f-,^e ' I lA(ro+t)I nf,

u SznSl,i-ss)e .df (1.38)

-

If the fitnge factor var:ies more napidly vuith n than the other two com-ponents, th:en the dominant term in the output will be

R(D;ti.,f6) = coszoT3sj-*u) (1.s01

For cellestial sources gr(=sin-lgs) varies approximately linearty wfthtime, i.e.,

R(e1 = cosenf*i-sings) (t,e7a)Ao- | J

which can also'be wr:itten as

R(t) = coreh\si-sin(eu+dt)) (t.lzu1

In Chapter 3 it is shown that the ter"'m 0r+ot contains the necessarJ pos.itioninformatiorn for a source, and equatjon 1.3I fs applled ts the convenilonalastronomical coordinate syst€m to establish the coondinates of, the source at s,

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25.

1.9 Source Diameter l4easurement and Aperture S.vnthesis

If the antenna beamwidth is smal1, then the integrand in equation 1.32exists for only a sma'|1 range of .Q, centred on 9o. The maximum of the banclwidthpattern B(D,11-[,f0, f) can be made to lie in the same direction as that of theantenna power pattern by adjusting the instrumenta'l deiay ti so that Si=[0,

Define g'in such a way that it is the angie between the pointing direction([o) ana the source i.e.,

g = 0o-0'

where .Q, = sin0

is the coordinate of the source. If the antenna beamwidth is narow only a smallrange of g' is of interest and

sing = sin0ocos0'-cosOosin0'

i sin0o-sing'cos0o

9.o-9, = .{,'cosgo

If u is defined as the projection of the baseline D on to the p'lane normalto the pointing direction 0er rn€oSUred in wavelengths, i,e.,

'1 .€. t

equation 1.38,

, = Dcosoo

tro ' then from

(1.38)

(t.sg)

factor F(0,L1-.Q,,fe) was usualiynd jf l,i=&o then for sma]'l

so-r)

Lg-L, = .q,'u9D

In section 1.7 it was shown that the fringethe dominant term in the interferometer output, a

excursions about the pointing angle

r- i 2"9{R(D,so,fo) = I ifo,fo1.u-"tro'

II

-@

. dl,

and by making the subst'itution for.Q,e-.Q, from equation 1.39 it can be shown that

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26.

(Srvenson and Mathur, 1968; Swenson, 1969)

R (u ,fo) =

r-| ^ i)*tto

I r(!,,f.,)eu'"'od.cJ

( 1 .40)

,r\= y[U,Tg/

i.e., under these conditions the output of the interferometer is the Fourier

transform of the brightness distributl'on of the source. The brightness distri-bution can be obtained from th'is spatial frequency spectrum by Fourier inversion.This is the basis of aperture synthesis. if observations are made. with a number

of different baselinesn sufficient conrponents of the spatial frequency spectrum

can be measured to permit reconstruction of the source. Bracevlell (1958) has.

shown that a source of angular extent A.Q, can be completely resolved by sampiing

its spatia'l frequency spectrum at intervais of u = I/L!,.

If the smallest detail to be measured is of extent A[*.in then the highest

spatiai frequency which must be sampled is Uru* = t/Agmin (Swenson, 1969). The

number of different baselines required to perform a one d'imensional analysis ofa source of extent A.Q, with resolut'ion At*in is ALlA0rrn.

1.91 Source Diameter Measurement

If the required range of baselines is available, and the phase of R(u) can

be measured as well as its magnitude, then the brightness distribution f(g'fo)of a source can be obtained by Fourier inversion (after equation 1.40). Ifonly a iimited range of baselines is avai'lab'le, and the phase of R(u) cannot be

determined, the diameter of a source can stil'l be estimated from the interfero-meter output.

Assume that the brightness distribution is Gaussian in shape, i.e.,

i(s,r.) =

As the transform of e-tx' is e-*st,equation 1.40,

io .-n(u- e'd\"

(i.41)

then substituting equation 1.41 into

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27.

R(u,fo) "

i,9,,

where

R,(u,fo)

= o,.ei?!r&su,fi .n-r'(ou)2

R(urfo)V(u,fo) = [-^ .- | r(s,fo).de

J

r r."ie"sou.it.a-n{s-u) u

o.i.

= "jftr[ou ,'rr(ou)

2

v(u, fo) ,= .iarr[ou.vo(u,fr)

Vo(u ,fo) = .-n(o'u) 2

J n Vo(u,fs)

are defined by

fo -z/= | ioe-n(l-n o'l /o2. ui2nuldg

J

(1.4A)

Equat'ion 1..42 eontains both the phase and ampilitude informatlon of 'the

intenferometer outp-ut, The fringe visibili'ty sr the visibillty function,Vofu,fo) is defined as the ratio of fringe arnplitude to the total flux neceived

from, the sourre. The csmplex visibiltty V(u,fe) is the norrnalized value of

} 0.4s)

trf tfire uwidthn!0f, a Gaussian dist,ribution is dEfined as the distance- b'etween

the psints where the arraplitude is l/e of its maximumi va'lue, the hal:f-width direc-tions of the source of eguation 1.41. are

s-lo

From equation 1.43

+d{,TT

-g- =fr

sf theso that the extremities

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28.

1-!,-.Q,,., = t - / -1n Vq(u,fo)" Ttu{ ( 1 .44)

Equation 1.44 suggests that for any observed fringe visibil'ity Vs(u,fo),provided that u t's known, the extremities of the equivalent Gaussian sourcecan be found. This is strictiy correct, but for small sources (o small) andshort baselines (u smal'l) then vo(u,fo)-1, and the width obtajned fromequation 1.44 wil'l be zero. Sinrilarly if a broad source is observed with a

long baseline, the fringe visib'ility vriil be very c'lose to zero, and difficu]tto measure. Assuming that the best results will be obtained vrhen the fringevisibi'lity is approximately .5, then the basel'ine should be chosen so that

where A.0 is the width of the source.

1.gZ Aperture Synthesis

It has been shown that the output of an interferometer of basel'ine lengthD metres is a sample of the spatial frequency spectrum i(u,to) of the brightness distribution f(L,fo) of the source under observati'on, corresponding tou = Dcgs0o i.e., the spatial frequency of the projection of the baseline,A6measureil in wave'lengths, on to the plane tangent to the ce'lest'ial sphere at thelocation of the source. If a number of different interferometers are availabiew'ith differing baselines, then a number of different samp'les of y(u,fo) may be

taken and a detailed picture of the brightness distribution of the sourceobtained by Fourierinversion.'In this way the equivalent reso'lution of a verylarge fil'led aperture te]escope can be achieved (Sr,renson and Mathur, 1968) . Ifa synthesis'interferometer consists of one fixed element and one mobile e'lement,then the time required to map a g'iven area of sky is proportional to the numberof different positions of the rnoveable element. The physical synthesised tele-scope would require the same time to map the same area of sky, as its beam wouldbe narrower than that of the interferometer elements, and only a small area ofsky could be studied at any one time.

A more recent extension of this principle, termed 'supersynthesis' (Ryleet al, 1965), takes advantage of the fact that the projection of a fixed base-line onto a plane tangent to the celestial sphere changes in length and

orientation with the rotation of the earth. If a source is tracked by theantennas of a fixed interferometer over a period of LZ hours, d large variation

u-ff,

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29.

of the spatial frequency being sampled by the system will occur. It can be

sitown that the locus of the project'ion of the baseline D on the ce1estialsphere describes an ellipse in the spatial frequency p'lane as the eartir rotates(Srvenson and l"lathur, 1968; Swenson, 1969). Using an east-west baseline and

making repeated observations with a number of Cjfferent baseline spacings D, itis possible to synthesis a large equivalent elliptica'l aerial, the major anci

minor axes of which are D* and Drsin6, rvhere D6 is the maxinrum baseline'length,and 6 is the declinat'ion of the area of sky under observaiion.

In combining observat'ions made with a synthesis telescope, it'is usual toassign different weights to the fringe amplitudes obtained with different base-

lines, corresponding to different spaiia'l frequency components, in order tocontrol the synthesised beam shape and the side-lobe'level (Swenson,1969).

This is analogous to weighting the aperture illumination of a physicai antenna,

except that the weighting is done after the observat'ions, enab'l'ing various

weighting funct'ions to be used with a single set of observations.

1.10 Confusion In Interferometry

The resolving povrer of an interferometer can be v'iewed in ttrlo different ways.

An interferometer possesses a primary resolving power, that of the individualantenna elements, and a secondaryresolving power, that of the fringe pattern,which is determined by the baseline length. The secondary resolving pouer can

be realized only in the study of sources which are sufficiently spaced to be

isolated by the primary beam. If more than one source is present in the prinnrybeam, fringes from adjacent sources become superimposed on one another so thatthe results are not easiiy understood. A source can be considered isolated by

the primary beam of the interferometer, however, in two spec'iai cases even ifit is not the only source present. These two cases are when the source is much

brighter than adjacent objects, or when its anguiar extent is such that it isthe on'ly source in the primary beam for which the fringe visibility Vo(u,fo)(equation 1.43) is not very sma11.

REFERENCES

BERAN, M.J., and PARRENT,

(Prenti ce-flal 1 ,

BRACE!,JELL, R.N. (tgSA):

I.R.E.,46 pp.

G.B. (1964): "Theory

New Jersey).

"Radio Interferometry97-105.

of Partiai Coherence".

of Discrete Sources". Proc.

Page 37: 2-Whole-digital Data Processing in Radio Astronomy

30.

DRAOEI'IELL, R.N. (1965): "The Fourier Transform and its Applications".(McGrar^r-Hi11 , Nevr York).

DRANE, C.J., and PARRENT, G.B. (1962): "0n the Mapping of Extended Sources withNonlinear corre'lation Antennas". Trans I.R.E., Ap-10 pp.126-130.

HAGF0RS, T., and M0RAN, J.M. (1970): "Detection and Estimation Practices inRadio and Radar Astronomy". Proc, I.E.E.E., 58 pp. 743-259,

HELSTROM, C.l,l. (1960): "statistical Theory of signal Detection". (pergamonpress, London) .

KENNEY, J.F., and KEEPING, E.s. (1963):. "Mathematics of statistics,, (part II).(Van Nostrand, New Jersey).

K0, H.C. (tgOZ): "Coherence Theory of Radio Astronomica] Measurements".

Trans I.E.E.E., AP-15 pp. 10-20

RYLE, M. (i952): "A New Radio Interferonieter and its Application to theObservation of weak Radio sources", proc.Roy.soc. (London), zl1App. 351-375.

RYLE' M., ELSM0RE, B., and NEVILLE, A.C. (i965): "Observations of Radio GalaxiesItith the One Mile Telescope at Cambridge". Nature, 207 -pp. 1024-1027.

SAUNDERS, A.M. (1968) : "A Des'ign Study of the Corre'lation Radiometer", M.E.

Thesis, University of Auckland.

SWENS0N, G.W. (1969): "synthetic Aperture Radjo Telescopes". Ann. Rev. Astron.Ap., 7 pp. 353-374.

SWENSON' G.l'l., and MATHUR, N.C. (1968): "The Interferometer in Radio Astronomy".Proc. I.E.E.E., !g pp. ?It4-2t30

W0ZENCMFT, J.M. (1961): "sequential Reception of Time-Variant DispersiveTransmissions". In "Lectures on Communication System Theory",Baghdady, E.J., €d. (McGraw-Hill, New york).

Page 38: 2-Whole-digital Data Processing in Radio Astronomy

J1.

CIIAPTER 2

In Chapter 1 it was shovrn horv in the absence of extraneous noise the outputof a correlation interferometer can be used to reconstruct a source brightnessdistribution' The characteristic problem in radio astnonomy however, is thedetection of a weak signal rvhich produces an increase in antenna power of severalorders of magnitude less than the power pr^oduced by the diffuse backgroundradiation and noise generated in the receiver. The sensitiv.ity lim.it, or,minimumdetectable signal' has been extensively discussed 'in the literature (Go'ldstein,1955; Goldstejn et al, IIST; Galejs, 1.957; Robinson, 1964; Tiuri, 1964;christiansen anci Hogbom,1969) and although there is agreement on the order ofmagnitude of this'limit there is much argument as to the relative minimum detect-able signals of the various types of te'lescopes. it is the purpose of thischapter to establish a relationship between the signal-to-noise ratio at theoutput of both phase-sw'itched and direct multiplication interferometers and theparameters of the systems.

Both types of interferometer have been mentioned in Chapter 1 and blockdiagrams are shown in Figures 2a and b. In order to ana'lyse the responses ofthese systems to an input which is of the form of noise, it is necessary toestablish the input-output relationships of their various elements.

2.1 Antenna Noise Temperature

An antenna' as far as the rest of the system is concerned, appears as anoise generator and can (electrically) be repiaced by a matched resistance R

at a temperature Tu so that the generated noise power is equal to that receivedby the antenna. The noise power is given by the Nyquist relationship (Kraus,ie66)

l,l(f) = k.T6 watts/Hz

vrhere k is Boltzmann's constant. It can be shown (Dicke,the same power that would be received by the antenna if itblack body at a temperature Tu, and Tu is thus referred toantenna temperature. The temperature Ts is related to theincident radiation and the effective area of the antenna.

(2.1)

1946) that this iswere enclosed fn a

as the equivalentf'lux density of the

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32.

TPUT

OUTPUT

Figure 2.1: (a) The phase-switched interferometer(b) The direct multiplication interferometer

2.2 Equiva]ent Noise Bandwidth

The predetection amplifier'of a radiotelescope usually contains a conversiondovln to some 'lower intermediate frequency. The statistical properties of thenoise are not changed if the processes are'linear, and the overa'll amp'lifier canbe represented by a power gain G(f), where G(f) is usually non-zero only over a

smali range of frequency centred on fe. If the input to the amplifier is a

noise spectrum l.l(f), the effective noise bandwidth of the amplifier, Bp, isdefined as the width of a filter with a rectangular characteristic and a gafnG(fo) which wou'ld produce the same total power output, assuming the input spectrumhl(f) is constant over the region of interest (van der Ziel, 1955)

l*rlBru = GTtoT'J G(r).dr

o

FILTER

't .9. , (2.2)

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33.

Assuming that the ampl:ifier has a gain G(fs) = GH and an equivalent nsisebandllidth of fu = Bg, the total pow€r output of the amplifier is given by

= 86.Gp.t^J'g (2. za)*

whe're Hg is tt're spectral intensl'ty of the nol.se (assumed constant)r.

The low-pass filterr can be d,escribed in a similar manner.h'as a trans;f-e,R f,unrction GL(f), its eguivalent noi,se bandwiidtha,s the width of'a rectanEu,lar filter of p.owe.r gain GL(O) whlchsame totaT p'ower output,, assu[ring a white noise input.

rBUn- 1 lr/rr= tilo)

.| GL(r)'dr

o

(2.3)

'As the nofse ba'ndwid,th of an ideal integrator of intEgration period r is1/2t (see ehapter 5)' the equivalent in,tegration ierliod 11 of d l;oil passfilter is defined as

(2.3a)

r*

'ln = .J

c(r).r,r(rJdr

.o

If .the fiiter.ts61 can be definedwould give t,he

whene Br* ls given b,y equation

If the input to a low passpower outp-u,t will be given by

2..3 .

filter is a noise spectrurn [(f)r th,e total

PlfP'! It, t

-)IBLNPo=G(o) | tr(f).df

Jo

= G(0).B1p.t.J;(f)

* Throughout this analysispositive frequencies

. . (,2.3b)

[,0 f ;t'P r'''r r.]' i

attributed toit is assumed that ail power is

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34.

if l.JL(f) is constan, ou.t. the range of frequ,ensies of inter^est.

2.3 TFF Bes'ponse sf a Squ,are Law Detector" tp. a No.ise Inpu!

The characteristjcs of a sguare law detector ca*-.be-describ-ed by (varn derZjel, 1.9551 Ricen 1945) .

Vottt = o,ViR" .

hli't'h a noise in,put tt111(t) the output Vo(t) of such a detector will be

Voft) =o,Vpe(t)r ..

The autoco,ryelatfo'n functi;on Y(r) of the orutput vo'ltage is then given by

y(t) = (vr{t) "vo(t+rD

+'(rlnu(t).vpa(t+r)) (2.4)

It can he shown (Goldstein, 1955; Rieer 194.5) that ttre autocsrnelation ofa function so,uared is given b1l

whe,re the angularn brackets repnesent, the time average

f-(rrtl) - lim 1 | J= t'*'L h

.| f(t) 'dt

t,lhere

and

(xo(t).xu (t+r)) = E.a+spe(1), II

V(r) = Stt),x1t+r)) i (a.s)I

vq = 4'(t)) ). By substitutlng this relatlonship into equntlon 2.4

v(t) = ou [ttr"'*av'(.)]

(2.5)

vthere Vs is the total po$Jer in the lnput noise and U(r) is the autocomelationfuncti'on of the lnBut noise. If the input is a rectangular spectrum of,'intensity trll and bandw'idth Bli, rfo is given: by

(2,7)tpo = tJi.Bi

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35.

Accordling to the }lliener-Khinchin uheorem the autocofrelation function arrd

the power densitjr spectrum of a random funqtiorn atpe a Fourief transfOrm pair(Helstrom' 1960i Lee, 1,960). The output power specfifurn l^Jo(fl of, a square lawdeteeto,r can be found from V(t) (equation 2.6) bV

rwe(f) = {' I

v(r).cos2nft.dtuo

(2.8)

The factor of 4 arises in thfs equation because (l) v(r) is an even,

function (Lee, 1960) and hence the cssine transform can be used which involvestaklng twice the iintegral from Or*n un6 (Z) if all powerr is to be,assigned tothe posit'ive half of the spectrum, then this"inte,gral must be dor,r,bled again.

substjtuting (t) frsrn equation.z.I into eguatio.n 2.g, the integral cai betaken in two halves.

l^Ir (f)

of, a f,actor offact that lrl(f)

.eosZnft.dr= oj],, *,

1.€.n

where 6(f) .is a

The seesnd

R,euensing

functlon sf a

The ,absence

resrults from the

= zofu.su

Ilh (f) = 2ct2{oa

Dirac de'lta fun,etion at

half, of the integral is given by

. a [*".uarft-drJo

.6(f)

f=0.

(3.9)

|ooI

W.z(f) = 4 | euzgz(t).cosznfr.drI

o

(2.10)

2.9) the autocorre'lationsp€ctrufir"

the Wiener-Kh.lrrchin relatfsn:ship {equationnandom fijnction cah be fsund fnom lts por,fer

r$(r) = I }.|(f).cosznfr.df

to

tllo in front ofis the one-sided

the cosine transf,orm integnal

Bowen spectrum. }{(f) is

Page 43: 2-Whole-digital Data Processing in Radio Astronomy

3'6.

des,cribed by a rectangularfl"equency fo,

intensity l,li and bandw'idth Bi centred on

l{i .cosZ.nfr.df

spec trum of'

[u*utJ o^-ry,

U(t) =

= hliBicos2rrf6t l'tit"gff]I nBit )

(2.11 )

Thus

S"(r) = l'lizBJt

and for bandwidths Bi<<fe, cosz(Znfet) can be replaced by its average value(van der Ziel " 1955).

2i.e., vu(r) -foi'ni't+tr] 1a.rra)

Substituting this U"(t) tnto erquation 2.10,

2

tca(f) = .cosZnft,dt

= 2s2l'.|izB1?,2 .cosZnft.dt

i .e. , t,lz (f) = Zcr2hli u(gt -f ) for O<fsBt ( 2.L2\t

Adding together bh(f') from equation 2,.9 and l,le(fl frorn equation 2.12r and

not'ing from eg,uation 2.7 that 1116 = I'li,Ei, the output spectrum t'loF} of a square'law detector for a nsise input is obtained.

hto(f) = 2o,st,'t,iuBitd(t) + Zoewiz(ei-t) (2.13)

Care must be taken in the intepreLation of this eq,uation as both lilr(f)and Wa(f) hdve been defined for positive frequencies only, tr{hen ['lr(f) is

vailue of

r4lro'Jo

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3V.

integrated'over the pass-band of,a low-pass filter to obtain a d.c. power,, theintegral of the de'lta function wr'lJ be llz and not 1.. This is not alwaysappreciated an-d has led to errors in some ana'lyses (Robinson, 1964).

2.4 Characterristics of a S:vnc.hro.nous Detectpr

The output Of a synchrOnous of phase-se-nsitive detector is the averagevalue of the product of the input, signa and,i ref,erence si.gnal (frneguenc.y fr),the average being takeh ove-r one cycie of the reference signal. For aR lnputVs(t) and a ref.er€'nce signal F(t), the output tlrill b:e

.vo(t) = (rtt).\rs(t)>

as in the limit the long term average of a perfodr'c function tends to theave:rage it|a'lue ovsr one cyc'le. If the referEnce signal is a square wave dffrequency fs and peak-to-peak arnplitude f6, Vo(t} is given by

(2r14)

_q'

r^srlo(t)=Hl s.rls(t)dt-.,'

]

?x

r'ffi I B.vs(tldt

JTro

(a) The Response to a sinuso'ida'l

Consider the case wl,rere

Ft'om equation ?.1,4 the

T"

[d5

input at frequency f5

vs(t) = Vsin(ost+Q)

= Vsi rurrst, cos$+Veosog t. si n$

output !,riil be znt- t*

vo(t) = #* .Ju

,uttnr,r5tcoss)Bdt# .|Jt:tnorstcoss,)Bdt

as the cosine tenns wlll vanisrh in the inteErail.

TI

i .e., \ro(t) = 99-

= ?E-r

FI eVst nurstcosQdtJo

.Veos,6 (2.15)

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38.

The ourtput is thus B tirnes the qean modulus of the ip-phas€ component of .

the signal.

(b) The response to a nams-ly band nsise input, centred on fs.

Vanr der Ziel (1955) has shor+n that any namo:u, band of notse at centref,reguency fo and of wi,dth ts (narnow band inplies fsaSB) nray be repnesentEd by

X(t) = Xq(tlcosurot - Xs(t)sinr,r6t I=R(r)cos[*r.o(r)] . I

(2'16)

where'R('t), Xc(t), }{s(t}and 0(t) alne al:l slowly fluetuat,ing quantf,ri.r. Itis also shown that

* <-) = 4} = (x.) = (*r) = f-*trl.oo (a.r6a)Jo

where l{(f) is the poh,er spectrum ot X(t) .

Assuming a noise input to the s3rnchronous dietector sf the form

llN(t) =Vc(t)cosost-Vt(t)sinost, .

if Vs(t) can be assumed constant o:ver one cyole of the l^efenence signal, from. ..

eguation 2.15

vo(r) = +vs(t)'

CombinlnE equations 2.16 and Z.Ll,

(2,17) ;

(uu'rdi = [,u"]' ( vr'tt))

and the autoesrrelation funct:ion of the output, vp(r) ,is 'given bJ

vo(r) = l[+J' (r'r(t).vs(r+t)) (2. L8)

Van der Zie:l (1955) has alrso shown that fora symmetricarl band sf noise as ,

defl'ned \y eqqafion 2.16,

Page 46: 2-Whole-digital Data Processing in Radio Astronomy

and

wPt

?o!1.

(vs(t).vs(t+t)) = #* (vn,lt).vn(t+r)) (z.rg)

if'VN(t) :is a,rectangular band of noise of width B and sp:ectral intensitythen from equation 2.1,1.

{(t) = (v*tt).vp(t+r))

= tlp8cos2*r"ffi (2.20)

'IOtl:lr.,r

I tDF

',. ff ll"'

j {z.zl)

C,ombin,inE equations 2,19, e.19,, and Z.Z:A,, the'autocorrelation functio,n of.the output in terms of the bandwidth and intensity of the input noisel is obtained.

vs(t) = [*J"ou tW]tJsln-g the Wiener-Khinchin relationship (equation 2.8) the output pouer

spectnum l,lo(t') can norr, be determined.

r,ro(f) = + [-p*]'r.ron [u*H*]."s2rrftdrjo.'

/(lo

=#ru, l, t#]cos2nrt.dt,n

=ggz R

? Wp for 0<fs f= 0 otherwise.

2 .5 Cha,rgeteri srtJ e g . of bn Anal ogue Mu I ti pl i er

In the direct multip-:licatlon correl,ation rinterferometer, the analogu,e

multiplicati,on and low-pass filtering are usuall.y perfo,r"rned togethern the outputof the mult'iplier being the time'average of the p,roducts of the output voltagesfrom the t-l*o channels, i.,e.,

vo(t) = r. ( v, (t) .vr(t) >

The voltages: \tr(t) and Va(t) will consist wholly of no.ise, and tt can be

assumed that they e&ch will contain a correlated component S(t) arlsing from

f ,;l

Page 47: 2-Whole-digital Data Processing in Radio Astronomy

40.

the signalr:drd fft uncorrelated compo:nent H(t) arising from background and

receiver noise. trf the csrreJated cornponent in Vr(t) is delayed by an iinterval

0 from that in Va(t), then

vr (r) = s(t) + rtr (t) 'l

I tz.zz,1

and vr(t)=s(t+o)+l,le(t) -J,

The multiplicat'ion a'lone 'wlll ba analysed, i,e,,

vo(r) ,= llr(t),vz(t)

and the averaging will not be considered.

The autocorrelat,ion function Ye(r) of Vs(t) is given by

v.q(d = (v1(t).vz(t) ,vr (t+t).ve(t+r):) Q.?3\

where Vr(t) and Va(t) ane given by equatisn 2.22.

Equation 2.23 can be expanded, noti'ng that if X(t) and Y(t) are indeperndent

(xf rl.y(t) ,x(t+r) ,v(t+t)) = {N(t).N(t+t) } . ( *(t},Y(t+r) )an'd also (Xttt.V(t+t) ) = 0 for al'l t.

i.e.,"

vr{r)

+ (r,r, 1t1.tl, (t+t) ) . ( t(t).s(t*r) )(*r(r}.N2(t+r) ) (stt1.,s(t+t) )

+ (n, ft).nl(t+t) ) . ( n.r(t).mz('t+t) )

In th.e case whers 0 = 0

vqr(t) = ds.(t).s*(t+t)) + (l*tr(t).,ur(t+r) ) . (s(t).:S(ttr) >

+ (ruu(t}.Nr(t+1) ) . (s(t).s(t+r)) * (n,(t).N11t*r) ), (nrtt).nr(ttt) )6 z. ?4a)

Definlns Ss(r) = (s:1t).s(t+t) )

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41.

and Ss(r) = (nf tt.n1t+") )and notinu t'o'r'llil::,;;:'il'=

(sr'), * a (s44srt+ty )athen equation 2.24.a becornes

vo(t) = Vsu(0) + 2us2(.) + {s(r).hlr(t) + {,s(r) fur(r) * gN,(r).u,nr(r)

(2.24b1

Assum'ing thrat ttr0 two ampiifiers (see Figure'2.Ib) have identi,cal rectanEularpass-bands of width B and celltre frequenqy fon then if the signal intensity attheirinputs is lilr and the background'and amplifien hoise }J,tr1 is equal in bothchannels, from equation 2.11

il5(t) = WsB coszrfrr lffiand {111r(t)= tXlr(t) = W,mBcoszrfr" l[+#]

Su,bstituting the,se into equation 2 .24b,

) (2.2s)

vu(t) = r,tszB'+Bacoszarfo.[W=]'[?*r'*r*rwll*l{nr] ft.?ac)

Applyi:nE the lllienet-Khinchi'n tlleory (equatton 2.8} the ffrst tenn inequation 2,?4c gives rise to a d.c. power term (ldr) and the second gives rise toa low frequency noise te,rnr (Wr).

,|*t^lr(f) = 4l tlf*tescos21fr.dt

I

= 2}IseB26(f) (Z.Z6,a\

and

r*w, (t) = a

I B2cosz2rrf.'

[+#F]'(r*rr*rrrwp+r{q2)cos2nfr.dr,o

If E<<fo therr cos'Znfsr can be replaced by its dvar&g€ value i.e.,

Page 49: 2-Whole-digital Data Processing in Radio Astronomy

l*, 2

r,J2(f) = B2(zuts2+zwsur.1+!,hz) .zI t+:+E]cos2rfr.drg 'i Jot

no'

= (2ur2+2l,Jsi'JN+l'Jll'z) (B-f) for 0<f<B

42.

(2.26b)

The output of an analogue multjp'lier for noise inputs can be obtained by

addi ng together t'h (f ) and Hz (f ) .

wo(f) = 2lrls2B2.6(r)+(zt'tr2+2wsl,lp+w1l') (B-f), 0<f<B (?.26c)

The inputs are assumed to have rectanguiar spectrums of vridth'8, each con-ta'ining uncorrelated noise of iniensiiy l,Jp and correlated noise of intensityllr. Care must be taken in the interpretation of the delta function, as mentionedfor equation 2.13.

2.6 The Sensitivity of a Phase-Svritched Interferometer

Consider a system of the form of Figure 2.1a, and assume that the cablesphase reversing switch between the antennas and the receiver are lossless.antennas are not necessari'ly identical , and a factor K. is defined by urh'ich

effective aneas of antennas A and B are related.

AeB = Ka, AeA Q.Z7\

For a source at an angle 0 from the vertical there will be a difference inlengths to the two antennas of

and

The

the

path

Assuming narrow band

phase difference 0 'in the

x = dsinO

operation, then thisvol tages at the two

, 2ndsi n0.A

path difference x will cause a

antennas

(2,28)

where ), is the wavelength at the-centre frequency of the operating band.

Let the antenna\ temperatures caused by sky background be Tn and T6, thena source at angle 0 to the vertical w'ill cause increments in these temperaturesof AT4 and ATg respect'ive1y. The trvo antenna noise powers kT4 and kTg areuncoffelated since the relative phase of s'ignals received at the two antennas

wi1l vary with angle. If the source at angle 0 is small in extent, then kAJ4

Page 50: 2-Whole-digital Data Processing in Radio Astronomy

and kATg will be c-omelat€d a,nd from equatipn Z.Z7

r,rmG = Ka,r@

.FT=$.{rr*n.*zc{'ffi.)

where c is the eorrelation coeff,icient.

ternperature Tf i,s given by,

T1 (-) - | {r6*re+AryaTe) -,/-^fifFB'-

43.

(2.?e)

and the voltage at A lags behind the voltage at B by an angle S (equat"ion Z.Zgl.

Let the nesultarlt anterllna tem,perature, referred to the Junction C be theinterf'erometer tempenatune T1, thcn when the antenna voltages are added in ph,ase,T1 is given by

T1 (+) = |,'(rg+rr+ATg+ars) *,fEqaTB (2.30a)

as whb'n two por+ens Pl d"nd Pa are aCded toEetlrer ttre tota'tr power fu ii given by

,11't1 'r

1L ?t.'-r\-ua,,-I .'-, ' rr,J

,l

,, t'-'lldhen the antenna outputs are added in antiphage, the resulting {nterferoneter

(e,gou)

If aT<<T, thre systen ternperature Trru can be defined

Try, = TR+ (Tg+Ts) (2.31) '

where T* is the noise temper:attrre of the receiver referr.ed to the junction C.The effective input noise terirperature T6 to'the receiver is, frori equ:ations2.30 and 2.31,

TE=Tsyu*@. (2.321

From equation 2.2ar the output of the high freque.ncy anrplifie,r (assuminga rectaltg,tllar pass-,band,) is a rectangular band of ngise, o^f wtdth 811 andintens'ity !16 where

ufH = q6m, watts/t1z (2r.33)

H,hen this rroise is applied to the input of.a square law detectsr, fromegUatfon 2.13 the output spectrum v{ill be .

Page 51: 2-Whole-digital Data Processing in Radio Astronomy

hls(f) = 2otutp12Bg26(f) + 2o2Wga(B.H-f), g*<f<Ep

The first teru in eguation 2.34 gives ris,e to a d.e. power.tetm

44.

(2 .34)

PDc = cral'l*zBrz

corirbining this with equations z.32 and z,3g it can be seenrepresents ,a f''luetuating d,c. voltage

VDC = oBgGpk (Tuy, t ,fZETTe)

i,e.., thene f s an Bverage d'c,. p:ower of

(tn,e) = crzBg2G11, kt.rryr, (2.35a )

uith a Suprerimposed square-wave at the switching frequency f, wiill peak-to-peaknagnitude

that this pow€r

Vpp o ZoBgGg

The s€co-hd term in equation p.34 isFi,gure 2,2).

/Tnq (e.3sb)

triangular spectrum of noise (see

k

a

an?{sn

Figure ?';q: The output noi Ee speetrrrrn from the squaFe law detector.

For frequencies f<<BH t,his c;an be eronsidered as, a flat,speetrurn ofintensity l^I1p where

WLF = EazNHaE$t .

It is this nolse which togethop with the square-wdve of equation Z.3Bb isamplifted by the low frequenc'1t ampl,ifier and fed into the sy,nchronous detector.Ideally' in o,rder to preserve the infornratfon in the square-wave, this amplifier

Page 52: 2-Whole-digital Data Processing in Radio Astronomy

45.

sltould be wide-band, extending up'uo about ten tintes the switching frequency.llolvever an amplifier o1'this type is easjly saturated by the wide-band noiseinput and usualiy, w'ith a slighi loss in sens'it'ivity, a narrovr band anplifiercentred on the srvitching frequency is used. Another systenr (Frater, 1965)uses a synchronous integrator to produce a comb filter response, '.,vhich ampiifiesthe odd ltarmonies in the square!,/ave rvh'ile rnaintaining a narrolv pass-band.

It is assumed for this anaiysis thai the amplifier js narror.r-band, with a

rectangu'lar pass-band of bandvridth Bv and power gain Gy, cenired on thesvtitching frequenc} fr. The square-wave input wi'll produce a sine wave outpuiof peak ampiiiude

.4is; t'imes the ampi'itude

by equation 2.35b. The

in an output rectangular

(2.36a)

of the

noi se

noi se

WN = ZsttJHtBHGv (2.36b)

provided that fs..BH.

From equation 2.15, the output from the synchronous detector correspond'ingto the sine wave input of equation 2.36a will be

frorn the synchronous detectoris a rectangular band of noise

cosX

and the switching signa'l .

(z.tt)

correspondi ng

extendi ng

H,,r = F.2o2tt;12Bpcu

Vpk=*/q-"uHGHk Mas ihe fundamental component of a square \{ave

square wave, the square wave input being given'input (equation 2.34, Figure 2.2) wilt resultband of width Bu and intensity

vo=T IneBsGsk/qa-Tf

sine wave

vo=F /q,.oGsBp1k/'m

From equation 2.21., the outputto the noise band of equation 2.35bfrom 0 to By/? hertz with intens.ity

tvhere X is the phase difference betleen theIf X can be adjusted to be zero, then

- l6a2}z ,, 2. ^-

-T rlH DHrrv

Page 53: 2-Whole-digital Data Processing in Radio Astronomy

46;

Substituting for" ldg from e,quation 2.33 this becornes

r,,n = S crBpGrzkzTgz

and as AT<<T, then Tgdr'ur i.e. o

w,u = *ts GyBgc6zkrTuyru (z.sa)

Assumirng that the'lsw-paS,s filter has a p@wer gain G1 and a nofse bandwidthBL = UT1 (equation 2.3) tfre total output noise from the interferometer is

P*, =9LJot ' t, n ,r" GuBpGp2keTsys'.Ti {2.39a)

and the outptt d.c. signal voiltoge is from equation. Z.3i

RAVs "F /frE.oGilBsk Fffi (2.3,9b)

The minimurn incrernent Jn antenna ternperatur"e rvhich the I'nstrunent candetect is limited by the nsise fluctu'ations at the outpnt (equation 2.39a). A

csnve'nient and standand defr'nrition for the mininrum d,etegtable signal is one

which pnoduces a steady output equa'l in magnitude to the F.rn.s. fluctuations ofthe output. From eqqations 2.39a and b this condition is that

i'€' n

From egu,ati on 2 .29 it can be, seen that

I,Tm = KuATncosS

so that the minimurn detectable ternperature at antenna A fnom a'sourc.e at an

ang'le 0 is given by

(ATn)min=fu-h tr

ffi;ryL ocHBHk[,^qErB ],,n = ryry.GHkr,y,r-'l['rysJrrn=#'# (z'4oa)

(2.40b)

Page 54: 2-Whole-digital Data Processing in Radio Astronomy

47.

For identical antennas Ku = 1

(AT)mi n

This 'is the mininium incrementproduce an output deflection equa'l

temperaiure at eiiher anienna which wjl'lthe r.m.s. no'ise flucluations.

and for ^-nO t

T=-_2/2

7,S,Y!-vDHrL

(2.aoc)

(?.41)

into

?..7 The Sensitjvity of a Direct l"iul tipl ication interferometer

Cons'ider an'interferometer of ihe type shorvn in Figure ?.Ib. To ob-uain a

result comparable vlith equation 2.40c it w'ill be assumed that the aniennas are

identical, the cables loss-less, and thai there is a po'int source vertical'lyabove the antenna system. If the two ampf ifiers are identical , each tl'itlt a

rectanguiar pass-band of w'idth Bp and gain Gg, centred on fo, and each wiiha noise temperature referred to the input of Tp, then the output of each willbe a rectangu'lar noise band of width Bp and intensity

vrhere T6 is the antenna temperature caused by the diffuse background radiationand AT is the increment in antenna tempenature caused by the po'int source. As

in the case of the phase-srvitched'interferometer the background radiation willproduce uncorrelated voltages at the tvro antennas because of the variation inphase difference with djrection, and if the two amplifiers are independent, thenoise temperatures Tp will also be uncorrelated, The noise power of equation

2.41 can be split in to two components for each of ihe outputs, |^l5 which is a

corre'lated noise present in both outputs, and l,J1 which is uncorrelated.

l,l5=GgkAT

t,JN=GHkTry,

1,J1 =GHt(Tn+Tp+AT)

where Try, = T4 + Tp

From equation 2.?6c it can be seen that the output of the multiplier wi1'l

be a tniangular noise spectrum plus a d.c. component, the overall power spectrum

I,Jo(f) being given by

l^lo(f) = 2l,ls2BH26(f ) + (2!^Js2+2tlsl.JN+l^lN2)(gH-f ), 0<f<Bp (2.a3a)

If AT<< Tsys, then l'Jr<<lhr, and equation 2.43a can be written as

(2.42)

(2.43b)lito(f) = Zl,Js2BH26(f) + wp2(Bg-f)

Page 55: 2-Whole-digital Data Processing in Radio Astronomy

Tiri s snectrglp

noise bandurjdtlr E;

and a lolv frequency

Su bs t'ituti ng

def i ni t'ion of the

i.e .,

is filtered by

(=1/2TL) whi ch

p^^' ul..

noise power (assunring

P11 = I'l,12BnGr.

for lJp and !i, from

minimum detectable

a 1or.r-pass f i l t.er vri ih a povrer

resulis in a dc power output

= lJr2Bp2G;

48.

gai n G1. and a

Q.aaa)

(2.44b)

prev i ous

(2.45)

B1<<8") of

i.,L

equati on 2.42, and us'ing the

signal

k6 T)mln BH = k ,rr, IT

(lr)*.,- = 1- ]'re-rrrrtr n /FL

This gives the minimum increment in antenna temperature for a directmultiplication interferometer which will produce an output deflection equal tothe r .m. s . noi se fl uctuati ons .

2.8 Ljnitations and Assumptions

In order to arrive at the sensitivity relationships of equations 2.40c and

2,45, the follovring assumptions have been made.

i. The jnput signal spectrums are flat over the.region of intenesi. In most

cases, if the bandrvjdth Bg<<fo (i.e., narro'rr band operation), thisassumption if valid.

2. Any conversion processes associated rvith the high frequency amp'lifiers arefinear, so that the statistical properties of the noise are preserved.This merely places a requirement on the amplifier design.

3. The high frequency amplifiers in boi,h cases have rectangular pass-bands,

and the bandwidth is small compared r,rith the centre frequency. Saunders(tg6e) has analysed the d'irect rnultiplication interferometer for a single-tuned band-pass amplifier and a rectangular band-pass amplifier, and has

shown that there is litt'le difference in the results obtained. As more

sophisticated amplifiers ulill come closer to a rectangular characteristic

Page 56: 2-Whole-digital Data Processing in Radio Astronomy

A

,hA9

than the single-tuned amplifier, this assumption r,v'i11 normally have littlebearing on the result. The narrow bandwidth requirement has already been

specified (1).

it has been assumed that ihere'is no phase difference betleen the correlateci

signals at the two aniennas, and that no phase difference is introduced by

the system. In the case of a phase-sr.t'itcheci int,erfer^onteter this implies

that the mininrum detectable ter,tDerature has been calculated for the case

where the response of the system is at, a maximum (see equat'ions 2.40b and

2 .40c) . For the di rect mul ti p'l i cati on i nterfenometer the correl ation

between the tlo correlated signals wili be greatest when the phase difference

is zero, so here a'lso the sensitivity corresponding to the maximum response

has been calculated.

In the case of the phase-slvjtched interferometer ii has been assumed thatthe bandwidth of the lolv frequency anp'lifjer is less than one-fjfch of the

sr.ritching frequency, anci rectangular in shape. It has also been assumed

that any phase difference betr.reen the outout signal waveform and the refer-ence square wave can be cancelled. Saunders' (1968) anaiys'is would suggest

that little error arises from the rec'uangular band assumption. The narrow

band assumption is valid in this case, because only the fundamental com-

ponent of the signal waveform has been cons'idered. Typically' bandw'idths

of these amplifiers are only a fel per cent of the suritching frequency

(L'im, 1968). It has been suggested (eoidste'in et al , 1957; Rob'inson, 1954;

Christiansen and Hogbom,1969) that an increase in sens'itivity af tr/2/2

(-1i%) will be obta'ined if all harmonics present in the square wave are fed

into the synchronous cietector. This factor can be obtained djrectly by

analysing the response of the detector to a square wave, but it must be

remembered that the calcu'lated response to noise is val'id only in the narow

band case. Simple phase shift circuits can be used to cancel any phase

difference between the signal and reference waveforms (Lim, i968).

6. in the case of the direc'u multiplication'interferometer it has been assuneci

that the arnp'lifiers are iclentical , and that noise generated in the tvto

anipf if i ers i s 'inclependent. Tne condi t'ion that they be 'identi cal 'i s readi 1y

e:*ic€in.t but compleie independence is difficul t, to obtain (SaunCers, 1968).>cr L | 5 | I gu,

Correlated noise oiher than that arising from a signal source seriously

Ceteriorates the performance of a direct multip'lication'interferomeier.

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vv.

7. it has been assumed that the antennas are identical. As rhey itave a

bearjng on'ly on AT, and as AT js d'irectly related to the aperture area fora Eiven source, it can be shorvn that'in the case of non-icjentical antennasihe equations are valid if the geornetric niean area is consiclered inrelatjng AT io a flux density (l(raus, 1966).

B. The conCi t'ion thai ihe cabl es be I ossl ess

will have the effect of lowering the ga.in

receiver noise.

not irr;portant, as 'iossy cablest,he sysiem and increasing the

all praciical astronomy

Tr^ severai hundred

1e

a$

9. The condition that AT<<Tsys rvill be saiisfied incases as AT is typically of the order of 10k, anddegrees.

LU. simi'lar1y the conditions that B;<<Bp1 and fr<<Bp wj'11 usually be met, astypically Bg-lMHz, fs-100H2 and BL is on'ly a fraction of a hertz.

As the interferometer output varies sinusoidally w'ith phase difference O,'if there is relative motion beiween the antennas and the source, the outputof the system will vary in a pseudo-sinusoidal fashion. This fact con-siderably enhances the detection of signals, as relative motion is usuallyproduced by the rotation of the earth. The frequency of this variationsets a lower lim'it on the bandr"r'idth of the low-pass filter, and so to thereduction of the background no'ise. The optimum filter if an ideal(rectangular pass-band) filter is assumed, is one which has a banclwidth B;equal to the frequency of these sinusoidal variations. t,lith a rea'l 1ow-passfilter, the sensitivity wi1'l obviously be less. For a simple RC filter,Griffiths (1956) has shown the minimum detectable signa'l to be Z.SdB higherthan for an ideal filter.

i1.

2.9 Comparison vrith 0ther Results

As the sensitivity of radio telescopes has been a topic of dispute it ispertinent to compare the resu'lts of equations 2.40c and 2.45 rvith those obtainedby others. The total power radio telescope, shown in Figure 2.3, is common'lyused as a basis for comparison.

if the resulis obtained in this chapter are app'lied to such a system, themi n'imum detectabl e si gnal i s readi 1y found.

Page 58: 2-Whole-digital Data Processing in Radio Astronomy

,/,qrursx xa

-ri-:

, ^...,u.* i-;f so' LAY/ LiLov/-eassL ourpurX ; I D.T. i IFILTER I

/ Bs.T;

For the purposes of comparison a factor k'is defined so that for anyte1 escope confi gurat.i on

where k is an index of performance relaiive to the total pov/er telescope.

From the results of equations 2.40c and 2.45, k = r/Z/2 for the phase-switched interferometer and 1//2 for the two-channel direct mu'ltiplicationinterferometer. In comparing these instruments with a total power telescopeit must be remembered that AT is the increment in temperature at one antenna(in the case of two identica'l antennas). If the two antennas were coupledtogether in a totai power arrangement, a source wou'ld produce tlice the increnrentin temperature that it would for a single antenna. Referring a1l sensitivitiesto the same total antenna area, k for a phase-switched interferometer is r//Z= 2.22 and k for the two-channe'l d'irect multiplication interferometer is/2 = I-4I- These two telescopes use the total antenna area less effectivelythan a total pov/er telescope. However, other factors which limit the sensitivityof a total power telescope but have not been included in equat'ion 2.46a usuallylead to a greater relative sensitivity for an interferometer configuration.

The factors obtained are in agreement with most of those in the literature(Goldstein et a'1,1957; Saunders,1968; Tiuri,1964) provided the total antenna

I

Figure 2.3: The total powen radio. telescope

Ttyt

t, 'f^. I S-VS

y DH.iL

/ rrf \\^'i m'in - ( 2.46a )

(2.46b)(AT)mi n =

Page 59: 2-Whole-digital Data Processing in Radio Astronomy

52.

area is considered in the interpretation of aT. There is much confu:sion in the'literature arising frorn this point (Goldstein,.19,55; Goldsteln et al ,19513Tl'uri, 1964). Robinssn's (iee+1 results are also jn agreenrent with thoseobtained here except for an error a;f /2 which arises in his anaiys.i,s of a squar.eJaw detector.

2.ICI The EffFc.t of teqeg-ted Observations

Because the constant output of a radio teiescope usually changes with time,as menti,or,led in section 2.8" there rr's a'lower limit on the bandwidth of the low-pass filter'r and so oh the neduction of- backgr.ound noise. The baekground noisecan be furth€r reduced hovlevef, without destroSring the signal information, bytaking the av,era.ge 0"f, several obsenvations of a sourc€.

Con:sider a fun.ction of time f,(t) which consists of. a siEr,ral S(t) and a

noise N(t). The signa'l S(t) is periodic with period T, and the noise N(t) isa stationary random process with a zeFo mean and an r.rn,.s. value,o. Let f(t)be sampled at Q points per cycle of s(t), so that the kth sarnple wi'll be

f(tk)=s(tk)+N(tk)

Now tk = O,+

=nT+tp

where k, n.n and p a:re integers and prcq..

Thus f(nT + tp) = S,(nT + tp) + N(nT + tp) .

= s(tp} + N(nr'+ tp)

N(nT+tp) will have a zero mean and r.m.s. o, so that the signa'l-to-noisera;t:io at the kth sample point willl be

s/,,r FIP]'

whete tp is deff ned by eguatian 2.41 .

If m. sanples takeill at int"ervals T are sununed, then the summation will be

i e.47)

Page 60: 2-Whole-digital Data Processing in Radio Astronomy

aJ.

m

nlrt(nl+to.) =

= m.s(to) +

Ine mean sguare value of the sum of m r'ndependent samples of l,l(t) will bemo.z (Lee, 1g60)o so'that ther signa:l-to-'noise,ratio after the summatisn of, nr

saniples wilt he

S/* = t's'(:o)" mo-

2

=m EA]Ldl

,.i, [,.0,1

+ N(nr+tp) |I

nl

I w(nr+to).n=1

The siQnal-to-noise ratio isaveragJng of m nepetitions ef the

thus increased nr times by the sumrRation orsignal, point by point.

Because of the rotation of the earth, a celestial soutce crosses therneridian at any point on the earth ohoe €VeFy sidereai dajr. For a celestialsource' the output of a fJxed radio telescope is thus perriodic wrlth a periodof one sidere:a'l day. If resuilts o;btained on m succ€ssive sidereail days areaveraged' then the signal-to-noise ratfo of the output of the :telescope wil'lbe irrlproved m times fro,m that for a s:ingle observation. Noti4g that fsr allof the t:nstruments discu5sed the ou:tp1,rt voltape is propor.,tional to the inputpoffef then thfs factor fn, the number Of observations sumncd, can be includedin the genenal re'lationship (eeuation 2.46b) as

(AT)rni n = (2.46c)

The effec:t of avergg.ing m obse;nvationsf ntegratr'on tirme T; of the lou, pass fi'lter m

to the signal

ean be consldened as, lncTeasJ,ng thetimes, wtitholrt altering'its response

Page 61: 2-Whole-digital Data Processing in Radio Astronomy

54.

REFERENCES

CHRiSTIAIISEN, l,l.N., and H.OGBOM, J.A. (1969): i'Radio Telescopes". (C.U"P,,

Cambridge).

DICKEi R.H. (1946): "'The Measurement of Thermal Radiat:ion at Mfcrowave

Frequenc'ies". Rev.Sci .Inst , , lJ pp. 258-275.

FRATER, R,H. i1965): "Synch:r,onous Integrator and Denrodulator", Rev.Sci,Inst. ,

36 pp. 634-637

GALEJS, J'.. (1957): 'fC,srn,parison of Subtr"actton-type and Multiplier.typeRadiometersr'. Proc.f .R,.E. , 45 pp. l4?0-,W22.

G0LDSTEIN, S.J, ("i955): u.A Cornparison of Two Rad,iometer Cir"cuits:*. Froc. LR,E.

43 pp. 1653-1666.

G0[-DSTEIN, S.,J., TUCKER, 0.G., and QRAHAM, M,H. (1957)r rlA Oornparison of Two

Radiometen Circuits". Proc.I.R.E. , 45 pp. 365'3'66-

GRIFFiTHS, J,ltl.R, (1955}; 'n0ptirnum .RC Fi'ltens", Wireless Engn., 9l P,p' Z6:8-210i.'

FiELSTROM, C.ttt, (1960): "statistical Theory of Signal Detectdon". f,Pergarnon

P'ress, Londsn).

KRAUS o' J,D. (1900 : "Radi o Astro'qo.my" . (McGtr."aul-,FJi J I , New YorkJ .

LEE' Y.lrl,. (t900,): 'rStat{stical Theory of Communlication". (tottlleyp i'lew Yonlt}.

LIM, J.C. (tS0S1l 'fNon-Uniformly Spaced Arrays :of Directional Elements", Ph.D.

Thesis, Universrity o:f Auckland.

RICE, 5.0. {:1945): t'Mathematical Analysi.s o,f Random Nofse". B.S:..T.,J,, .!!,pp. 4'5-155.

R0BINSCIN, 8.,J. (196,4): '!,Receivers for Cosmic Radio tr'laves'r, Ann,. Rev. AstroR.

AP", -2 PP. 4o'1'-432.

SAUNDERS, A.M. (1968): "A Design Study of the ,Correlation Radiometerr!. M.E-

Thesisi University of Auckland.

TtrU,RiI, M.E. (i964) : ilRadio Astronony R:eceivers", Trans. I.E.E.E,, AP-12

pp. 931-938.

Page 62: 2-Whole-digital Data Processing in Radio Astronomy

\.''.:: D:i Z:;l-, A. (1955): "liojsc". (Cira:::crr dtici ilall, London).

Page 63: 2-Whole-digital Data Processing in Radio Astronomy

56.

CHAPTER 3

The Interferometer In An Equatorial systern of coordinates

In this chapter the relationship between the output of an interferometerand the incident radjation established in Chapter 1 js extended to relate theoutput to the pos'ition of a celestial source and the rotation of the earth.The coordinate system is defined and the concept of sidereal tjme is established.The output of the interferometer is then found in terms of the pos.ition of a

source refemed to these coordinates, and the position and orientation of theinterferometer base'line. It'is shown how thjs relationship can be used todetermine the coordinates of the source from the interferometer output.

3.1 &qlgThis system of coordinates, conrmonly used fn astronornical work, is referred

to the ce'lestiaJ sphere, an imagjnary sphere of infinite radius with the earthat its centre. The intersection of the p'lane of the earth's equator with thesphere is the celestial equatorn and the intersections of the earth,s axis withthe sphere are the north and south celestial poles. It is convenient to regardall heavenly bodies as be'ing projected on to this surface, and the coordinatesof a body can then be defined on the sphere in a manner similar to theterrestrial coordinates of latitude and lonqitude.

The right ascension (R.A. or o) of a point on the celestial sphere isdefined as the angular distance along the equator from a reference point (thevernal equinox, sometimes called the first point of Arjes), measured eastwardsto the hour circle of the point in question (the hour circle is the great circlepassing through the poies and the point). The declinatjon (dec. or 6) of a

point on the celestial sphere is the angle between the celestial equator and thepoint. Right ascension may be measured in degrees, minutes and seconds of arc,or in hours, minutes and seconds of time (24h=3600). Declination is expressedin degrees and lies betrveen r90o (positive north of the equator).

The right ascensions and decljnations of stars are nearly constant; theyvary slightly because of real motion of the stars, and precessional motion ofthe earth's axis, and a]so periodically because of nutatjon and aberration(H.M.s.0., 1961).

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57.

3.2 The Measurement of Time

The most natural unit of time for terrestrial purposes is the so'lar day,the time corresponding to one rotat'ion of the earth with respect to the sun.Because of the annual rotation of the earth about the sun, the directjon of thesun is continually changing with respect to the celestial sphere, and a solarday does not correspond to one true revolution of the earth about its axis. Forreference to points on the celestial sphere, it is more convenient to use a un.itof time based on the true period of rotation of the earth, the sidereal day.This represents one complete rotation of the earth with respect to the celestialsphere.

The sidereal day is defined as the interval of tinre between tlo successiveupper transits of the vernal equjnox over the sarne neridian (l{.M.S.0,1961;Hosmer and Robbins, l94B), an upper transit being that instant that the pointin question crosses the upper branch of the meridian. The vernal equinox, orfirst point of Aries lies on the line of intersection of the plane of theequator and the plane of the earth's orbit (the ec'liptic). It is the ascendingnode of the ecl'ipticn the direction of the sun vrhen it crosses through the planeof the equator from south to north, during the northerr, spring. The directionof the first point of Arjes moves slowly westward because of the earth,sprecessional motion, and oscil'lates slightly about this motjon because ofnutation. Owing to precession, the mean sidereal day is about 0.01s shorterthan the actual period of diurnal rotation of the earth (Hosrner and Robbins,1e4B).

The sjdereal day is divided into tlenty-four hours, each of which isdivided into sixty minutes, and each minute is divided into sixty seconds, inthe same way as a solar day. The beginning of a sidereal day (00h) is known assidereal noon, and at a given meridian is the time of the upper transit of thevernal equinox. The sidereal time at this meridian is then equivalent to theang'le through |,rhich the earth has rotated since the upper transit of theequi nox.

The solar day is defined as the interval of time betleen two successivelower transits of the sun's centre over the same meridian (tlosmer and Robbins,1948), d loler transit being the instant that the point in question crosses theloler branch of the mericlian. The so'lar day is defined urith respect to the'lower branch of the meridian in order that it may begin (00h) at midnight (the

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58.

civil day).

As the earth rotates about the sun jn an elliptical orbit, its angu'larvltocity in accordance with Kepler's second 1aw, the apparent angular motion ofthe sun is not uniform, and the length of the solar day as defined varies fromseason to season. The solar time nornrally used is that defined with respect toa fictjcious point, tlte mean sun, which is imagined to move at a uniform ratea'long the celestial equator, making one revolut.ion in a year. The time indi-cated by the position of the mean sun js called mean solar time, and thatindicated by the position of the actual sun, the apparent solar time.

Universal t'inre (U.T.) or Greenwich mean tjme (g.t'1.t.) is civil tinre (solartime beginning at midnight) for the meridian of Greenlich. This is the solartime on which most astronomical calculations are based.

3.3 Solar and Sidereal Tirne Intervals

Referring to Figure 3.1, let C be the position of the earth at the tirne ofthe vernal equinox, then the observer at 0 has both the sun and the first pointof Aries on his nreridian. After one true rotation of the earth, the observeris at 0' and once again the first point of Aries is on his nrericlian, the earthhaving moved to C'. The time elapsecl is by definition one sidereal day. Butit can be seen that the earth must rotate further by an ang'le SC'X before thesun is again on the meridian of the observer at 0". This means that the earthmust move further on its path around the sun to c". The arc cc", and hence theangle SC'X, is almost one degree, so that a solar day is almost four minuteslonger than a sjdereal day.

If C' is the position of the earth at any tirne after the vernal equinoxthen cc'represents the tinre elapsed since the equinox. The angle sc'xrepresents the accumulated difference (in sidereal time) between solar and

sidereal time. As these two ang'les are equal, it can be seen that after one

complete revolution of the sun by the eartho solar time is 3600 (one siderealday) behind sidereal time. The tropical year (equinox to equinox) is 365.24220mean solar days (H.M.S.0.,196i) so that this interval corresponds to 365.24?20+ I sidereal days.

i.e.,

or

and

366.24220 x 1 sidereal day =

sidereal/solar ratio

solar/sider ratio

365.24220 x l solarday

.99726957

t.0027379L

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59.

Figure 3.1: Solar and sidereal time intervals

This nr,eans that ornc sidereal secsnd is .9972695;l solar seconds or" thatthe solar second is .27379L:1; long,er than the sidereal s,ec,o,nd.

3.4 Rig[t Ascension and S:idereal Tirne

The local ,hour ,angle (L,H.A.) of .a point sn the celestial sphere isdefined as the arc of the equator (sr angle at the pole') ffiedsur€d l'iestwar.ds

from the locarl menidian to the hour circle of the point. The Greenwich hou,r

ang:le (G.H.A,) of a Boint is the hour angle at the meridfan of Greenwich.

In.Fi'gure 3.2, 0 is the position of, an observer, S th,at s,f a star, and thehour circle through G is the Greenwieh meridian. For" thre ohserver at 0, thelscal hour angle of the star S is the arc 0'S' and the Greenwich hour anEle ofthe star is GS', The arc G0' is the west longitude of the observer at 0" so

that the f.ollowing re'lationship exists,be,tween Greenwich and local hour angl,es:

0rS' = GS'-G0'

L.H,.A. = Q.H:.A.-weSt longitude (3 .1)

As the side'real time at any meridian is equal to the time elapsed since

the upper transit of the vernal equin:ox, then the local sidereal time (L.S,T.)

0t any point is equa,l to the local hour,angle of the vernal e,quinox. The Star

Almanac (H.NI.S.0., 1970) tabulates a quantity R which is defi:ned as the differ*

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60.

NC.P"

I

I

I

I

JI

Figure. 3.2: The nelationshi'p betwe€n Greenwtch

nd local hour an;g:les

enrce be:tween the Greenwich hour angle of Aries (Greenw'ich sidereal tfne, G.S.T.)and un,ivensal tinre (Greerwici,r rnan time, G.l,l.T.), This quant'ity is egual tothe angle SCiX in FiEure 3.1 and increases by 3m 56.55536 s every day (H.M.S.0.n

1961 ) .

G.S.T, = U.lT.+R

As sidere,al timre is the hour arrgle of the first point of Aries, and a

re'lationship has been e-starblished (requation 3,1) between Greenwich and local hour

angles, local sidrereal time can be calculated from Greemrich sidereal time.

From equatisn;3.1

(3.2)

G.3)

i.e.'

0r

In Appendix 6 a

valu'e of R and U.T.,

L.H"A. = G.H.A.-west Iongitude

L . S ,T, F G. S., . -w€St ,lonEi tude

L.S,T. = U.T.+R-west longitude

cgmputer pfogFffrfl SIDER is described, wlri:ich given a startingtabulates L.S.T. at intervals of local zsne time (Auckland).

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If in Figure 3,2 the poJnt v is the v,ernal equ.i:nox, then t:he

definition the rfght ascension of the star s, A relations,hip canbetween r{ght ascension, local hour angle (h = arc gfS,) and localtlme (T = 0'V).

. + L.H.A.

h

= G.S.T.-G.H.A.rru

= ;R-E

61.

arc VS' is by

be found

s,i dereal

(3.4)

(3.01

i .,e. ,

OF

i' . €,. r.

e variesdevirates from

0'S'+VS'

L.s.T.

T

0,\l

R.A

o*

When a star is on the local meridian, its local hour angle is zero (h=0).Thu's the sidereal time at fhat meridian is nurnerically equal to the r:ightas.cension of thc star, or the right,asceR:sion of any star is the (Iocal) side_;real t.;ime sf its uppe_r transit.

3.5 The FiEht Asce,nsio,n of the Sun

Universal time, as defrlned in section 3.2 is equal to the Greenwic,h houran.gle of the mean sun less twe,lve hour"s. If the hour angle of the actual sundiffer.s frsm that of the filean sun by a quantity e, then

G.Fl.A.sun = u.T. + 12h + e.

The Star Almanac (H.1,t.S.0., lg70) tabulates a guantity E (=12h+e) tromuthich the Greenwich hotrr angle of the sun can be calculated.

G.H.A,sun = U.T.*E (3. 5)

From eqgatisn 3.rl

R'A'ron

R.A,ruo

approximately within the range *15 mins so that the actual surrl

th€ trUe sun by about t4o.

3.6 The_0utput of gn Interrferometer iJr Tellrs of the Eqqatsrial Cqofdinatesof a Source

In section l.E it was shown that if the antenna power pattern lc(g)12 andthe bandwidth patterrir B(.e) are wi,de compared with the fringe widthn the output

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62.

of a come'lation interferonreter is given by

D

R(0) = cos Zna-{gi-sino)4o

where 0 is the angle betueen the sor.mce and the no:rma'l to the inter^ferometerbaseline in the plane thr"ough the baseline and the source. The length of thebaselline i's D metres and the centre operating frequency is c/., . .The quantity0i coffe:s'ponds to an instrumental delay. It is desirable to ^o reJate 0 tothe hour angle H and decltnation 6 sf the source, and the hou,r angle h anddeclination d of the r-nterferometer pole. The interferometer psje I is definedas the interrsection of the tbase'lirle f,rom antenna l to antenna 2 with theaelestrial sphere, (see Figure 3,3),

Fig,ure 3.3: The definition of the lnterferometerr pole

The spherical triangle of Figure 3.4,represents a section sf the cerlestialsphere. P is the nor"th celestiai pole, S i,s the souro€i I is the interferometerpole" and 0 fs the centne of the sphere.

(1.9r)

Figure 3..4: The sprhericalbebleen the position of

showing the rrelatjonand the baseline

triangl e

the source

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63.

From the spheri ca'l tri angl e formu I a for cos i nes (l.losmer and Robbi ns , 1948) ,

cosa = cosb.cosc + sina.sinb.cosA

a

the fol 'l owi ng rel a ti on i s obtai ned:

cos(te) = cos(|ol .cos (|a) + sin(to).sin(td).cos(h-H)

i .e., sin0 = sind.sind + cos6.cosd.cos(h-H) (3.7)

Substituting this value of sin0 jnto equation 1.37,

r1R(H,6) =.or2nDlei-(sin6.sind + s6s6.cosd.cos(H-tr))l (3.8)

trsL J

. This equation can be used to determine the coordinates (H,6) of a sourcefrom the interferonteter output. D, d and h are properties of the antenna systemand can be measured either by normal surveying techniques or by calibrationfrom a known source. lo and Li are propert'ies of the receiving system.

From equation 3.4 it can be seen that the hour ang'le H of a source isrelated to its right ascension o and the sidereal tinre T at the point ofobservation by

T=cr*H

Denoting the sidereal time at the interferometer pole as TO, then the hour

angle H in equation 3.8 is given by

H=TO-a (3.9)

and refemed to the pole, h is zero. Equation 3.8 then becomes

R(TO,cr,6) = ..r +[ni-sin6.sjnd-cos6.cosd.cos(fp-o)] .

For a particu'lar source, cr and 6 wjll be constant, and R will vary in a

pseudo-sinusoidal fashion with time. If O. (TR - o,) < n * then as TO increases,cos(tp-a) will decrease and the argument of R(TO,o,6) wil'l increase because cosd

and cosd are necessarily positive (-n1, < 6,d < + r/Z).

* This condition implies that the source is in the visible range of thei nterferometer.

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zero

a

64.

tt.t'gt is_a time at which a zero occurs in R(To,q,6)n and if roo2 is a

n half cycles later and Tpo3 another zero m half cycles after Tpe2, then

(s.toa)

and

?Put -si nd. si n6-cosd. cos6. cos (Tpot-o) ) = (N*|),,

Tkut-sind.sind-cosd.cosd.cos(Tpo2-o) ) = (ru+|n)n (3.10)

lkot -sind.sin6-cosd.cos6.cos(Tpo3-o) ) = 1N+|n+m1n

where N is an inteqer.

It is preferable to use the zeros of the output as points of referencebecause their positions are unaffected by the modulating effect of either theantenna povler pattern or the bandrvidth pattern.

From the equations 3.1.0, by subtract'ing the first from the second, and thesecond from the third,

$osa.cosd [cos(rpor-o)-cos(rooz-o)] = n

$osa.cosd [.or(tnor-s)-cos(rpos-o)] = m

These two equations can be further combined to yield

f,-.-1r.lnfos (T,,o2-o)-cos (Too3-o)_] = m fos

(Tpq1-o)-cos (rpez-")_l

provided cosd.cosdlO. If cosd.cos6=0 then there will be no fringes as a functionof time. The arguments of the cosine terms can be expanded, giving

* = k.n _ tan-r m.cosTool-(m+n)cosTpo2+ncosTpo3 (3.11)

where k is an inteqer.

The approximate value of o will be known from the pointing angle of theantennas and the local sidereal time, so a unique solution should be obtainedfrom equation 3.11. The declination 6 can be calculated by substitution ofthis result for cr, into one of the equations 3.10a.

The shortcom'ing of this nrethod of ca'lculating the position of a radio

1

I

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65.

source is that lf Tpol- Tpo2 and Trs3 lie close togeth,er, both the denominatorand nunerator of equation 3.11 will be small. Superior methods of performingthis calculatiion have been sugg,esued (Read, 1963i Swenson and lrtathnr" 196S)birt these involve the assumption that the interf,erometer baseline,is horizsntalat the point of observation. If this is so, and the baseline is orientated inan east-west direction, then equatlon 3,8 beconres

time

h-H

at the sbserver's meridian,

1T=lm-u-y

R(Trnu,d) = cos Tftt-sss6.sintrr-o)] .

(3.13)

d = q6g-r mr2D1 ;;;)-

=cos-l mfuAs an a:pproximate v'alue of e will be known, c can be

R(H,6) = cos *[-t-cos6..cos(h-n)]

and lf T, is the local s{dereal

which leads to

If the bearnwidth of thereducing this equation to

antenna amay is srnall, then lTm-ol is snratl,

(3' ta;

occur in th,e output as

R(Tr,,c,d') = cos +[-t-(Tm-r) ..uru]

If Tmol, Tlno2 and, T6e3 are the times at which zerospreviously defined for Tp, ttlen

fl*t-(rmor-o) "coso) = (N+|)n

f, *.r-(rmoz-s) .cosd) = (N#n)*

from which a solution for. 6

ei -(T*6-o) .cosd)

can be obtained

= (N#n+m)r,

1s. rra)

found by substitution

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66.

into equations 3.13.

An alternative method for solving equation 3.8 in the genera'l case, and

ohe readily rea'lized in a digital computer, involves an iterative procedurefor finding u and 6. The major portion of an output record corresponding tothe transit of a source can be nonmalized by dividing it by the approximateantenna power pattern. The resulting record can be corrsidered as consistingof the fringe factor only. As the approximate values of c and d will allaysbe known from the pointing direction of the antennas, q and d can be calculatedmore exactly by an iterative procedure to find the curve which gives the leastsquares fit to the record.

3.7 Coordinates of the Interferometer pole

If the parameters d, D and h in equation 3.8 are to be calculated by geo-detic surveying methods, then it is necessary to relate them to the measurableparameters of the interferometer baseline.

Referring to Figure 3.5,7 is the zenith at the point of observation, and

has latitude 1,. The baseline is inc'lined at an angle e to the horizontal atthe point of observation, and its projection on to the horizontal plane makes

an angle 0 with the meriCian p1ane. 0 is the centre of the celestial sphere,I is the interferometer po'le with hour ang'le h and declination d, and P is thenorth celestial po1e. The plane NEO is the horizontal p'lane at the point ofobservati on .

srcPZ=*-1

NZ:INE: I :lZEI:eEZ =IyPl:+-d

Figure 3.5: The

and the

relationshio betleenmeasurable parameters

the i nterferometer pol e

of the basel'ine

Nl

II

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67.

From

applfed to

ttt

i.e.,

A:lso

i,€., cos(h) = sinq - sin[''sfnd

If Tm is local sidereal tine atthe pole Tp will be given b,y

the zenith

the cosin:€ fule for spherical triangles (Hosmer and Robbins, lg4g)triangle PIZ

cos({-d1 = co.s(}.e) .eos(Fe) + sin({-1,) . sin$e},cosCI

sind = sin$,sine + cos!,dcoss,cos0 (3.14)

^^-, L\ _ cos(F"l - cos(tr).costialcos(-hr =

.c(3. 15)

Z, the local sidereal time at

To=T*-h (3.16)

Thus if e,0, and l, can be measured, and if sidereal tirne at the ob,server'smeri'dian is known, then the sideneall time at the interferometer pole TO can be

calculated.

RETERENEES

H,M.S.0. (Her MaJesty's Statfonery Office), (1961):

the Astronomical Ephemeniso. (London),

H.M.S.,0" (Her Majestyrs Stationery 0ffice), (t9ZO):

Surveyors for the year 1970r'. (London).

HOSli,lER, G.L. , and ROBBINS, ,J.lil, (lg4E): npractical

llal I , London).

"Expl anatory Supplement to

"The Sta:r A:lmanac 'for La'nd

Astronomy". (Chapman and

READ, R.B. (tgga): n'Accurate Measurement of the DeclinationAp.,l. , 13E pp. 1-29 .

SI,IENS0N, 6.W., and lltlATFlLfR, N.e . (tS0S1: "The lr;rterferometerFnoc. I.E,E.E., 56 pp. ?114-2130.

of Radio Sources'!.

in Rad'lo Astronony".

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68.

CHAPTER 4

The Specification of a Data processing System

The preceding chapters have established the relationship betneen the outputof a radio'interferometer and the incident angular power spectrum. The sensi-tivity of an interferometern and the information concerning the positions ofradio sources which can be obtained from the output have also been discussed.In Chapter 2 a method of improving the sensitivity of a radio telescope t/asdemonstrated. This consisted of taking the average of a number of daily observ-ations; records on different days at the same sjdereal tirrre and at the same

declination being of the same area of sky. Averagirrgr of this kind can be per-formed by the manual addition of analogue records, but the process is tedious(McLaughl in, 1962; Pownall , 1969). If the observations are available in digitalcomputer acceptable format holever, the averaging, and any subsequent analysisof the averaged record, can be carried out rapidly and efficiently by a digitalcomputer. Further, it has been shown that records obtained with different base-lines can be combined to produce a map of the sl<y brightness distribut'ion by a

process of Fourier transformation. This technique of aperture synthesis requirescomplicated manipulation of the data which can only be realized in a digitalcomputer.

In this chapter the general requirements of a data processing system forthe acquisition, storage and analysis of the data are discussed. The systen has

been designed primarily for use with the present 200 |'lHz telescope, but as therequirements of this instrument are ntodest, sufficient flexibility has been

maintained to accommodate poss'ible future extens'ions of the telescope. In thefinal section a bnief descrjption of the system deve'loped from these requ'irementsis given, and the design and developnrent of the'individual elements of this systemare discussed in the subsequent chaoters.

4.L The Universjty of Auckland Radjo Telescooe

The present 200 [IHz telescope is located on the roof of the School ofEngineering in the centre of the city of Auckland, at a latjtude of -gO0 S1' 18'and a'longitude of n4o 46' 11r' east. It consists of two small antenna arrays on

an east-l'/est basel i ne , operated as a phase-srvi tched 'i nterferometer. A bl ock dia-gram of the overall systern is shorvn in Figure 4.1.

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69.

Figure 4.1: The 200 MHz interferometer

4.11 The Antenna System

Four short-backfire antennas are used in the present system, two combinedin a simple array to form each e'lement of the interferometer (see plate 1).The short-backfire antenna was developed for satellite communications (Ehrenspeck,1969) and is remarkable for its s'inrp'licity and high efficiency. The 200 MHz

antenna has a half-wave dipole placed midr.lay between two plane reflectors. Themain octagonal reflector is trvo wavelengths (-to tt) in diameter, and is sur-rounded by a rim a quarter wavelength wide. The subreflector is 0.64 wave-lengths (-3 ft1 in diameter and is positioned one half wavelength from the centreof the main reflector. The reflectjng surface is made of l" galvanised steelwire mesh supported by a rvooden space-frame. The coaxial feeder cable enters thehollow subreflector support near the centre of the main reflector. The feeddipole is mounted on this support, vrhich contains the matching balun. The wholestructure is mounted on two tripods rvith an east-west ax'is, and can be steeredabout this axis 600 either side of the zenith in the north-south plane. The gainof each antenna is approximately 15.5 dB, corresponding to an aperture efficiencyof more than 957i. A more detailed description of the short-backfire antenna, itsdevelopment and operation, is given in Appendjx 4.

The two identical amays each comprise two short-backfire antennas spaced2.24 wavelengths between centres on an axis skewed vrith respect to the inter-feronreter baseljne (see Figure 4 .2a), The calculated half-porver profile ofthe resultant pattern is shorvn in Fjgure 4.2b. A more detailed computed patterncontour plot, for the array pointed at the zenith is given in Figure 4.3.

FI LI ER

STRIP CHARTRECORDER

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70.

ttl(oLL,o

G'cg(uPc.o(u!rF.v,(J,u-o(u

+,ho(Ugo

HII

!,J I

EIdt

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71.

rFli

<lI

w

N

:,v\

r-\?.-/ \-

4=2G.50

(q) (b)

Figure 4.2: The antenna amay and its half power pattern

The main beam,

right ascensiol.l and

tolards the zenith.

at the half-poler points is approximately

24o r.,ide in decl ination trrlten the antennas

The peak s'ide-lobe level is 12 dB below

140 w'ide in

are directedthe rnain beam.

The te1escope operates on the trans'it principle, the bearn being scanned

in rigrht ascension by the rotatjon of the earth, and in declination by steering

the antennas about their east-west axis and jntroducing a phase delay into the

leading antenna of each array. The effect of this steering is to reduce the

effective north-south spacing and the skew angle o with increas'ing angle from

the zenith. The computed pattern shorvs very'little deterjoration in the steer-

able range, making the visible sky those declinat'ions between +23o and -900.

The variations of array right ascension beanuidth and peak side-lobe level as a

function of pointing angle are shown in Figure 4.4.

The two arra.ys are spaced about 60m apart and are at different elevations

(see Figure 4.5). The projection of this baseljne on to the ltorizontal runs

directly east-west, the tvestern array being at the higher elevatjon.

The antenna arrays are coupled to the receiver vja long runs (-150 yarcis)

of coaxjal cable, with a resultant attenuation of the s'ignals of 20 dB. To com-

pensate for this loss preamplifiers are located at the arrays to ampfify the

signa'ls before they are transnritted down the lines. These preamplifiers use a

sing'le b'ipolar transistor in a conmon base configuration producing a gain of

13 dB, vrith a noise temperature of 100001... This gain is insuffjcient to conrpen-

sate for the losses in the cables, and consequently the cables make a consjderable

contribution to the total system nojse tentperature.

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72.

I-t/f/_

=I

'1r

!I'-/,

III'

15{-

r,f

,l

,l

V,#,

ulsfili

rgileT

EF2.ulN

:EoE&LtJJcr'z A*+l

II

t,

II

>./

/r' coRtours in cs

lslqw mExirn,gm

,gsin,

plot of the pourer pattern of themay.

,{

Page 80: 2-Whole-digital Data Processing in Radio Astronomy

73.

HALF.POWERBEAMWIDTH

PEAK SIDE-LOBE LEVEL

BEAMWIDTH

..-.o---+PHASING LE LENGTH

- Yr- 3)/4-- ----

LOBE LEVEL

Figure 4.4: Pattern

for the

deteri orati on

skewed antenna

with pointing angle

a rr ays

Figure 4.5: The interferometer baseline

4.12

Before the antenna output voltages are added together at the input to thereceiver, the signal from one antenna is passed through a phase reversing sr,litch(see Figure 4.1) which inserts an extra half-wavelength of cable during alternatehalf cycles of the switching signal.

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The phase reversing switch uses a hybridin Figure 4.6. l.lhen the inrpedances from B and

phase of the output at C is reversed exactly.open circuit respectively, then there vrill be

74.

ring circuit (Smith,1961) as shown

D to ground are interchanged, theIf the impedances are a short and

no losses in the switch.

INPUT OUTPUT

Figure 4.6: The phase reversing switch

Germanium sr,ritching diodes are used to perfornt thc switching operation.Using an impedance transformation, the "011" properties of these diodes havebeen considerably inrproved (Aitchjson, 1962). A ctuarter-vrave transformer has

been used to achjeve this transfornration, so that the "0ll" state appears as an

open circuit, and the "0FF" state as a short circuit. The reactive componentpresent in the open cjrcuit case has been removed by the addition of a shortedstub. The switch layout is shovrn in Figure 4.7, and jts design is covered indetai'l in Appendix 3.

These switches provide an isolation of better than 20 dB rvhen shorted(diode 'rOFF'r) and cause an insertion loss of less than 1 dB when open (diode

"0N" ) .

4.13 The 200 l4Hz Rad'iometer

The recefver is based on a unit previously used in a 42 MHz instrument. A

200 MHz R.F. ampfifier and a 20G'42 l4Hz conversion stage have been added. ThisR.F. anrplifier uses a similar circuit to the antenna preamplifiers, and a dualgate metal oxide field-effect transistor is useci as the converter. The basic42 llHz system also uses metal oxide field-effect transistors in its highfrequency section, the 10.7 l'|Hz I.F. section uses integrated circuit cascode

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75.

O.226,\ SHORTED75N STUB

75N COAXIAL CABLE ARMSOF HYBRID RIN6

O.23 A LENGTH OF153N CABLE

lOOO pF DlsK FEED-THROUGH CAPACITORGERMAIIIUM

DIODE

SWITCHINGSIGNAL

Figure 4.7; The diode switch confjguration

ampl ifiers (yarral I , 1968) .

The noise temperature of the receiver is about 1000ok, and the 3 dB band-width (including preamplifiers) is BOO rcHz.

The I.F. output is demodulated by a square law detector, so that the outputvoltage is proportional to the input pob,er, rnodu'lated by the switching signa'l .

4.14

The narrol-band selective amplifjer and synchronous detector r,lere alsodesigned for use in a 42 l4l-lz installation. The discrete component amplifier usesa twin-tee feedback network to obtain a 3 dB bandwidth of 12 Hz centred an 423 Hz.At the nearest harmonic of the nains supp'ly frequency (4oo Hz) tfre gain is downby 12 dB. The phase-sensitive detector is linear over a range of t400 mv output,and its operation is essentia'l1y unaffected by the presence of noise on the modu-lated waveform (Lim, i968).

A simple RC filter with a switched time constant of either 10, 20 or 30seconds (T = RC = 1/4 Bp) is used to remove h'igh frequency noise from the output.A high-input-impedance unity-gain amplifier follor^rs this filter to preventloading by the analogue recorder. The output impeclance of this amplifier is-200 o (Yarra'tl , 1968) .

4.15 The Pqrformance of the 200 liHz Interferometer

Figure 4.8 shovrs the analogue strip chart record of a drift scan through

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76.

the Crab Nebuld, o = 05:31:30, 6 = +Z1o 58, (Kraus, 1966). For this observationthe antennas were pointed 580 north of the zenith 1o-+zto1 and the filter tjmeconstant was 20 seconds. The transit occurred at approxinrately 11.00 pm localtime, when terrestrial interference is relatively 'low. Short spikes of inter-ference can be seen qu'ite clear]y on the record. The 3C list of radio sourcesgives the flux density of the Crab llebula as 1420 x 10-26g/nf lHz at 178 l4Hz(Kraus, 1966). Taking the maximum peak-to-peak def'lection of the fringes torepresent 3000 x I0-26!1/m2lllz, then the average peak-to-peak noise deflectionis approximately 1200 x I0'26i[,/nr2/Hz. Assuming the peak-to-peak deflection ofa noise waveform to be four tinres the r.m.s. amplitude, the r.ffi.s, noise fluctu-ation of the system appears to be of the order of 300 x 10-26v/nz/Hz.

I,t l, t I

;..| [, ; i'tl , ,l

IIIttt

| '. ) t

lro

-l

| , .'', * '

I\.rlr

Fjgure 4.8: The analogue chart record of a drift scan through thecrab l.lebula on the zOth Decenrber Lg7o. Antennas pointed to

6 = + 21o; filter t'inre constant Z0 seconds

The theoretical value of these fluctuations can be ca'lculated from

1'l It'{.:l

iII(rt-ot-

equati on?.40,

/^T\ - li\^'/min - Zfr

Tsys

'zEH.tf

For a source of flux density S W/nz/Hz, if the sourcewith the antenna beamrvidth, then the increment in antennaby (Kraus, 1966)

is small compared

temperature AT is given

ATAI

where Au 'is the effective aperture area ofmean in the case of an interferometer, and

(1.38 x 10-2t;/0f) . The nrinirnum detectable

the antenna, equal to the geometric

k is Boltzmann's constantfl ux densi ty wi 11 tlren be

Ae

2kr (+.t1

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From equation 2.31 the system noise tern;leratureferometer is

77.

(4.21

for a phase-slitched inter-

(as )mi n = . Tryt

/Blr,.TL

k.nAe./2

trrs = TR*>n(TA+Tg)

where Tp is the receiver noise temperature and T4 and Tg are the antenna tempera-tures due to the sky background radiation. At 200 l4Hz the effective sky back-ground temperature is approxinrately 10000K (Shklovsky, 1960). The receivernoise temnerature for the present confjguration is about 7,5000K, most of thisbeing caused by the losses in tlre transm'ission lines. l^Jith a high frequencybandwidth of 800 KHz and an effective integrat'ion period of 40 seconds (nc=Zos)the calculated minintunt detectable temperature increment is 1.4lo1. For theshort-backfjre antenna arrays, A.-14m2, s0 that the r.m.s. fluctuations at theoutput are equivalent to a source of flux density 290 x l0-26!,/nz/Hz.

4. 16

Future improvements to the present interferometer system can be dividedinto two groups: (1) thcse improvernents a lready be'ing worked on, ancl (Z)improvements planned over a long period, of a much more indefinite nature.

At present nevr preanrplifiers and a nev,r receiver are being developed. Theseshould be in operation within the next six nionths. Preliminary tests on apreamplifier circuit (Bryant, 1971) indicate a gain of 29 dB and a bandwjdthof 1l'1H2, with a noise temperature of about 1000oK. This should reduce theminimum detectable temperature to .Z7ay,, i.e., a minimum detectable fluxdensity of 53 x i0-2tw/^r/Hr.

One of the major limitations of the present system is the site. In additionto a very higrh terrestrial noise level, it has the disadvantage that thebaseline of the interferometer cannot be extended beyond its present length.It is possible that at some future clate the telescope may be shifted to amore suitable site. If this is done then both the baseline and the antennaarea wi I I be extended.

0n the present s'ite, no major a'lterations to the present configurat'ion,other than the scheduled rece'iver improvement mentioned in (i) are at the momentp1 anned.

1.

2.

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78.

4.1"7 The Possi bl e Observation of pul sars

Up ti'11 the present time at the University of Auckland, attention has beenprinari'ly directed tovrards measurements of nelative flux densities and positionsof radio stars, and general observations of the sun. Nith the discovery of pu1-sars in 1967 (Smith and Hervish, 1968) a possible new sphere of interest was

created. This netJ class of radio source is characterized by the radiation ofshort pulses of energy at precise intervals, typically of the order of one second.Since thejr discovery they have been intensively studied at many differentfrequencies and at many different observatories. To date, more than fiftysources of this type have been located. Hewish (1SZO; presents a summary of thepresent knowledge of pulsars.

The average flux density of these sources is typica'lly of the order of1g'zorrtr1^z/Hz, and the peak pulse flux, subject to great variation, is usualiyof the order of 20 x 10-2'\rl/n2/flz (Booker and Runrsey, 1969; Ginzburg et a1 ,1969). To observe the individual pulses, very short time constants (-10 ms)

must be used on the low-pass filter of a telescope. This requirement reducesthe sensitivity of observations to such an extent as to put pulsar receptionout of the range of all but the largest radio telescopes. However the detecta-bility of the signals can be enhanced by making use of the accurate repetitionperiod of the pulses, and averaging over a number of periods. If for instancea twenty milli-second time constant was used, averaging 1000 pulses wou'ld bringthe sensitivity of the observations to the same level as for a single observationwith a twenty second time constant. I'Jith a one second repetition period thjsvtould imply averaqing over a period of seventeen minutes. Such averaging can beperformed by an on-line general purpose digital computer (Booker and Rumsey,

1969), or by a specially designed signal averager (Deardorff and Trimble,1968).The period of time over whjch averaging can be satisfactorily performed islimited by variations in intensity of the pulses. For reliable observationsthis period should not be longer than a few mjnutes (Booker and Rumsey, 1969).

When the present telescope has been extended to its maximum perfornrancewithin the present site limitations, it is proposed to evaluate the feasibilityof pulsar study in light of the sensitivity of the instrument. If such a projectseems 1ike1y to produce useful results, special purpose pulsar signal averagingequipment will be developed. This possibility'is to be borne in mind in thespecification of a general data processing system which fol'lorvs.

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79.

4.2 The Function of a Data processinfl System

Data processing in any field is concerned with the collection of data, theconditioning of this data, and the ana'lysis of the data to extract the requiredinformation (Preves, 1964; Clark, i970). The collection of data usual'ly involvesthe conversion of physical quantitjes into electrical analogues. Because theprocessing of large amounts of data js often best performed digitally, it isthe function of the conditioning section to convert these analogues into digitalform, and store the data ready for the final stage, that of analysis. If thedata has a coordinate (e.g., time) r,rhich is fundanrental to the analysis, thenthis coordinate must either by stored and identified with a set of data, orinplied by the storage location of the data.

The essential functions of a dig'ital data processing system can be sp]itinto four sections (Figure 4.9):

1. The interpretation of the physical phenomenon by electrical analogues.

3.

4,

2.

The processing of the stored data to interpret the results.

The conversion

conversion) and

The storage of

of these analogues jnto numbers (ana'logue-to-digitalthe establishment of any coordinates.

this data (and coordinates).

DATA ACQUISITION DATA ANALYSTS

/--.^-,

\'TRANSDUCE RS

DATA

DIGITIZER

DIGITALDATA

PROCESSER(COM PUTER)

EXPERIME N TAL

RES U LTS

Figure 4.9: Elements of a digital data processing system

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80.

The ntanner in which the digital data is to be stored will be influenced bythe type of processing to be performed. If this processing is complex and notroutine in nature, the ntost efficient processing will often be achieved by ageneral purpose digital computer. In rnny cases the rate at which the data isacquired will be well below the capacity of a digital conrputer and it is oftenadvantageous to store the data off-line - that is to store the data on sometemporary storage mediunr (punched ca'icls, punched tape, or magnetic tape) whichcan'later be processed by the computer in much less time than the duration ofthe experiment.

4.3 The specific Requirements of_ the 200 MHz Interferonreter

In a recent review of astronomical information processing systems (Clark,1970) it was stated that the essential prob'lem is merely decjding what is required,and then producing a system to meet these requirements. From the general digitaldata processing systent described in section 4.2, and the details of the 200 MHz

interferometer given in section 4.1., this sectjon will establish the basicrequirements of the system.

4.31 The InterPretation of the Physjcal Phenomenon by Electrical Analogues

The function of data collection is performed by the ex'isting antenna/receiversystem. The physical quantity of interest'is the power in the incident electricfield from a particular direction of the sky at a particular frequency. It hasbeen establishec,l in the preceding chapters that the output voltage of a radiotelescope is proportional to this quantity.

4.32 The conversion of the Electrical Analogues to Digjtal Form

The conversion of electrical analogues to digital form implies both ampfi-tude and time quantization. This process is performed by an analogue-to-digitalconverter. In an electrical-numerical system numbens are usually represented inbinary form. Each binary digit can represent either one of two states, and thetotal number of states which nray be represented by the conrbination of N binarydigits is then 2N. An analogue quantity nrust be amplitude quantized in order tobe represented by this finite number of states. Because of the fjnite timerequired to store these digits, and a finite storage area, the analogue quantitymust also be tinre quantized or discrete'ly sampled.

The interferometer output must be sampled at a sufficiently high rate topreserve ai1 frequency components present, and the resolution of the amplitude

Page 88: 2-Whole-digital Data Processing in Radio Astronomy

quantization must be sufficient to resolvenoise level to saturation. This asnect ofdetail in Chapter 5.

the entjre range ofthe specification is

81.

the signal, fronr

discussed in

The number of binary digits to be stored into both the number of digits per samp'le, and theHence the data storage rate will be dependent on

any interval will be proportjonalnumber of samples per second.

the quantizer specification.

4.33 The Establishment of Coordinates

It is necessary to relate time to samples of the interferometer output inorder to calculate the positions of radio sources, and also to average collateralsamples*. 0bservations of the sun are almost repetitive with a period of ?4

solar hoursl for these observations the coordinate required is solar or universaltime. Observations of stars are repetitive with a period of ?4 sidereal hoursand thtts for these observations the coordinate requirer, is sidereal time. itwould be possible here also to record solar time as a coordinate, and to calculatethe cornesponding sidereal time during the subsequent analysis. However samp'les

taken on successive days would not necessarily be at the same sidereal time, and

interpolation would be necessary before the observations could be averaged. Itis then preferable, for observations of stars (other than the sun) to recordsidereal time as the coordinate and also to ensure thai; samp'les taken on succes-sive days correspond to the same sidereal time (i.e., are collateral). Forobservations of the sun, solar time should be recorded as the coordinate and

samples taken on successive days should correspond to the same solar time.

If the storage of successive samples of the interferometer output issequentia'l (as opposed tc randonr) and the sample inter',,a] is fixed, then it isnecessary to record the tjme coordinate only once during any one scan as theposition in time of any sampie relative to this will be implied by its storagelocation. In order to avoid the loss of large amounts of data if an error shouldoccur in the system, the data can be stored jn blocks of a suitable lengtho theends of block of data being marked by records of the time coordinate. The choiceof block length r^ri'11 be based on a consideration of the permissible data wastage,the rate of occurrence of errors of this kind.**

* The terms collateral and sequential are appfied to the interferometer sampled

data as follows: sequential samples are successive sarnples of the output,forming a continuous record; collateral samples are samples corresponding io thesame point in the sky, taken on different days.

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B?..

This requirement may vary from one experiment to another. For a singleobservation of a source any data lost vrill be irreplaceab'le, and the blocklength should be small. For a series of observations which are to be averaged,data lost in one observation can be replaced by the averaged data from theremaining observations, and so the block length may be longer.

4.34 Storage of the Digjtal Data

The process'ing to be performed on the interferometer data may vary from thecomplex manipulations of aperture synthesis to the sinrple arithnretic of averaginga set of numbers. Processing of such a qeneral nature is best performed by a

digital computer. As the processing will norma'l1y involve combining observationsfrom several days, the data should be stored off-line onto some temporary storagemedium to be later read into the computer for analysis. The choice of a storagemedium wjll be governed by the input facilities of the available digital cornputer.

The University of Auckland computing systern is based on an IBM 1130 computen

equipped vrith a high speed card reader/punch, a high speed line printer, and a

low speed paper tape reader. The 1131 central processing unit uses a 16-bitword, and has a 16,000 word storage capacity w'ith a 3.6 micro-second cycle time.An additional 106 words o'F storage are available on tlo random access magnet'icdisks connected on-line. Each disk contains approxinrai;eiy 500,000 words ofstorage with an average access time of 30 rnicro-seconds. The 1403 line printerwill print up to 600 ljnes/minute; each line contains up to 120 alphanumericcharacters. The 1442 card reader/punch will read up to 300 cards/minute orpunch up to B0 card columns/second; the 1134 paper tape reader will read up to60 tape characters/second (IBt'1, i96g).

The high cost of a card punch, coupled with the fact that its high speed

capabilities would not be fully utilized by this project, rules out the use ofpunched cards as a temporary storage nredium, leaving punched paper tape as theonly possibiiity. Paper tape has the advantage of being the cheapest of themachine readible media to implement, and the djsadvantages of the'lovr speed,noise and unreliability inherent in mechanical dev'ices (Clark, 1970). lloweverthe relatively lorv data rate of this project is vrel'l within the range ofinexpensive paper tape equipment, making its choice as a temporary storagemedium desirable as well as inevitable.

** These may be caused by electrical interference, for instance.

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83.

The 1134 paper tape reader is designed to handle standard one inch wide,eight channel paper tape. Data fronr the tape can be read direcily into corestorage without code conversion as an image of the holes in the tape (.i.e., a

hole is read as a binary 1, no hole as a binary 0) by assembler subroutineq ortapes punched in PTTC/8 format can be decoded by stanclard Fortran subroutines.The PTTC/B code uses one entire tape character to represent a single a'lpha-numeric character. Because only data is to be stored on the tape (no commentsor statements) a direct binary representation wil'l be more economical of tape,hardware and reader time. The slor,r reading speed of the 1134 combined with thecycle-steafing concept of the 1130 (IBl1,1968) makes complex non-standard high-density data formats preferable to standard low-density formatsn because decodinqcan be performed during the read.ing operation.

Although the Unjversity is at presentnew conputer, a system based on paper tapeother paper tape punches are in use in thedata for analysis by the present computer,equipped vrith paper tape peripherals.

negotiating for the purchase of a

w'ill not become obsolete as sevenal

University for recording experimental

and any future computer r'ri11 be

4.35 Anglsis of the Stored Data

As suggested in section 4.34, analysis will be carried out by the IBM 1130computing system. As details of the analysis rvill vary according to the investi-gation being carried out, it was the aim of the author's research to develop theprocess'ing system only to the point vrhere individual experiments would diverge.standard software is then required for the following procedures.

1. The transfer of data from the temporary storage medium (paper-tape) to thecomputer bu'll< storage (nragnetic d'isk) . The data should also be checked forerrors occurring in the acquisition portfon (hardware emors).

?. A digital filter to produce the nraximum filtering of the data rvithout dis-tortion. The philosophy behind this technique is discussed in Chapter 5.

3. The averaging of data from a number of observations.

4. The rejection, during this averaging, of data marred by excessive noise.(e.g., the spikes appearing on the record in Figure 4.8).

5. The output of the reduced data in a form directly comparable vrith theanaloque strip chart output of the telescope.

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84.

6. The transfer of the stored data from the magnetic disk (a senri-permanent

mediunr) onto punched cards, a ntore pennanent mediunr, enab'ling a more rapidstorage of the data if it should be subsequently required.

The data, once stored in the computer should be kept in a standard form,

and returned to this standard form after any other operations. A fully indexed

file system should be provided so that at any tinren details of the data stored,and its present stater can be readily obtained.

4.36 Internal Requirements of the System

As it is necessary that in aclcljtion to recording a tinte coordinate tosamples of the interferometer output, samples on successive scans should be

collateral, then the same time-keeping equipment which generates the coordinates

could also be used to generate the sample interval. In addition, this time-

keeping equipnrent could be used to initiate and terminate the acquisitionprocess at set tjnres durinq the day, rvhen sources of interest were in the antenna

beam.

4.37 General Considerations

The processing system specified in this chapter can be divided into two

basic functions - data acqujsition and data analysis. The acquisition or hard-

ware sectjon takes the output from the interferorneter, quantizes it, and records

it on paper tape together with time coordinates. The analysis or softlareportion of the system consists of a series of cornputer programs designed to

store the data from paper tape jnto the computer, reorganized this data into an

easily manageable form, and perform some pre'linlinary processing on the data

From the general data processing system of Figure 4.9, the specificationhas developed to the system shown in Figure 4.10. A genera'l description of the

data acquisition system is given in section 4.4 and the development of the

various elements in both the acquisition and analysis systems is covered in the

subsequent chapters. The data processing requirements of the existing telescope

are very modest, and an attempt has been made to keep foreseeable improvements

to the telescope wjthjn the capabil'ities of the system.

4.4 A General Descriptjon of the Data Acquis'it'ion System

The data acqu'isitionin this chapter is slrown

to meet the requirements specified

form jn F'igure 4.11. The principalsystem deve'loped

'in bl ock di agram

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85.

Existingten

Acquisition orllardwere Sgrsten

Analysis o.r

Software System

Fiqure 4.lQ: Thie interpretation of the data processing systemspeci fication.

ReceiverAnerlogueRee ord err

Analogue-to-Di.gita1,Converter

Progrannab)-Control

n''ormat

Co,ntrol

3ap:er Tape

torageAnelysi s

Digitax

eomputer

Chart-TypeOutput

Nurnericel.Reeu1ts

Page 93: 2-Whole-digital Data Processing in Radio Astronomy

86.

units of this system are a digital clock, an arialogue-to-digital converter, and

a paper tape punch.

A high stabil ity 5 l'lHz crysta'l oscil lator drives a digital clock vrhichsintultaneously produces both solar and sidereal times in b.c.d. format (hours,minutes, seconds, I/70 seconds). A six digit numerica'l display can be srvitchedto show either one of these times. Control circuitry, lvhich derivcs its timingwaveforms front the clock, produces sample instructions at a programmed interval.These cause the analogue-to-digital converter to sample the radjometer outputand transfer the resultant digital word into a buffer register ready to bepunched onto tlte paper tape. After a nreset number of samples, a block markinstruction is produced r^rhich causes the digital output of one of the clocks(either the solar or the sidereal) to ne transferred into a buffer registerready to be punched.

I'lhen any data is transferred into the buffer register, it is divided up

into five-b'it bytes whjch are punched, together vrith two identification bitsand a parity bit as one eight-bit word on the paper tape. A digital mult'iplexercontrols the grouping of t.hese bytes rrrhich are punched in a preferred sequence,and only those words in the buffer into which data has been entered are punched.

SYSTEMPROGRAM

CON T ROL

C I RCUI TRY

BUFFER

R EGI STE R

5 MHz

OSCI LLATOR

DIG ITAL

C LOCK

DIGITALMULTIPLEXER

DISPLAYPAPER TAPE

P UNCH

Figure 4.11: simplified block diagram of the data acquisition system

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87.

The design and development of the three principa'l units, and theirassociated systems, are described in the following chapters. A'lthough thedigital clock forms the heart of the systern, controlling the entire acquisit'ionprocess, the analogue-to-digital converter provides the vital link between thetelescope and the computer and its specificatjon must be carefully considered.The sampling rate and dynamic range requirernents of this unit are deterrninedby the frequency spectrum of the interferometer output. Before the design ofthe analogue-to-digital converter is descnibed in Chapter 6, a detailed dis-cussion of the effects of filtering and sampiing on the interferometer outputis given in Chapter 5.

REFERENCES

AITCHISON, R.E. (1962): "The Use of High-Speed Silicon Computer Diodes forR.F. Switching". Trans. I.E. Aust., El{4 pp.7-10.

BOOKER, H.G., and RUI'1SEY, V.l-1. (i969): "Radiot{ave Diagnostic Studies of theEarth 's Pl asrna Envi ronment" . Uni vers i ty of Cal i forni a , San Di ego ,

Prooosal Subnri tted to the lla ti onal Sc'ience Foundati on,

BRYANT' P. (tgZt): Fl.E. Thes'is, University of Auckland. (to ne pub'lished).

OLARK, B.G. (rgZO):

Astronomy"

DEARDORFF, J.8., and

Averagi ng "

EHRENSPECK, ll.rr,. (1969): ,' 'Backf ire' - Antennen,'

Zeitschrift, 22 pp. 286-292.

"Information Processing Systems in Radjo Astronomy and

Ann. Rev. Astron. Ap. , 8 pp. 115-137 .

TRIMBLE, C.R. (1968): "Cal ibrated Real-Time Signal. Hewlett-Packard J., 19, l'lo. B, pp. 8-13.

Nachri chtentechni sche-

GINZBURG, V.L.,7HELEZNYAKOV, V.V., and ZAITSEV, V.V. (1969): "Coherentl4echanisms of Radio Emission and Magnetic l4odels of Pulsars". Ap.

Space Sci., 4 pp. 464-504.

HEWISII, A. (1970): "Pulsars". Ann. Rev. Astron. Ap., B pp. 265-296.

IBM, (1968): "IBM 1130 Functional Characteristjcs". IBM Systems Reference

Library, Form A26-5831-4.

KRAUS, J.D. (1966) : "Radio Astronomy". (l,lcGrarv-Hill, New York).

Page 95: 2-Whole-digital Data Processing in Radio Astronomy

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Llllvf ' .r.C. (1968): "N'on-U6ifonmly Spaced A1 rays of Dirrectiorral Elernents,r.Fh.D. Thesis, Univers;ity of Auel,,la.n,d.

McLAUGFILIN, J"C. (196?): "A Data Digitizinrg and Pro:cessing System for a RadloTeleseopet'. M.Se . Thesis n O,hio State U:nlvefsity.

P0I'INALL' M:"J. (lOeo1: 'lA Data, Processing system for a Rotating lnterferumeter'il.M,. E. ThesJ s , Univ.ersity of Aue.kltand .

PREVES, D.A. (1964): "The Acqu'isition of Analogue Data in a Digital Format,..Unive-rsity of Illinois, R,R.L, publication 26,5.

SHKL0TVSKV, I.S. (1960) : "Gosmic Radjo wave,6". (l{arvard Univerrsity press n

Massactucetts).

SMITFI' F.G. (1961)' nR.F. Switching Cir"cuits and htybrid Ring Circuits Used inRadio Astronomy". P,Foc. I.E,E,, l0B pp. Z0I,-ZM.

sl{xrll, F.G,., and HE!'tIsH" A. (eds.), ([96B): ,,pulsating stars,,, (MacmillannLondo'n)

VA'RRALL' J.W. (leeel: "A 42 MHz Radiometer using Metal Oxide Fiel.d-Effect. Transistons and Integrated Circurits". M.E. Thesls, Un,fversity of

Auekl and.

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CHAPTER 5

Filtering And Sampling The Interferometer 0utput

The problem of specifying the capacity of a digitizer in terms of sampling

rate and avai'lable bits is re'lated to the dynanric range of the analogue signalto be converted, the noise in the analogue system, and the use to be made of the

digitized s'igna'l (l'4elton, 1967). In this chapter the requirements of a data

digitizer are established vrith reference to the spectrum and dynamic range ofthe interferometer output. The output spectrunr is dependent on the characteri-stics of the 1ow-pass post-detection filtern and having the data in digital form

opens the possibility of using a dig'ita1 filter, s0 relaxing the requirements ofthis analogue filter. For this reason, all tlrree functions, low-pass post-detection analogue fjltering, data digitizing, and post-sampling digital filter-ing, must be considened together.

5.1 The 0utput Spectrum of a Correlation Intenferometer

In Chapter f it was shor'rn that the output of a correlation interferometerfor a point source, as a function of source position 1,, was the product ofthree factors: (1) the antenna poh,er pattern lG([)l', (2) the fringe patternF(l) = cos(znn.p./l) and (3) the bandrvidth pattern B(L) which is usual ly suffi -ciently wider than lG(,Q,)lt to be ignored. If the signal output as a functionof L is denoted S(g), then

where D is the baseline length inpattern, I e(f.) l' ir conveniently

= |G(o)lr.F(s)

= lc( L)l'.cos(z"p) (s.1)

metres. For a single lobed antenna power

represented by a Gaussian function.

,L *2

lc(e)12 = u-r[;l

s( r)

If the half porver r,,idth

so that f,g = sinog * 0g, then

maximum n

of this pattern is Zeg radians,defining 0=0 as the djrection

(s.2)

and if 0g is srnall

of the pattern

"[tj = 1nZ

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90.

i, .€, , o = 9'B'

F/L'lnZ,/ 1l

ri ?0g,

value of o lnto equation 5.9.,Substituting this

where

and

of the source re,l at'tv;e to the

rewri'tten as

can b-e lvrri tten as

s(*1 = .+[*-rj

n[Ft:) 2

s(t) = .-4-[6-u 1 .coszfst'

which gives the output sf the interferometer as a function of t', an angle whiich

var"ie-s linearly with tr',me at a rate of Zn r.adian,S/day" Fon t' deftned inseconds 0f tfrne, then

(5.5)

nfr, l2le (s) ;z = *-4[e-s;

and thus equation 5.1

Fron equation 3 ,,7 , lo ean be relrated'parameters of the baseline,

f, = sind.si nd*cos6,,Gosd. cos(Tp-e)

where the source has p'ight asciensiion'o, declln,ation d, andthe interferometeropole has de-clination d and lscal siderea;l time Tn. Fnom thr's eguation, when

(Tp-cr) * rll, then L varies app'rqximate'ly linear.ly wr:th time. For. a horieontalea:st-w€,st baseii re this dmpliers observations near the zerll'thn whi,oh is co,nsist-ent with the co'ndi'tion that 06 is small. From equatfon 5.3n

E + B(T+t)

* p.tr

F = eo-sd.cos,6 "

T = tand.tan6

t, = (Tp-o) -rl2 isi nterfe,roneter zenil th.

(s. zal

n.cosZnf,. (5.1a)

to the pos'ition s'f the source and the

(5,3)

(5.4)

the hour angle (in r"adians)

Equation 5,la can now be

Page 98: 2-Whole-digital Data Processing in Radio Astronomy

91.

6 - COsd ' 965't ?rB = -ilAOiAO-

radians/second

The fol'lowing limiting assumptisns appty t0 eq:u6tf,o,n 5.5.

f Jl'€!i]' -iznrt,3,(r)=j.atoe-J.e" dt,

16

- | - -j2nft,i,1r1= | .ouzokt' .. dt'

')'tr

(s.6)

1,, Trhe antenna power pattern Js narroq go that foF excu,rsions 0 about itscentfe, 0 I sino.

2. The,antenna power pattern is eentred ln the d'irection of'the baseline

zenl'th in order that (Tp-al * nlg.

if the sig;n:al output, (equation'5.5) ls to b€ low.pass filtered and sampled,

then it is:of interest to know,the frequ'eney spectnum of S(t). From equation,

5.5 this spectrum $(f) .uo be written as

fr-g.fg]' ^ I -j2nru,3(t) = I lr-alry cosznftt'1.. - .dt'.

JL A J

Let.

and,

then

e,(u) = e, tr)*$- 1,r} ,

where * rreBr^esents eonvolution (Bracewell, 19,65).

Now c. r' = g.-on[Tlu r-l t'' ts

t Becauise of the Fourier trransfor:m relationship between c(*)n the antenna vOltage

pattern, and g(x) th6 antenna aperture distributr"on, then Sr(f), t'he Fouri'er

transfst"m,of lG(gls is 1/B times the autocorrelation func,tion of the apet'ture

distrlbutJon, with f/6 substituted for x.

Page 99: 2-Whole-digital Data Processing in Radio Astronomy

and

i.o.,

i,rfl = *gCn-Tl - lnft-iqlt'

$(t) = FL.-u''F,'#,]'

This 'spectrurn is shown in Figure 5,!..

ISU,F-5.!: The output spectrum of a c'orrelation iriterferorneter

As a functio;n of source declination 6,, the product, cosd,cos,6 has a maximum;

value of cosd (0<cosdct) corresponding to a source at the,equator., and a minimum

value of 0, comesponding to a source at a pole. For any particular s,ourcedeclination" the outprrt sig;pa1 spectrum of a correlation intrerferorteter will be

gi:ven by eq,uation 5.7 and Figure S.1o whers B i.s dete,rfiined by,equation 5.6.Fot'9,=6 (a source at a po'tre) the spectrum r'rill he a delta function at f=0, f ,e.,the ourtpu:t fs c.onstant and thene are no f,.ringes. In the analysis g'iven in thischapter,, i't is,the highest, freque,ncies prre-sent in the signal output which are ofinterrest.or concern, For this reasen the cese of a sourrce at the equator (e=0;

and a t-rue east-west baseline (A=0) wilt be oonsidered. From equation 5,6,

F = "r-%.

= 7.28 x 10-5 radians/seeond.

For the 200 l{Hz interferom:eter, 206-160 and D=40},, giving

# = 2'6 x 1o-4 I'lz

,92.

*.-4"[t*'4']1 (s "r)

and ry E 29 .L x Lo'* Hz.

Page 100: 2-Whole-digital Data Processing in Radio Astronomy

93.

In addition to the signal spectrum of equation 5.7, the output of a cor-relation interferometer also contains a noise spectrum (equations 2.38 and 2,43)vrhich can be considered flat at frequenc'ies much less than Bp, where Bg is thebandlidth of the high frequency section.

5.2 Analogue Filtering Techniques

In Chapter Z it was shown that the sensitivity of a correlation interfero-meter is defined by (equation 2.46b)

K.Tsys(AT)mi n = ,/m

(5.8)K.Tsys

where (AT)min is the ntininium detectable increment in antenna tenrperature, K isa factor determined by the type of interferometer, BL is the noise bandwidthof the post-detection 1ol-pass fi'lter, and Bp1 is the noise bandvridth of thehigh frequency section. The minimum detectable signai is then proportional tothe square root of the noise bandwidth of the lovr-pass filter, and for maxinunr

sensitivity the bandwidth shou'ld be as narrow as possible without distortingthe signal. If the intenferonreter is to be used to observe sources at alldecl'inations, then from F'igure 5.1, for no signal distortion the pass-band

should extend fronr zero to DBn,u*/tr lrertz.

At these 1ow frequencies, realization of higrh-order circuit approximationsto the ideal filter (e.g., Butterworth or Chebyshev) is impracticable because

of the high LC products i'equired (Griffiths,1956). For this reason active RC

filters of one or more stages are nonna'liy used (Criftiths,1956; Yarrall,1968;Cooper' 1970) although other novel forms have been suggested (tluchinich, i969).

For f]at noise spectrums and monotonic sinusoidal signals, Griffiths (1956)

has computed the optimum cut-off frequency in terms of the sinusoid frequency,of a number of low-pass fjlters. The opt'inrum filter is one wh'ich produces themaximum improvement 'in signal-to-noise ratio. He has also calculated the lossin signal -to-noise ratio compared r^rith an ideal 1or'l-pass f ilter, under theseoptintunt conditions. Three consideratjons significant to radio astronomy have

been neglected in Griffiths' analys'is.

1. It is important that the post-detection filter should give a fast step-functio

Page 101: 2-Whole-digital Data Processing in Radio Astronomy

2.

3.

94.

response r'rjthout significant ovenshoot, to prjnimize the time required tocalibrate the system by the injection of a hnown noise signal into theinput (Cooper, 1970).

As the real-time output of an interferorneter contains valuable informationconcerning the positions of sources, significant non-linear phase lag inthe post-detection filter rvill gjve rise to dispersion as well as timeshift, destroying the information.

Because of the sntall signal-to-no'ise ratio at the output of a radio telescope,extraordinary disturbances often cause large deflections of the output.The recovery time from such transient d'isturbances is obviously a significantfactor in the choice of a lou/-pass filter. Disturbances of a long durationwill be covered by the step-function response criterion (1). Short termdisturbances however, will cause deflections corresponding to the impulseresponse of the network.

Table 5.1 oresents a summary of the properties of several "optimised" low-pass fflters. The ideal lovl-pass filter and ideal integrator have been includedfor purposes of comparison. The "optiniised" filter is that filter giving themaximum signal-to-noise improvenrent for an input sinusoid at frequency f5 pluswhite noise. The input signal-to-noise ratio is such that the output signai-to-noise ratio for the opt'imised ideal lor,r pass filter is one. Al'l propertiesof the optim'ised filters are given in terms of the sinusoid frequencV fs. Thederivation of this table follotrs fronr Griffiths' (tgSO) and is given in Appendix5.

The duration of the impulse response is taken as the interval during whichthe magnitude of the response for the normaljzed transfer function exceeds 0.01.Because of the non-linear relationship betleen this duration and the filterparameters, the 0.01 level impulse response duration is plotted in Figure 5.2as a function of fs for the optinrjsed filters.

In considering the optirnum signal-to-noise ratio given in Table 5.1 relativeto that for the ideal 1ow-pass fj'lter, it nrust be remembered that the outputvoltage of a multiplying interferometer is proportional to the input power atthe antennas. Thus a loss in signai-to-noise ratio of l,l dB at the outputrepresents an increase in (ar)rin (equation 5.8) of onlv (il7r) og.

Page 102: 2-Whole-digital Data Processing in Radio Astronomy

95.

U)

Ooa,/1UJ

LTJ(nJ=o-=H

Eo+-.'roLE

tt\cn\()

tnq-

r\cf)

Refer to Fiqure 5.2

a)luftd-or(u3->

a(Fc!

UIq-F\C\I

t^q-

(\j

r.o

th t^ tnFq-q-c\, c! r\t/|NcoN(F

sf sf (r, cr)

lnAtF q-CO c\l\o \o(o(Y)

LrJ(nz.

v)Lrlc.o-tllFa

t+)LO(Ur)>-<-)tn

ES.Cl

a(uCoz.

c)coz.

(l,c,oobeba=, Z. r{ rf)

(Ugoz.

c)v\Fa,,

'-Eiq.Pf)t)

tnq-

lr,rt\^o

th(F

t-.CE

v,q-

.-{COf-.

alnul.n q- q- q-q- \- \. -\f\ C\t Nlr-{ C\l tft COr.o r\ + cf)

tta(F q-\.\|.r) rr)coto \0

F

. ut,z,+FF

Ef]EO

cc:oOc!

co

Oct

co ao of ocrO -g 1J -O

ro o) or (\tC\l (\.l Fl r-{

co coE'O(Y) GJ

(\,t c!

JtlJ6LIV'*cr-

oJJq-F

C!

o+tq-tr

C\,I

tht{-q-

I

,d{J

^ l..rc{^q-l o\\l lts9- I *-.v ltF|.-n lv = = =c\rll

lr{I

'o+J

oq-tF

I crd+J

z,

U)

Fc,

co! O

(orf)(Y)

I

l'*-Ot

=fI

Of\(C)tr)Ost(f)@+sfcDC!tttl

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co cf)ll

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qfr-lcf)

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@ (f,tf) F\<r =t

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OL)

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tl

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tnLl-

F\fr)

tl

F

tn(F

tl

otF

t^ .flr.t- l.l- a aCV F{ tf- q-ca c\,1 (.o Fl\ \aa

C\l r{ r{Ilttitlooooq-+Frts

aq-

Hq-ll tcE=vr(f)f\l |F\co<frIlloooq-q-tF

q-

LrJLL6ul

=.<HF(-)

U.

o(tsrot+ +)tFt(\ .r?Ol(ts Ct+x(F

=

o+)q-(\,'-)

I IFI(FltrlF'-1trol

L)f-trlo(\,lltr \\l\t F{

-rl(Fl.- lll'-)l+ol?-a t+-

lot

ol+-

+-

otF===

(F

\t'r?C\t+r-{

l=l- L)l^ &,totrl(Fc!Fll \-

l+- Fll-I '.? lll+lr-lolsrF

Et!, l{Fo-J>-HFLL

otr.'lrO

-l.g=GJo-cJ

Lo+JfdL

rcJro9qJc-OH

(J

cJ

oLN

rr)ro (v.ccr\H

niltlLN L' LN

L(U

LoI.IJ

CFtoc)(J rlqJ caV) LII

ot() Ft

vlEOG)'c+) +)ruu

- G,l

O tJl@

H(JN,

z,

vlr-0,+)

(F

thtn(ooI

=o

E(uah

FPooo)Eoaq-oaq)

+)l.(Uqot-o(u

F

-rou-octF

Page 103: 2-Whole-digital Data Processing in Radio Astronomy

96.

Ideal Loir-Pass FiIterIdeal IntegratorSimple RC Filter

-+--+ r. = 0.7 I second) 0rder

-r-{-i = 1.0 J Filters

il cascaded RC sections as forsecond order fi lter with ; = 1.0.Second order filter with c = 1.5as for simple RC filter,

\

10

v,oz(JUt

zoFEJot!6zovlUE

u3q

3:

0.20.001 !.UJ

sIGI.iA:- FRiCUENCY

0. I 0.3uFoT? |

some optimum fj I ters.

(t'5 '

ofFigure 5.2: The .01 impulse response duration

Page 104: 2-Whole-digital Data Processing in Radio Astronomy

97.

Table 5.1 shows that the optimurn ideal 1ol-pass filter produces the best

improvement in signal-to-noise ratio for an input sinusoid plus white no'ise.

The idea'l lor^r-pass filter is however, physica'l1y unreal'izable even in digital

form, as its impulse function exists for an infinite t'inre. 0f the real filtersljsted, the underdamped second-order filters give the nrost improvement in

signal-to-noise ratio. The N cascaded isolated RC filters come only to within

3 dB of the ideal response for large values of I'l (Griffiths, 1956) and other

high-order f ilters show on'ly a sf iglrt improvement for added complexity (Cooper,

1ei0).

The ideal integrator, which can be physica'l1y realized (Tavares, 1966)'

gives the fastest step-function response tvitlt no overshoot for a given ft. l'lo

analogue filter, of any order, can procluce a better response (Cooper, 1970)'

If I% overshoot can be tolerated, then a secorrd-order filter with 6=9.825 has

a rjse-time only L2% longer than that of the ideal integrator. On'ly a slight

improvement in this rise-tjme can be achjeved by higher-order filters (Cooper'

1970). If 5% overshoot can be tolerated in the step response' then the second-

order filter with 6=0.7 produces a rise-time only 3% longer than that of the

i deal 'i ntegrator .

For a given s'igna1 frequency f5, the ideal iow-pass f ilter gives the

smallest peak cleflection for an inrpulse input, but it can be seen frorn F'igure

5.2 that for signal frequencies greater than 0.005 Hz, most of the other

fjlters produce a deflection rvhich lasts for a shorter period than the ideal

low-pass filter. 0f the realizable filterso the ideal integrator gives the

smal'lest impulse deflect'ion, and apart from filters designed for signa'l

frequencies irr the range 0.0037 to 0.18 Hz, the duration of this response is

less than that of any of the other filters.

Table 5.1 has been clerived by considering a signal of a single fixed

frequency. l,lhen transmitting the Gaussian spectrums encountered jn interfero-

metry the amount of distortion introduced by the filters must be consjdered,

because as previous'ly mentioned, the tinre varjation of the signa'l conta jns

valuable information. Al'l of the RC filters exhibit a non-linear phase delay'

and at the s'igna1 frequency fs this delay is qu'ite significant (n7O for the

simp'le RC filter, greater for the others). As r're'I1 as producing distort'ion of

the Gaussian spectrum for any particular value of B, if the interferometer is

to be used to observe sources at different declinations, then the average time

sh.ift of the s'igna'l w'i11 vary fronr declination to declination. As far as

analogue filters are concerned, such heavy filtering as implied by the optiirum

Page 105: 2-Whole-digital Data Processing in Radio Astronomy

98.

filter is not of great practical interest, because of the severe distortionproduced by the dispersion of the filter (Cooper, 1970). Recovery time fromtransients is also long for these filters. Even the ideal integrator whichhas a linear phase response produces d.istortion because of its non-linear amp'li-tude response. Generally, where optirnum signal-to-nojse ratio is requ'irecl itis preferable to use a moderate amount of analogue filtering and to follow thiswith some form of digital filtering (Cooper, 1970), by rvhich near optimum

signal-to-noise ratio can be ach'ieved r.rithout undue distortion of the sionalspectrum.

Tavares (1966) has computed the l'imitjng filter parameters of a number offilters for a maxitnum distortion of 7% of signals in the range G'f, hertz. For

three of the filters discussed, these parameters are sholn in Table 5.2,together with the corresponding noise bandwidths in terms of f' and the lossin signal-to-no'ise rat'io compared wjth the ideal 1oi.r-pass filter. The stepresponse and impulse response of these "I% distortion" filters is also given.Distortion is here defined as the r.m.s. difference betleen the input and outputof the fjlters, with suitable delay and normalizat'ion to minimize this distortion,when the input is a flat spectrum extending from 0 to f, hertz.

It can be seen fronr this table that forthe signal-to-noise improvement of an ideala simple RC filter, but not as good as thatThe ideal integrator g'ives the fastest stepimpulse response, but tlrese are not a greatsimple RC filter.

a maximum of I% r.m.s. distortionintegrator is greater than that ofproduccd by h'igher order filters.response and the least significantimprovenent on those produced by the

5.3 Sampling and Frequency Al jasing

A fundamental property of the sarnpling operatjon is that of "frequencyfolding" or "aliasing" (Martin, i959). The effect of sampling a s'igna1 at a

rate f6 is to produce jn the frequency domain an infjnite number of images ofthe orjginal spectrum centred on inteqer multiples of the sampling frequency(Bracervell, 1965; l,lartin 1959) . If the sanrpling frequency is less than twicethe hjghest frequency present in the signal spectrurn then some of the firstharntonjc spectrum will fold back into the origina'l spectrurn, causing aiiasingof siqnal components symmetrically d'isposed about f6/2. This leads to thewell knotvn sampling theorem (Bennett, 1948) that'it is necessary to sample a

signal at trvice the rate of the highest frequency present in the signal in orderto be able to fu'l'ly recover the s'ignal .

l,lhen sampling a signal in the presence of noise, if prefiltering has been

Page 106: 2-Whole-digital Data Processing in Radio Astronomy

99.

t49(us.Ga+,.cLlagAt .F!LCDag()nt cl_.FE-sEF6

q.€N

4Lo'

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o^gtl.g +, +,\o. !rgr=.Ei-l aF*i t-(l,+fvi, +, th4, F (!t

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Page 107: 2-Whole-digital Data Processing in Radio Astronomy

100.

kept light in ot"der that the fu'|1 amplitude of the signal ls retaiRed, then evenif the signal-plus-no,ise is sampled at twice the h'ighest frequency i'n the:signalspectrumn the first hannsnic nois,e speetrum will quite Tikely overlap the origin,alsigna.l sFeetrum. This "reflected{ noige cannot be removed, even by subsequentdig'ital filtering if the f'ull signal gpectrum is to be pre,ser,ved. This is il,lus-trated in Figure 5.3

It'T-lI/

.------/-,--=*._/::'

j' -

Figu;r'e 5.3: The, eff,ect of sanipli'ng on a sigmal-p1us-no,lse(a) Input data befone s,anrpling(b) Data sampled at, a frequeneJ fd, shouihg

inrage speetrums

(c1 Transfer functisn o,f digital filter fonnnaximum signal -to-noise improvement

(d) Sample<tr data after fr'ltering uith theoptimurn filter shoryn in (c),

If sampling is to int'roduec no add,itfsnal noise, then signal-plus-no'ise

wU)

Page 108: 2-Whole-digital Data Processing in Radio Astronomy

101.

must be sampled at a sufficiently high frequency to ensure that no noise in thefirst harnonjc spectrum is folded back inside the transfer function of the sub-sequent digital filter. If no post-sampling filter is to be used then it isnecessary to sample at trvice the frequency of the highest significant componentof either the signal or the noise spectrum to ensure that sanrpling introduces no

additional noise.

The shape of the noise spectrum of the input data (Figure 5.3a) is deter-mined by the transfer function of the presampling filter, and jf the input noiseto this filter is white, then the shape of its output noise spectrurn rvil1 be thesame shape as its transfer function.

At this point it should be noted that jt is preferable to sample the signa'lwaveform as slowly as possible wjthout deterjoration, in order that (1) thedata recording speed is l<ept to a min.imum, making the most economical use of thestorage medium and perhaps reducing the cost of the recording equipment, and(Z) reducing the computer storage requirements and processing time for a givenarea of sky.

It L% nofse reflected into the signal spectrum is permissiblen then thenecessary sampling frequency f6 can be computed rvhen the filters discussed insection 5.2 are used as presampling filters. The right hancl colunrn in Table 5.2gives the frequency at which lH(t)lt = 0.01. If the input noise spectrum isflat, then this frequency fx is frequency at r^rhich the noise polver is i% of itslow frequency pob,er. Assuming that an ideal transfer functjon can be achievedin the post-samp'ling digital filter, then the only concern is for" noisereflected inside the original signal spectrum. For I% reflected noise therequired minimum sampling frequency is

f6=fr+ft

For a simple RC filter, designed for l% maximum signai distortion, therequired sampling rate is 47fr, wh'ich corresponds to 1.6 samples per filter timeconstant. The ideal integrator requires a sarnpling rate of f6 = 20fs or 2.4samples peLintegration period. ilowever by careful adjustment of the sampi ingfrequency to fa = i the portion of the harnron'ic spectrums reflected into the1ow frequency signa'l spectrun correspond to nulls in the filter transferfuncti on (see F'igure 5 .4) .

For J = 'tt75/fs, the filter giving I% distortion, the required sampling

Page 109: 2-Whole-digital Data Processing in Radio Astronomy

102.

frequency is B.5fy and the reflected noise from the first harnronic spectrum isonly 1.3?i at the edge of the signal spectrum. This is essentially the functjonperformed by the integrating digita] volt-meter, rvhich integrates the inputsignal over the sarnpling interv,rl. Although this type of digitizer leads to a

very efficient systenr (Cooper,1970), as noise reflectecl into the signalspectrum increases rapidly with frequency (o fu near f=0) the realization ofthe'low noise requirement is very dependent on the transfer function of thepost-samp1 i ng fi I ter (Tavares , 1966) .

w(f )

Figure 5.4: The first irnage spectrum when the outputof an ideal integratoris sanrpl ed at one sampl e per i ntegrat'ion period

Considerable reduction in required sampling frequency can also be achievedby using a second-order presampling filter, for vrhiclr the minimum sanlplingfrequency is only 13ft for I% reflected noise from the first harmonic spectrum.This is less than 1/3 of the sampling frequency requ'ired nith a simple RC filter.llowever, as with the ideal inteqrator, the reflec'ued noise increases rapidlywith frequency and this low noise condition is dependent on the post-samplingfilter, Usual'ly, because of non icleal post-sanrpling filters, a sampling frequencyh'igher than f s wi'l 1 be requ i red .

1.,

\\\\\

\\\\

5.4 Digital Filtering Techniques

Consider a function y(t) sampled at a frequency fdGT/1^). If the firstsample is taken at time t, then the value of the kth sanrple !p will be

Yg=Ylt,+(k-i)T61

yk=y(te+k.T6)0r (s .e)

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where

to as

k isa set

103.

an integer and to = t, - Td. The samples y(to + kTd) rvill be referredof sampled data.

A digital or nunrerical filter is one r^lhich actsto produce an output Jo(t) where (tlartin, 1959)

on a set of sampled data yk

Yo(to+pt6) = i Br .y(to+k .16 )k=--

t\ltr2yo(to) = ,.1., Bk.y(ts+k.T6)

K=l\ r

(5.10)

Usually p is an integer, so that the output replaces a sampled value for a

particular to, and Bp is non zero only for a fjnite range of k. Redefining theorigin for k, equation 5.10 can be revrrjtten as

Thus the filter consists of a set of (ttr-llr+l) wejghts Bp, .... BNz, andthe output is a r.reighted average of (ilr-Nr+1) sampled data values. Noting thatthe action of filtering vievred in the tirne dornain consists of convo'lving thefilter impu'lse response with the input data, 'it can be seen that the weights Bg

correspond to ordjnates of the impulse response of the filter. As a zero phase

shift fjlter has an irnpuise response symmetrical about t=0, zero or n radiansphase shift at all frequencjes can be achieved in a dig'ita1 filter by nnkingBk=B-k (l4artin, 1959), i.e., by making the weighing symmetrical about te.l,lriting -N,=Nr=ll, equation 5.10a for a zero phase shift firter is

N

16(to) = I Br.y(to+k.T,1)k=-ll

vthere B_k = Bk.

If the desjred filter transfer function l-l(f) is knovln, then the weightsBp can be ca]culated from tlre filter impu'lse response h(t),

Bk = Td.h(kTa)

(s.toa)

(5.10b)

(5.11)

the samp'le

the convol ution

where the 'impulse response ordinate h(kra) has been multiplied byinterval T6 in order that the sumrration of equation 5.1.0 replacesintegral.

Ideally, any filter transfer function can he procluced by a digital filter.From the theory of matched filters (Turin, 1960), optimum signa'l-to-noise ratio

Page 111: 2-Whole-digital Data Processing in Radio Astronomy

104.

will be ae'hieved by a tnansfer function the complex conjugate of the sighalspectrun. The spectrum of sig,nails o,f i;nterest is approXirnately re:ctangular f,rom

zero to fs, (DE*.o/l), and the optimum filter will be the ideal 'low,-pass filterwfth fo=fr. $lowEver the ideal lovrpass filter transfonms to a weighting functionwhich deeays rather slowly with tinre (see Figure 5.5) and needs to be trunca&dfor practical purposes. The mos.t rapid filtoring w,ill be achieved with as fewweig'hts Bg as po,ssible, as'therre will be fewer c-omputations for each flltereddata value. It is of interest then to o,bserve the effect of truncating theimpulse t"esBonse of' an i,deal 1ow-pas,s filter.,

Consider the ideal low-pass filter with a cut-off f,requency fo. Its transferfunction and impulse response are

H(f) =

h(t) =

u(f+fo) - U(r-fo)

sin2nfqt(s.lz)

Znfst

uhere U(x) is a unit step at x=0. From these equatiiohs, the weights Bp of thedigital fonn o.'f this filter will be

B,k = 2foT6 sinZnf6kT4ZnfekT6

oF Bp = ?r t#f;51

wher,e r = foT6 = fA/fd, the ratio s'f cut-off frequencJ to sampling fr,equrency.

If r is small, as it wil'l be for liEht presampling flltening, then Bp is sig-nificant f,or large values of k (see Figure 5.5), and h.e'nce the evalu,ation of thefilter or.ltput ofi any particul,ar tine involves a larEe n,ulRber of samples, unlessthe imprulse response is truncated.

Csnsider the truncated filter with Bk giv,en by

Bk = z? ti$# forn I r.I o

for lkl

response ht (t)

=0

tolra

to/rn

then

If this filter has an irnpulse and a transfer function H'(f),

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105.

and henee

h'(t) = t"[t).tu[r+so1 - u(t-ro)]

H,'(f ), = H(f)'t lJ=^Zttttr .

nf'(5.13)

by equation 5.12.

putting x=Znfto,

where * repr"esents eonvolutis:n, and H(f) and, h(t) are given

I'lrJrt:ing the convolution inteErail for. eguattorr 5.13, and

then,

l2nto(f+fo)H'(f) = #

|'Znts(f-fo)

si nx( 5.13a).dx

Fi.gqfe 5..5: The impulse response of the f deal low-pass filter

The tnansfer functton of this tr.uncated fiitern is plst,ted i'n Figure,5.6for various value,s of't6. The corresponding impu:lse response can be obtainedfro,m Fi,gune 5.5.

The mai'n faature o,f the transfer functioils o these trtrncated filters isthe ripple in the ampilitude r€sponse in the reg'ion sf the crt-off freguency,which increases with increasing to. This is a direct resu'lt of the truncationof the impulse'response, and it can be shown (Fapoulis, 1,9:62) that if theFourier tran'sfonn f(t) o.f a discontinuous function F(f) is truncated fs,r ltl>tq,then the comesponding frequency functio,n F'(t) does not Eive a satisfactory

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106.

,oFl*-l*o

tl*o- l*otlo

.o

tt

o

o

,,8o r.p

- vlGtL(,(uEP;rU FL

.e .F)lF

vlF.nL.u {dQ.-t==ctoc

F'E

ct +,oPlatrslq:al

(l,

oan6atlFo,o+r

fg(/l (,gEo=.r 9-+J {-t(,go-=c,(F +'

tJ1

o,lrFl(tI

EILl+,

- l*olAl

,^l*O''1(\r

tl

o

t,

oF

"it:l:to1

iilr

-l.ie

/

xII

I

*f*o

Page 114: 2-Whole-digital Data Processing in Radio Astronomy

appt"oximratisn to F(f) in the vicinity of the discontfnuity, no matterto i,s chosen, unless it is infinite,, This;behaviour of F'(f) near anuity of F(f) is ,hnoWn aS Gibbs' ph:enonenon.

107.

hovl I ar.ge

di sconti -

(5, t4)

If the Fouriep trransform r(t) ef r(f) is nrultiplied [y the tniangular pr.rlse

of Figure 5.7a, rather than the sguare puilse of Figure 5.7b rrrhich corresponds tothe truncation previ,ously discussed, th,en the resultant frequenqy funct'iorn F,'(f)d,oes not contain nipples near diseontinuities in F{f)n but changes monotonically(Papoulis, 162; Craig, 1964). The o-vershsot, of the Gi:bbs'phenomenon is elimi-nated, rhowever a slolver chan,ge results.

fi{ure 5,7; The tr'to impulse respon.se truncati,ng multipliers discussed;(a) the tniangular multiplier^, dftd (b) the step multiplie-r"

Applying this fol"m, of truneation to the irnpulse response h(t} of theideal low-pass filter (equa,tion 5"1.2), the modified im'pu]se response h"(t) and

its transfer function H"(f} are Eiven rby

h,'(r) = h(t).(t-l'l/.0).tU(t+101 - ;U{r-ro),I

H'(f) = H(f)*to sin-arrtls)(nft6)2

The second term in the convolutrlon,

i's knov,n es the Fejdr. kerne'l ,

of the ideal loru*pass filter.0rar'9, 1954) .

to sin2 (r6xo1

(nfrs) z

and this appraxinatisn t'd t:he trahsfer f,unctlsn

is knorun as the Fej6r fiLlte,r (,Papoulis, 1962i

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108.

By performl':ng fhe eonvolution for H"(f) and writing x=nfton trhen

lnts(f+fs)H'(f)=*l tin;t'd*

I'nto(t-fe)

(5. r4a)

This transfer fu,nction h,as been ev'alu'ateol for vari.ous values of tq, and isshown in Figure,5.6 plot,ted, on the same greph as the corresponding step-truncaredfiltel". It can be seen that the transfer funct'ions of these Fejdr filters do notcontain any amplitude ripple near the cut-off frequency but do not give as sharpa cut-off as the step-trunca,ted filters f,o.r the same ts.

The step responscs S'(t) and S:"(t) of these filtens can be evaluated by

the inteEration of their impu'lse respo,nsc,s, i.e.n

rls,(t) = I h,(t),dt

J

andrt

S"(t) = I h.'(t).dtJr0O

=0, fort"-to

1t= | zro sil2nfot . dt, fo,r ltl: to

.| &rfot-to

r+to= | zfo sinZnfot dt, for t>to

.| Z?rfot

-to

=0, fort<'-to

rt= | rto tlnl"lrt tt.qJ.dt ror ltlsto

J ' Znfnt

-te

= l'orru *":# rrJ$:oti ro' r>rsJ zrfot-te

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109.

.f*otl

o

u

-l-o

;Lo+)

(F

atl.nE{o(uo.+,I rltBQoc-E

-*t(6a'>ttF.rL6Tlro5+, ol.oc

C)(r'E.r5!t+)+,olEIolutiq-Iolatl(l)A^gElo(ue+,U, aatou3-g

=cL l-(l.,+,{-ttao-oE .IJ(lJ !r).!r;la(t I

olcl(u-cF

critrrl

I(ulLlJIo{

rrllr- |

.^l*os'l cl

ll

otl

o

g

Page 117: 2-Whole-digital Data Processing in Radio Astronomy

110 .

The step responses corresponding to the normalized transfer functions(H(0) = 1) of the step-truncated filters and Fejdr fjlters shorvn in Figure 5.6have bcen calculated and are plotted in Figlure 5.8.

For short truncations (to = l/2fo) both filters have step responses lvhichrise monotonically, and the FejCr filter has the faster rise-time. For largerto the responses become indistinguishable near the step and tend towards theresponse of the iCeal filter which is characierized by a 9% overshoot and under-shooto and a rise-time of 0.615/fo (see Appendix 5).

Various techniques for approximating r,reighting functions corresponding toparticular transfer functions have been developed (l,lartin, 1959; Cooper, 1970)

but in general, results for 1ol-pass fjlters vrill be sjnri'lar to those obtainedhere. For a finite r"reighting function the degree of sharpness of the amplitudecut-off will be dependent on the weighting function iength; the'longer theweighting function the sharper the cut-off, and for a particular vreightingfunction length, ripple in the amplitude response can be reduced only at tlreexpense of the cut-off rate.

5 .5 General Fi'l teri nq Cons'iderati ons

It can be seen from the results obtained in the preced'ing sections thatsimilar amplitude responses can be ach'ieved riith both analogue and digitalfilters, although in genera'l a digital filter can oroduce a cut-off rate r.rhich

can on'ly be equal'letl by a very conrpiex analoaue f ilter, the limjtation on thedigital filter being the nunrber of data pojnts it is convenient to involve inany One calculation. Dispersion in an analogue filter can produce considerabledistortion vthen heavy filtering is used, and any time delay produced must be

allowed forin source position calculations. llowever a digital f jlter can be

designed to produce no time de'lay by using a synrnetrical lveighting function, and

the input signal isthenmodified only by the shape of the amplitude response.

The necessity irlplied by digital filtering, to accumulate a iarge number of datapoints before filtering can be carried out, introduces the possibility ofediting out interference spikes prior to filtering. Thus the effect of thesespikes vrhich can be quite significant with analogue filters and may marr a vitalpart of the signal can be elinrinated (Cooper, 1970).

If optirnum filtering is required to produce the nraxinium signal-to-noiseratio wjthout distort'ion, it seems preferable to use a relatively srna'll arnount

of presanrpllng analogue fjlterinq, enough to rationaiize the samplinE raterequirements without producing significant distortion, and to follow this vrith

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111.

some form of digitai filtering to produce the desired optimum signal-to-noiseratio.

5.6

Considerations in the previous sections of this chapter have been directedtowards the sampling rate of a digitizer and its effect on the sampled dataspectrum. The sampling process was assumed to be ideal, i.e., the sample datawas the exact value of the input data at the sample instant. Holvever digitalsampling inrplies quantization of the data, and the effect of amplitude quanti-zation must now be considered jn order to establish a requirement for thequantizer step size.

The dynamic range of the input data is definecl as the ratio, expressed indBn bett',reen the maximum and minimum siqnals of interest. In most cases theminirnum signal level is doterrnined by the noise present on the data, and thedynamic range is then the ratio betrveen the nraximum signal level and the noiselevel (l'1elton, 1967).

The process of ampfitude quantizjnq rvith a quantizer step q introduces an

error eO vthich is uniformly probab'le over the range tq/2 and has a mean squarevalue oet = q2/Lz (Bennett, 1948). Defining the dynanlic range Do of a

quantizer as the ratio of peak cl.c. input power which rvill be quantized withoutlimiting to quantizer nojse, then

Do = 201 ogro(zU/r) + q.B dB

where 2v is the peak-to-peak voltage range of the quantizer.quantizer this becomes

(5.15)

For an N-bit binarv

Dq = (6u + 4.8) dB (5.15a)

the dynamic rangeIn order that the effect of quantizing should not reduceD, of the i nput data, then

Ds.Dq

The question arises that if the signal-to-nojse ratio of the samp'led datais to be increased either by digital filtering or by averag'ing collateral datasets, what is the dynanric range of the input data? Firstly it can be establishedthat the processes of filtering and averaging are essential'ly the same. The

impu'lse response of a signal averager is a train of inrpulses and this leads to a

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LT?.

filter transfer function resenrbl ing a comb, vrhere the spac'ing of the teeth jsinversely proport'iona1 to the sanrp'le interval and the width of the teeth isinversely proportional to the number of samples (Trimble, 1968). The signal

averager can then be treated as a nrultiple band-pass filter. ConverselJr 0S

the function of a filter in the frequency domain js the multiplication of the

signal spectrum by the fjlter transfer function, tlren in the time domain the

function is one of convolution - i.e., a weighted average of the signal.

Consider as in sectjon 2.10 a signai S(t) olus a noise N(t) where the noise

has an r.m.s. value on. If m prec'ise samp'les of thjs data are averaged the

result vri'll be the average of the m values of S(t) plus a noise of r.nt.s. value

on/fr. |^ljth quantized samples there will be an added uncertainty because ofthe quantizer noise. Provided Q << on then the quantizer noise can be assumed

to be independent of the sampled data value, as this will cross several levelsbetween. samples (Ohlson, 1971). If m quantized samples of the input data are

averaged, the result will still have a mean equal to the average of the m value

of S(t), but the noise vril'l be increased to an r.m.s. value 'qN + o77nl.

As oet = q'/n, then for o'n >) g, this noise rvill be negligibly greater than

the noise for the precisely sanrpled case. For g = on/4 the increase in r.m.s.noise is approxinrately 0.1/". Provided the noise has been samp'led rvith a suffi-ciently sma'll quantizer step q, then the average of m samples will allays be

equal to the nrean signal level vrjth an r.m.s. uncertainty of on/ffi, even ifthe mean s'igna1 level 'is well below the original noise level . For reasonable

detection of the mean signal S hol'rever,5 should be greater than on/fr, or

If the dynamic range D, of the input data is defined as

D, = 20]ogro(V/on)

where V is the peak modulus of the input and op is the r.m.s. noise, then the

condition that q = ofl4 imol'ies

Dq = D, + ?2.8 dB (5.16)

It can be seen from these results that iight prefiltering, vthich vtould have

the effect of reducing D' would also reduce tlre requjrements for DO. The

signal -to-no'ise ratio could then be improved by post-sannling f iltering. liotvever

the lighter prefiltering \,tould mean thai higher frequenc'ies l^,ere present in the

m> t-

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113.

input spectrunr, and a higher sampi'ing rate would be required.

5.7 The Effect of Aperture Time on the Q1,p611ic Ranqe of a Quantizer

Although the effect of amplitude quantizing has been tal<,en into account insection 5.6, it has been assumed that the sampling orocess can be performedinstantaneousl.y. For practical quantizers this process requ'ires a finite"aperture tirne", and in considering the dynamic range changes in r.he fnput dataover this interval must be taken into account. (Hoeschele, 1968).

Consider an N-bit binary duant'izer with a basic step q. The peak inputwhich can be quantized ulithout distortion is then

\u* = *zN-l' q

The inherent error in the quantizing process is tq/Z (Bennett, l94B;Hoeschele,1968) so it can be assumed that the aperture interval will jntroducen0 appreciable emor provided the input changes by no more than q/2 during theinterval (the exact effect of this change on the quantized data will be dependenton the type of quantizer). For a sjnusoidal input of frequency f and amplitudeA' the maximum change in voltage over a short interval t (t..11t) is 2rftA.If the aperture interval'is tu, then the condition for the change in the inputto be less than q/2 over this interval is

A<

I- --TI--) z''. zrf ta

(5. 17 )

(s"17a)AAr.*

Expressing this amplitude A in terms of A*u* then

which gives the normaljzed amplitucJe of a sinusoid at frequency f which w'ill notbe significantl,v distorted by the effect of sampling vrith a finite apertureinterval ta. A/A--_ expressed jn dB as a function of ZNtut is plotted inFigure 5.9. 'max

The dB ratio can be considered as a'loss in dynamic range

at hjgher frequencies.

For signals which exceed this frequency-amnlitude linrit the form of errorwill be dependent on the type of quantizer. llor.rever most quantizers rvill givea sarnpl ed val ue rvi th an uncertainty of 2ll .znf tuA/A*u*.

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1111.

0

_4.ftp{dB)

Figure 5.9: The loss in dynamic range resulting fronr a finite ape.rtureinte,rval t" for an lt-bit binary quanitizer

REFERENCES

BENNETT, l.rl.R. (1948): "spectra of QuantizEd sig,nars,t. B.s.T,J.,3I p,p.r$46-472.

tsRACEW'ELL, R.[1. (1955): 'The Fourier Transfor-m and i,ts App:licatiors,,.(Mc6l.aw-,Flil1 , lrlew york) .

000PER,, B.,F.C. (1970:) ; "Fost-Detector Filtering irn Radiometry,'. pr oc. tr.R.E.,E,.

Aust." 3! pp. 41-49,

CRAIG' E.J. (ls6q): rLaplaee and Fourier Transfonns fsr E'lectrical Engi,neersf,.(Holt, Rinehart and kJiniston, llew york)

GRIFFITHS, J.['1.R, (lgs6): ,,0ptimurn RC Filters". Wireless Engr. lx pp. ?96-|l7a.

HOESCHELE, D. F. (te0s1 : "Anal ogue-to-Djgital/DlEital -to-Analog.u,e Convers,r'on

Techniques " . (Wi t ey, l{ew york) .

FHRTI$|' M'A. (1959): rFrequency, Dornain Applications to Data Frrocessi'ng'i, Trans.I . R.E. , S.ET-5 pp. 33-41 .

Page 122: 2-Whole-digital Data Processing in Radio Astronomy

115.

MELTCIN' 8,5. (1967): 'lAnalogue-to-D,igi'tal O,onversion- A Problem or 'DecibeJs-to-Digits' ", Trans. I.E.E.E., QE:S, pp. fg-ZE.

0llLS0ftl' J.E. (1971): 'rEfficiency of Radl'ometers using Digital Integrationi',,Radio Sci, 6 pp. 341-345.

PAp0tl-IS' n' (t,gea): "T'h'e Fourier Integr.al and its Applications". (Mccraw-Flill,.New York).

'TAVARES, s.E. tt00o;: "A Co-nrparison 0f Integration and, Low-Fass Filtering".Trans. I.E.E.E., Il.l-1=5_ pp, 3J-38.

TRIMBLE, C.Ro, (19681: "What is Signal Af;eragirngfil Hewlett-Fackard J., 19,,

l,lo. I, pB. Z-7,

TURtrN,, 'G.l-' (tgSO): "An 'Intr"oduction to Matclred Fi'ltersr'- Trans, I.R.E. IT-6,

pp" 31.1-340.,

1'IUCHINICI|, D' (tsgg): "simple Ultra Lor^r-Pass Filter (njqde tsnake)"', Elestl"on.Irett. , ,tr p. 137 .

YARMLL, 'J..hl.

(1968): I'A 42MHz Rad'iometer usr'ng Meta'l 0xide Field-EffectTnansistors and Integ'rated Circuits!'. M.E. Thesisn Un{vers'ity ofAuckl and,

Page 123: 2-Whole-digital Data Processing in Radio Astronomy

116 .

CHAPTER 6

The Design and Development of an Analogue-to-Diqital Converter

The requirernents of the ana'logue-to-digital converter are dictated by the

characteristics of the interferometer output, and are essentially independent

of other considerations. In Chapter 5 the effects of sampling on the signalcharacteristics t,rere discussed and principles established for the choice of a

suitable sampling interval and quantizer step. These principles are now appliedto the characteristics of the interferometer output, and a quantizer specifica-tion formulated. In view of the numerous techniques of analogue-to-digital con-version available the design of an economical unit to meet this specificationis explained.

6.1 The Specification of the Analogue-to-Digital Converter

The specification of an anaiogue-to-d'igital converter should include con-

siderations of the follorving requirements (Hoeschele, 1968):

Sampl i rrg rate.

Dynamic range, or quantizer resolution.

Aperture time.

Input vo'ltage range, and input impedance.

Digital output.

0veral I accuracy.

Following the analysis of quantizer operation in Chapter 5, these require-ments can now be considered, and a specificatjon formed.

6.11 The Input Spectrum and the l'ljnimum Sarnplinq Rate

It was shourn in section 5.2 that for general observations the output signalspectrum of a correlatjon interferometer can be considered to extend from zero

to DB,n6x/), hertz, vrhere D js the length of the interferometer baseiine anci

Bmax = #ffi* rad/sec

1.

2.

3.

4.

5.

6.

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II7.

The declination d of the interferometer pole can be obtained from equation3.14. For the 200 i'1flz interferometer this maxjmum signal frequency is2.9 x 10-3 Hz. If the signal spectrum is to be distorted by 'less than 1%, therequired time constant of the simple RC low-pass fi'lter from Table 5.2 isRC = 12 seconds. For less than I% noise reflected onto the signal spectrum theminimum sampfing rate fd, also fron Table S.Zn is fd = 0.133 Hz, or one sampleevery 7.5 seconds.

6.LZ The Dynamic Range of the Infrut Data

It was shotvn in Chapter 5 that in order that the information contained inthe data is not distorted by the quantizing process, the dynamic range Dq of thequantizer should be related to the dynamic range D, of the data by

DO r D, + 22.8 dB

For an il-bit binary quantizer this relationship becomes

6N>Ds+18

where Dr is the dynamic range of the data, expressed irr decibels.

In Chapter 4 the noise level at the output of the present interferonreterwas shown to be equivalent to an incjdent radiation of flux density 300 x 10-26W/n2/Ilz. flovtever improvements scheduled for the immediate future should reducethis figure to 50 x 10-26w/n2/Hz with a 20 second RC time constant, or 65 x 10-26l'Un2/Hz r^rith a 12 second time constant. The strongest ce'lestial source in thearea of sky visible to the interferonreter (excluding the active sun)is CentaurusA, rvhich has a f'lux density at 200 MHz of approximately 3000 x 1g-zey16z/Hz. *As the output voltage of the interferometer is proportional to the input por./er,

the dynamic range of the output would then be z01og,o(rooo/os) = 33.3 dB. Houreverthe dynamic range of the present system is limjted to about 32 dB by non-iinearitiein the synchronous detector and the limiteci operating range of the diode squarelaw detector (Lim, 1968; Yarrall, 1968). This range does cover all visible.sources excluding Centaurus A and the sun; the Crab i\lebula, the next strongestsource has a flux density of approximately 1500 x 10-26',!1n21Hz at 200 MHz. Forobservations of the stronger sources, limiting in the detectors can be avoidedby inserting some attenuation in the I.F. section.

* This figure has been obtained by interpolation of quoted flux densities at86 l4Hz and 960 f4Hz.

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118.

The number of binary digits N required by a natura'l-binary-coded quantizeris then

6ll >32+18

8.3

Thus a nine-bit binary quantizer will have anrple dynamic range to cover theinput data satisfactoni'ly. For a non-natural-binary-coded quantizer which hasa resolution of n equaily spaced steps, n will be specified by

201og,o(n)r32+19

n >317

6.13 Restrictions on the Aperture Tinre of the Quantizer

The effect of a finite aperture tirne, shown in F'igure 5.9, is to reducethe dynamic range of the quantizer at h'igh frequencies. The dynamic rangefalls off at a rate of 20 dB/decade, the same rate as the amplitude responseroll-off of the oresampling RC filter. If the cut-off frequency of the RC

filter is less than the break-point frequency of the dynamic range then thedata will not be affected by this loss in dynamic range. The breakpoint inthe dynamic range of an N-bit binary quantizer .is

E_ I'-ilEwhere tu is the aperture time of the quantizer. The required cut-off frequencyof the presamnling filter has been calculated to be 0.0133 l{z (RC = 12 seconds),and the capacity of a natural-binary-coded quantizer specified as nine bits.The maximum permissible aperture time is then t6 = 23.4 mllliseconds.

6.14 The Input Voltaoe ranqe and Input Inrpedance

The output voltage variation of the'interferometer is limited to t400mV

by non-linearities in the synchronous detector. As these are also the'limitingfactor in the dynamic range, the quantizer should give full scale deflectionfor these I imiting vo'ltages (i.e., t400mV). l{ovrever the output will often be

well be'low this level, and it vrould be an advantage to be able to increase thesensitivity to aoproxirnately t100mV full scale.

The output inrpedance of the interferometer is determined by that of the

N>or

0r

Page 126: 2-Whole-digital Data Processing in Radio Astronomy

119.

low-pass filter. By the use of an isolating amplifier this has been reduced to-200n. For the loading effect of the analogue-to-digital converter to be lessthan 1/2 the quantizer step (in keeping with the genera'l accuracy) the inputimpedance should be at least 100Kn.

6.15 The Format of the Digital Output

If a natural-binary-code representation is used, the minimum quantizercapacity required js nine bits. As the natural-binary-code utilizes a]l possiblecombinations of binary digits, no other code can achieve the same resolutionusing feler bjts. The natura'l-binary-code has the added advantage that it isthe code used within the IBM 1130 computer, and data in this format can be

directly interpreted r,rithout code conversion. 0f the range specified, one halfwi'll be used to represent positive numbers and one half to represent netativenumbers, imp'lying the use of one of the nine bits to represent the sign. As

the representation in the IBl4 1130 is two's conp'lement, then it will be desirablefor the ana'logue-to-digital to also use this system.

There remains the question of whether the nine-bir output should be inserial or oarallel form. The recording medium is by nature parallel-bit, serial-word, but because more than one tape word rvill be requfred to record a sing'lesample, some conversion betleen serial and para1le1 bit forms rvill be required.lrlith the output in serial form, one group of bits could be punched in one word,and the remainder in the next, but because of the slow punch rate, some formof storage would be required to de'lay the second group. Holever, with theoutput in para'lle'l form the two grouns could be punched one at a time by

switching between tvro sets of data lines, prov'ided the output persisted for theduration of the recording. The choice of a para'|1e1 data output is suggestedby another factor, that of a visual display. With a para11e1 output which per-sists between samples, the current binary output can be displayed by a row ofI amps.

6.16 Overall Accuracy of the Analogue-to-D'igital converter

The specification so far has assumed the quantizing process to be exact,the only errors occurring being the inherent quantizing error (tq/Z where q isthe quantizer step) and tire error of the finite aperture rvhich has also been

restricted to tq/?. Hovlever other errors vrill occur jn the system, because ofnon-linearities in the electronic comDonents for jnstance, and in keeping rviththe inherent quantizer error, the overall equipment error should be less than!q/2.

Page 127: 2-Whole-digital Data Processing in Radio Astronomy

120.

6.t7 Other Considerations

The specification contained in the preceding six sections fulfils the

requirements of the present interferometer and the improvements planned for thisinstrument in the immed'iate future, The speed requirementsn that is the require-ments of sampling rate and aperture time, are very modest by present-day stand-

ards. lloting that a high-speed analogue-to-digital converter could be utilizedin a pulsar signal averaging unit (see section 4.17) it was decided that the

converter should be nrade as fast as possib'le without significantly increasingits cost. The requirements of dynamic range would be great'ly reduced at high

sampling rates, because of the much greater noise level inrplied by the very

short time constant.

6.18 A Summary of The Specification

The specification of the preceding sections can be summarized as follovrs.

1. Samp'l i ng rate A mi nimurii of 0.133 sampl es/second, preferab.ly

greater than 1000 samples/second.

Resol ution

Aperture time

1 :317 mi nimum (g ul t N. B. C. )

Maximum 23.4 nrsec, preferabiy -50psec fors-bit accuracy at f6 = 1000 Hz'

2.

3.

4.

5.

6.

7. Equipment Accuracy

t400mV, with gain to extend to t100mV.

>100Kt

Parallel bitn natural-binary-code, with two's

complement sign representation.

t0.2% full scale.

6.2 A Survey of Analogue-to-Digital Conversion Methods

Present-day methods of analogue-to-digital conversion can be divided intotwo broad sections: (i) those rvhich convert the input analogue voltage'intosome more readily measurable quantity, usually time or frequency, and

(ii) those which compare the input ana'logue vo'ltage rvith an internally d'igita11y

generated voltage. The characterjstics of these two types of converter are dis-

cussed in the following paragraphs, and the convers'ion method best su'ited to the

spec'if i cati on establ i shed .

Input voltage range

Input impedance

0utput format

Page 128: 2-Whole-digital Data Processing in Radio Astronomy

t?t.

6.21 Voltage-to-frequency and Voltage-to-time interva'l Converters

These converters are generally characterised by 1ow conversion rates'

good accuracy, and low complexity (Hoeschele, 1968). Voltage-to-frequency con-

verters, or jntegrating digital voltmeters generate a frequency proportional

to the instantaneous input voltage. This vary'ing frequency is gated into a

counter over a set period, and the resultant count is then proportional to the

integral of the input voltage. This type of converter performs the functjon of

an ideal integrator, and for th'is reason has found application in rad'io te1escope

systems, whe.re it performs both the filtering and sampling functions (Heeschen,

1961; Mclaugh]in, 1962). As shown in Chapter 5, with such a system much loler

sampling frequencies may be used than with RC'low-pass filters, but the removal

of ref I ected noi se 'is very dependent on the post-samp'l i ng di gi tal f i I teri ng .

Converters employing the voltage-to-time interval principle are very similar

in operation (Hoeschele, 1968). By integrating the input voltage for a set

period, and then reducing the integral to zero at a constant rate' a time jnterval

is generated which js proportiona'l to the average value of the input voitage. A

standard clock frequency is gated into a counter during this period to produce a

count directly proportional to this averaEe vo'ltage. This type of converter

also performs the function of an ideal 'integrator, but here the integration

period, and hence the convers'ion tirne, is proportional to the input voltage and

for a given c'lock frequency conversion speed can be improved only at the expense

of resolution. This converter obviously cannot be used in place of a low-pass

filter, since for smal'l inputs the integration period wjll be small and the

reflected noise hjgh. Because of this dependence of integration period on input

voltage, such a converter is not suited to thjs application.

6.22 Discrete Comparison Analogue-to-Digital Converters

These converters range between low and medium speed, are highly accurate'

and are of low-rnedium complexity (Hoesche'le, 1968). An analogue comparator is

used to indicate vrlren an internally generated analogue voltage from a digital-

to-analogue decoder is equal to the input signal . The cument d'igita'l 'input to

the decoder is then the numerical representation of the input voitage.

In the counter-ramp analogue-to-digital converter, the digital input to

the decoder js steadily increased from its minjmum value, one step at a time'

until equa'lity is reached. This converter has a conversjon time dependent on

the magnitude of the'input voltage, but no averaging'is performed. The dig'ita1

output represents the instantaneous value of the'input voltage at the end of

the conversion period. Thjs converter suffers from the same speed limitat'ions

Page 129: 2-Whole-digital Data Processing in Radio Astronomy

t22.

as the previous pair; conversion speed is determined by the maxjmum frequency

at vrhjch the counter will operate, and the maximum conversjon time is the time

taken for the counter to accummulate its maximum count-

In the ,u...rrive approximatjon converter, equaiity of the decoder and

input voltages is achieved much more rap'id1y. Starting with the most significant

bit (rn.s.b.),. each bit in the digital-to-analogue decoder js successively set

to a,,1.", drd the output of the decoder compared rvith the analogue input vo'ltage.

If the decoder voltage is the greater, then the bit is returned to a rr0rr; if the

input voltage'is the greater, then the bit'is left at a rtlrr. The next ntost sig-

nificant bit (n.m.s.b.) is then set to a rrlrr and the process continued until the

least significant bit (l.s.b.) has been set and verified. For an N bit converter,

the time taken for tlre conversion js equal to the tjme taken for N comparisons'

much less than for the counter ramp converter where the maxjmum time taken is

equal to the time taken for (ZN-t) comparisons. 0nce again no averaging is per-

formed by the converter, and the process'is very dependent on the constancy of

the input voltage over the conversion period.

6,?3 The Choice of an Analosrue-to-Digital Converter

There are nuny more varieties of analogue-to-digital conversion methods than

the four mentioned in the previous paragraphs (ltoeschele, 1968), however most

of these are special cases of the types mentjoned, or else are too obscure to

warrant consideration. The choice lies between the voltage-to-frequency' counter

ramp and successive approxinration converters. The first two suffer from the

same speed limitations, but are in genera'l 'less complex than the latter. The

various properties, advantages and djsadvantages of these three conversion

methods are tabulated in Table 6.1.

In spite of the higher sampling rate requiredn it was dec'ided to use a dis-

crete comparison type of converter because of its greater flexjbility in both

sampf ing rate and filter characteristjcs. A successive approximation converter

was chosen in preference to a counter ramp jnstrument because of its greater

speed capabilities,'in light of its poss'ible use'in a pulsar signal averager.

The general operation of a successive approximation analogue-to-d'ig'ita1

converter js shown jn Figure 6.1. The design of such a converter is covered in

the rema'inder of this chapter, each element of the functional d'iagram (figure

6.la) being considered separately. At the tirne the design of this unit was

begun, large-scale-integration microelectronic successive approximation con-

verters vrere available, but thejr cost precluded their use in this proiect. The

Page 130: 2-Whole-digital Data Processing in Radio Astronomy

, 1,?3.

,nLoPLocoI

C'+,g|

'EIo

+,I

(u5qtoG,E'Eo(l)t+,lFocovl!G'AEo(J

-'i I

-lCJl

5lrdlFI

so+tE

xoLoa(u

.nano(Ju=ta

oE.uE!(uPE=o(J

tqo,=gotto

+)Io

Ct)at+,o

'oP|r'Ul.rLLCvrotfi|o.n+Jq9r!olFE(, .F .- (,o).Flt-.FgEA.E

$.dEctGtotn(og.h

Lc,PE(u('E(u+tc(6(trg,(l,Ec.r 'lJ .n .!t .rlFg(J-q+t

(l,.F(JC,gro-+r(u=otAorF'-E.F*,)(FFgLclQ-.r(1)+tE+r.F+tGt(FLr(f=5utor(toool3-.F.F-C

+t-vf6L(F+)t/|(,.c(urFO c, (, O-.r

=rJo

cf)

.+tPtg.F ]h

=tnavrl--c'u|(U(|J.rCr#OTt(uoa..c.Ec{d(ut(u'Cr(uL+,E!-(uLf(t.('.ctES!.e-t-trtt-titP.-={]rJorLJqCr.r-U)(U(U(J-(UE,ILECLO!

-c,c,.FO-G,!L{rQ-eE(ll(uFO-.O+rL+,P{DEt,qo.ut+-cfo(u+rL.FtnlUIFaFF(l|.FUT

oo-rFrtsLrFCq)EO.FO..-goc'U)-.F (J VlE+r+).FEg(lJ-(1'--.F15=Ec.u!gQ-.nctg€,F(UOE.nE-Cl(J.a.Frgi.fOtn.Ftl)f+)Ul11;P(u(JXCLL!-gq'c'OE+r(U.-+rLO-Htro--

Fl (\l

F{ (\J

'0(l,L

=q(uLL(u1J+r(uo.F O-tF rh

g) o)gC

eaFEct(o,n aa(I)tt-cL(u

=ooZJ

t-l Nl

o=(')o(tt

((tIo

+JI

.o+,g)

'(J(Fo

+,.rLL(u(6 -(t(uoE(.l.-(UrE

uE(u5gu3-rFIo

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='-qlo=rrGto(lj+rvtFEo

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(,

F=

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=-co=sl O'r.d -c

LrJo-F

&.Lr.fFE,lrjz,o(-)

t(uUI.E+tEC'.It.t'vl'o

ol'tt c(u(l,+,OC,vto

lFEo+,'|: '.t!1 xuvt(J'('L(U,tTL€+)(u!(f!cEE(Ju(Jt9, ao(g(Jntrg.ttlFrg-

Page 131: 2-Whole-digital Data Processing in Radio Astronomy

124.

Vs Sa,riol0utput

Anotogue

Input tli,

M,5.8;

Eit 2

'Bit 3

ait 4

'V;

v9

b

' ,a-'Porolt,etOutgut

(a)

1,.,',,,,

j'-'-

SeriolOutput

Figure 6.!: (a) The suecessivre approx'imation analogue-to-d'igitaleonverten, and (rb) typical opellatJng wave fonms.

Page 132: 2-Whole-digital Data Processing in Radio Astronomy

125.

converter v,as designed utilizing t.t,l . (transistor-transistor logic) integrated

circuits and available analogue components.

6.3 The Digital-to-Analogue Decoder

The analogue-to-dig'ita] converter js to have a n'ine-bit capacity, and as

one of these bits is to be used for sign representatjon, a digital-to-analogue

decoder of eight bits is required. An R/2R ladder network tvas chosen for this

decoder, in preference to a vreighted resistor network. The advantages of a

ladder network are (i) closer resistarrce to'lerances are easier to obtain when

resistance values do not vary widely, and (ii) as the analogue switches are all

carrying approximately the same current, the effect of switch offset voltages can

be ignored.

The overall accuracy of the decoder should be vlithin the overall converter

equipment specification of !0.2%. This error js best analysed by considering

separately the trvo chief sources of error; errors in the ladder network' and

errors i n the el ectroni c equ'ipntent.

6.31 Accuracy Requirements of the Ladder Netvtork

An t,l-bit R/zR ladder netvlork is shovln in Figure 6.2. The netvlork has an

output resjstance R and an output voltage of

vo = vR [rAr+ ?t. Bt+ ....- $]

(6. 1)

where D* is the logical state of the *th bit (1 or 0) '

2R

Ra*

Figure 6.2: An N-bit R/2R ladder nettlork

It can be shown (Hoeschele,1968) that if all the resistors in the ladder

vr

0v

Ran-z

2R

D4

bo

2R R7

D3

R

2

o

Page 133: 2-Whole-digital Data Processing in Radio Astronomy

have a fractional tolerance te, then the maximum error in the output voltage

occurs when the m.s.b. 'is a L and all others are 0. This error has a worst case

value of te/? of the full scale voltage. If the decoder is driving a nu11

summing junction then it is the short cjrcu'ited output current which is the

quantity interest, and the error

must be taken into account.

in the output resistance of the ladder

Refem'ing to Figure 6.2, if Rr has a fractional error e (i.€., Rr=2R(l+e))

and all other resistors have the'ir exact valuesn then the output resistance of

the ladder is R(I+e'/?). If R2 has a fractional error e (i.e., Rz=R(l+e)) and

all other resistors have their exact values, then the output resistance of the

ladder js R(I+elil. Similarly if Rm has a fractional error e and all other

resistors have their exact values, then the output resistance of the ladder is

R(1+e/2m). For an ll-bit ladder, the contribution to the error in the output

resistance of an error e, in resistor.,h it 4n/rm for 1<m<(2N-1) (see Figure 6'2)'

and for m=2ll the contribut'ion is e*/21'l-r. With all resistors of the same

fractional tolerance e in an N-bit ladder, the worst-case error ee in the output

resistance is then

t26.

(6.2)

1

16- h...... + ' -

,3rzr,-r))1

.E2''-

?2n ""

The most probable value of es 'is given by

to'- "(f,+

i.e., eo * t0.5'i7e 10. za )

As the output resistance, and hence this effor' are'independent of the Dt

states, then'it would seem that the error would produce only an absolute error

in the output current, and no relatjve errors between output currents coffes-

ponding to different states. The sw'itches however will not have zero resistance,

and this resistance may vary w'ith the state of the switch. If the switch resist-

ances are included aS errors in the ladder resistors, then the output resistance

will vary from one state to another, wjth'in the range specified by equation 6'2'

The short-circuit output current Iq is given by

Page 134: 2-Whole-digital Data Processing in Radio Astronomy

.voI9=F;

so that the worst-case emor in Io is equal to

Ro.* The largest error in Vo occurs when Vo =

of this is 1e.Vq. The worst case error in Re

case error in Iq is tZe,Io. However for Vo =

scale value, and hence this worst cose error inThe most probable error is */E or t0.707e.

L27.

the sum of the errors in Ve and

Vp/2 and the worst-case value

is te.Ro, and thus the worst-

Vg/Z, Io is half of its full-output current is texfull-scale.

If the overall accuracy of the decoder is to be better than t0.2%' then

the tolerance of the resistors in the ladder network, including errors introduced

by the switches should be less than t0.2%.

6.32 The Development of an Analogue Switch Circuit

The requirements of the analogue switch circuits are specified by the overall

accuracy requirements and the input logic levels. For the t.t.l. integr'ated

logic circuits used in the converter, the logic leve1s are (i) low < 0.4 volts

with up to 16mA sink current, and (ii1 high - 4 volts with a source resistance

of 1504 (mut t ard, 1968) .

A bipolar transistor switch was chosen in preference to one using field-effect transistors because of the less complex driving circuits required by the

former. When used in the inverted mode**, bipo'lar transistors have a low satu-

ration voltage (VfCsat < 10mV) and are quite satisfactory for use in digital-to-analogue decoders (l-loeschele, 1968; Mann, 1968). To achieve the single-po1e

double-throw action required, a circuit of the type shown in Figure 6.3 can be

used.

This circuit may be operated with either positive or negative reference

supplies. tlhen used with a negative reference (-Vn), the transistors have a

* This is not strictly true as errors in Ro and Vo are not independent. However

as the worst-case voltage error and the worst case resistance error do not occur

simultaneously, these figures are on the safe side as far as design is concerned-

**If the excess base curent flows through the base-collector junction when a

transistor is saturated, then the transistor is said to be operated in the

inverted mode (Hoeschele, 1968) which is characterised by a low saturation vo'ltage

vEcsat'

Page 135: 2-Whole-digital Data Processing in Radio Astronomy

128..

c.unr,ent gain of Bp, the forrnnrd curyent gain, when nOving through the active

region, hovever an input logic swing of zero to -Vp volts is required to operate

the switch. With positive references voltages (:+Vn), the input logic swing

requir.ed is zero to +V* volts, readily avai:lable from. t.t..l. ci:rcuits' but the

transistors have a current gain of Fp, the rPVBfe:E current gain (BR - 0.18p) when

moving through the active region.

LogiiInput

vr.r

To LnddcrNetwork

FJgu!e 6.3: An inverted mode bipolar transistor double-throw switch

A satisfactol.y design was achieved uSing a pos'itive reference of fourr volts.This deslgn,, shown i.n Figurre 6.4, requires no active drivirtg circuitry when

driven from t.t,l. eircUits, in spite of the low current gain sf the transistors.

The S1gitch op.er.ates from inverted logic levels, the lsw leveil input is interpreted

as a logical I and h'igh leve'l input as a loglcal 0.

+ 5 volts(:t.t.l. suppty )

, Figure 6.4: The decoder ladder switch

The operati,on of the cireuit san be described a,s follols:

(A) tlhen the input is lsrv (a logical 1)' Vf is <0.4 vo:lts p'ovided IL.16mA.

The base of transistor Tz will be at 0.11 volts, and Ta will be cut-off (for

Logic \1Input L

ta-on i;

Page 136: 2-Whole-digital Data Processing in Radio Astronomy

silicon transistors no current will flow

supply of Tf is effectively a voltage of

779{1. The collector-base junction of Tr

current 16, of 5mA florvs. If the output

the transiitor r^rill be saturated and the

vol ts.

(B) hlhen the input is high (a logical 0), VL =

ance of 1500 (VL = 4.0 + 11.150). Assumjng that

tions, the equivalent circu'it is shown'in Figure

L?9.

unless vbe - >0.6 volts). The base

2.5L volts with a source resistance of

is then forvrard biased and a base

current Io is less than Ibr.9R, then

output voltage Vo will be (4-Vrgrur)

4.0 volts with a

Ix is zero underel

6.5.

source resi st-these condi -

Figure6.5:Theequivalentcircuitfora.high.input.

The base supply for Tz is a voltage of 4.L73 volts with a source resistance

of 4540. The base-collec.tor junction of Tz is thus forward biased and a base

cuffent 15, of 7.86 mA flows. If the cutput current -Io is less than 8*'I5,

then Tz will be saturated and the output voltage Vo vlill bt VECsat' Under these

conditions V6, = 4.02 volts, so the assumntion that I3, was zero is valid'

The complementary transistor pair used (Bc108/8C178) were found to have a

very stable saturation voltage Vggrat of 2-3mV for Ig = 5mA, and a dynamic

resistance of less than 10 under these conditions. The effect of the saturation

voltage can be offset in the reference supply. The 1ow dynamic resistance rnade

it possible for a IK/21( ladder to be used. A low ladder resistance was des'irable

with this discrete component system to keep the propagation delay to a minimum'

The ladder was built up from l;W, 5% tolerance lFJl carbon resistors, selected to

atoleranceofllaQ.Comb.inedtviththeswitchresistanceoflQ,thisresultsina maximum error of 0.1% in the output short-circuit current, withjn the design

specification of t0.2%.

390^

The four-volt reference 'is supp]'ied by an integrated-circuit voltage regu-

Page 137: 2-Whole-digital Data Processing in Radio Astronomy

130.

lator from an avai'lable +15 volt rail in the system. It can be shown that the

cument flowing through the terminating 2R resistor of an N-bit ladder (RZn,

Figure 6.2) when alf inputs are L's approaches V*/3R when N is large and the

output is driving a null sunming junction. The maximum output current occurs

under these conditjons also, and this'is equal to (ZN-t)VR/(2NR) rvhich isapproximately VO/R. The maximum current drawn by the ladder is then 4VR/3R

amps. Hovrever the base current drawn by the transistor switches is significantand must be taken into account. Referring to F'igure 6.4, for a logical 1 input

the current drawn from the reference supply is Ibr + Io = 5mA + Io. Thus the

maximum current drawn from the reference supply when al'l logical inputs are l''sis

Iru* = :p+ N.16,

1A= t+8x5mA

= 45.33 mA

By using a small power transistor (ltJE9602) to increase the ga'in of the

integrated-circuit regulator, the output resistance was reduced to 0.020,

producing a drop in output voltage of only 1mV at the nrax'imum load current.

The reference voltaqe is then stable to within 0.025%.

6.4 Sign Determination and Voltage Comparjson Circuits

The input Va to the sign determjning circuit is assumed to be a voltage

in the range tVref (t4 volts). The purpose of this circuit is (i) to generate

a sign bit, and (ii) to modify the input voltage so that when the decoder output

is the negative of the modified voltage, the decoder digital input, together with

the sign bjt, forms the two's complement representation of the input voltage V6.

The input to the comparator is the sum of the modified input voltage and the

decoder output. The output of the comparator must be capable of driving t.t.l.circuits, and must change state when the input changes from +q/2 to'q/2, where

q=4/28=15.6mV.

6.41 Two's Complement Sign Representatjon

In the two's complement system, drY integer in the range +(Zn-l) to -(2n)

can be represented by n+1 binary dig'its. if N is positive or ze?o, then the

digitsformthe natural-binary representatjon of N; jf N is negative they form

the natura'l-binary representat'ion of (Zn+l+t't1. For example a system of 3 binary

Page 138: 2-Whole-digital Data Processing in Radio Astronomy

131 .

adig'its can represent anY

system is shown in Table

integer in the range

6.2.

+3 to -4. The coding of such

Table 6.2: Two's comPlement coding

This can be interPreted

numbers have a sign bit (the

bits form the natural-binarYpos'itive numbers have a sign

binary representation of N.

Thus the

-Va when Vu

The sign bit

in another b,ay. In an (n+1) bit system, negative

most significant bit) of 1, and the remaining n

representation of the positive quantity (2n+m);

bit of 0 and the remaining n bits form the natural

nrodification of the'input voltage V6 should produce an output of

'is positive, and an output of (-4vo1ts -Vu) when V1 is negative'

should be a 0 for v1 positiven and a 1 for vu negative.

6.42 The Voltage Comparator Circuit

If an operationa'l amplifier is to be used as a comparator, the output of

the digital-to-analogue decoder can be connected directly to the null summing

junction. If the input voltage range is to be tVr.r, then the modified input

vo'ltage should be connected to this same iunction via a resistance of R (=lKO),

since this is the output resistance of the ladder network. The gain of the

operational amptifier should be sufficient for the output to swing between high

and low t.t.l. 'levels (+4 volts * 0 vo'lts) with a change in 'input voltage of

15.6mV, j.e., the gain required is at least 250. The response time of the com-

parator is also important, since it wili probably determine the overall operating

speed of the analogue-to-digital converter

A comParator circuit was designed

inexpensive 14C1439G integrated-ci rcuitis shown in Figure 6.6.

The closed looP gain has been set

to meet these requirements using an

operational amp'lifjer. Th'is comparator

010,r, | ,r;101 | 110

N

zn+1+N

Bi naryCod'ing

to 1000 by the 1140 feedback resistance'

Page 139: 2-Whole-digital Data Processing in Radio Astronomy

132,

and d sipvolt Eener diode connected from the output-lag tei"rnil'nal to g'round

restriets, the output uoltage to the range +5 volts to -7 volts, per,rnissible

ex.eursions for t,t.l. clrcuits. Figure 6.7 slows inp-ut and output oscilloscope

trages for this circuit when driven by a 15.6mt/ peak-to-peak s.quare wa\re. The

output takes apprbximately 5 pseconds to swing from a logical 0 to a logical 1

when the input changes f,rom +7.8mV to -7,8mV.

Modif iedlngut

Loddar0utput

Figure 6.6i The voltage comparator cirrc,uit

LogicOutput

Figure 6:,-7i

and

(a) The 15.6mV peak-to-peak sqqare-wave'input'(b) the +5V to -2V output waveform.

T:he time-.base'is Susec/dJvi sion.

Page 140: 2-Whole-digital Data Processing in Radio Astronomy

133.

6.43 The Sign Determination System

The sign cleterm'ination system must perform tlvo basic functions; (i ) the

decision as to wlrether the input Vu is positive or negative, and the generation

of the appropriate sign bitn and (ii) as a direct result of this, to modify

the input voltage in the mdnner specified in sectjon 6.51, i'e', to produce an

output of -Vu when V. is pos'it'ive' or an output of -4 volts -Vu when Vu is

negati ve,

A comparator

to determine the

the correct form

is sufficient to

circujt of the same form as shovrn jn Fjgure 6.6 has been used

sign of the input voltage. The output of this comparator is infor a two's complernent sign bit, and its sensitivity (t7.BmV)

g'ive a definite output level for all input voltages of interest'

The overall sign determination system is shown in Figure 6.8. The sign bit

is used to drive a switch, of the same type as used in the decoder, through an

inverter* to give an output of +4 volts t'then the input is negative' and zero

volts when the input'is posjtive. This voltage is added to the input voltage vu

in a unity gain invert'ing ampljfier, urhich produces the desired modified output'

The operation of this system for an'input bipo'lar sjne wave is illustrated in

Figure 6.9.

6.5 The Progranrmi nsr Log j c

The requirements of the programming logic can be assessed by considering

the operation of the converter. In the followjng description the response time

of the comparator is defjned as T. The comparator output is high when the ladder

voltage is too snrall, and jow when the ladder voltage is too 1arge. The sequence

of the conversion process can be described as follows.

1. 0n the recejpt of a sample command the m.s.b. of the ladder is set to a 1

and all others to 0.

Z. After an interva] of at least T,'if the comparator output is low then the

m.s.b. is reset to 0; if the comparator output is high, the m.s'b' is leftat a 1.

3. The n.m.s.b. is set to a 1.

4. After an interval of at least T' if the

is reset to 0; if the comparator output

comparator outPut is low this bit'is high then it is left at 1.

is given in APPendix B.* A l'ist of 1og'ic symbols used in this thesis

Page 141: 2-Whole-digital Data Processing in Radio Astronomy

lMn

r34.

+4v rali

lnputvq

Sign Bit

Output toCompor.qtor

figtt,re 6.8: The sign determinatio'n system'

vo

+ l+v

Figur:e 6.9,: The_openati6n ot.the sign de'termination system foran input sinusoid-

-6vs[Fbrt+5v

Page 142: 2-Whole-digital Data Processing in Radio Astronomy

135.

5. Steps 3 and 4 are repeated for each bit until theleast significant bithas been set and verified.

6. An end-of-conversion messaqe is transmitted.

The programming system of a successive approximation analogue-to-digital

converter usual'ly incorporates a flip-f1op data reg'ister to store the finaldigital word, and to supply this word in paralle'l form to the digital-to-analogue

decoder. Cjrcuitry to generate the contro'l signals is also required, i.e., to

set each bit in the data register to 1, test the magnitude of the resultant

decoder vo'ltage, reset or leave this bit, and pass on to the next bit (Hoeschele,

t96B). This control or'strobing'circuitry'is usually based on either a counter

or a shift register. Counter strobing genera'lly jnvolves a higher component

count than shift register strobing and for this reason it was decided to use a

programmer based on the latter principle.

The logic system developed to perform the programming is shown in Figures

6.13 and 6.14. A detailed description of the operation of this system is given

in section 6.53. In order to clarify this description, the function of the

word-'length switch must be explained, and the properties of some of the logic

elements establ ished.

6.51 The Adjustable Vlord Length Facility

In addition to the features specified for the converter, facility has been

provided in the logic system to reduce the output word length from the maximum

of nine bits to seven or five bits jf desired. Th'is reduction in rvord length

is accompanied by a corresponding decrease in aperture tinte, a feature which

would be an advantage in pulsar sjgnal averaging (see section 6.17) where high

sampling rates would be required at a reduced resolution-

The word length switching is achieved by terminating the conversion process

after the fourth, sixth or eighth bit of the ladder network has been set and

verified. If the unused bits of the ladder are 0 then the total resistance of

the unused portion of the ladder to ground'is 2R, the correct termjnating resist-ance.

6.52 The Properties of Some Logic Elements

The converter has been designed using a positjve log'ic representation, i.e.,a 0 corresponds to the low voltage 1eve1 and a 1 to the high voltage 1evel. The

ladder network operates from negative logic levels however (0 corresponds to the

It

Page 143: 2-Whole-digital Data Processing in Radio Astronomy

high level and I to the'low level) and the inverted

data register must be available to drive the ladder

136.

s.tate of each bit in the

swi tches .

The fol'lowjng three elements are of particular interest in this chapter.

(a ) The master-sl ave J-K f'l i p-f I op

The FJJlll master-slave J-K flip-flop used in the programming systern is

shown symbolically in Figure 6.10a, and its truth tab'le is given in Figure

6 .10b.

c(o) (b)

Figure 6.L0:(a) The FJJ111 master-slave f'lip-flopand (b) its truth table.

J

I

K

The flip-flop accePts data from

(T) is high, and the resultant Q and

A 0 applied to the S inPut sets Q to

applied to the C input sets Q to 0.

(o)

Figure 6.11: (a)

and (b)

the J and K inputs when the clock input

Q appear at the outputs when T goes low'

1 irrespective of other inputs, and a 0

( b)

FJJ131 tYPe D fliP-f1oPtruth table

(b) The type D flip-flop

The FJJl3l type D flip-flop is shown symbolically in Figure 6.11a and'its

truth table in Figure 6.11b. Data is transferred from the D input to the output

Q when T goes from 0 to 1 (positive-go'ing transition). The S and C inputs per-

form the same set and clear functions as with the FJJl1l.

Tto* - Thigtr

Dn Qn*,

0 0

1 1

The

its

Ttrigtr -+ Tlo*

Jn Kn Qn* t 0n*'

0 0 Qn 8n

1 1 qn Qn

Kn fn Jn Kn

Page 144: 2-Whole-digital Data Processing in Radio Astronomy

137.

(c) The capacitively coupled gate

If a logic driving source is capacitively coupled to the input of a t.t.l.gate, the output of the gate responds only to the neqative-going (1*0)

transitions of the driving source. Under steady state condjtions the output'is0, imespective of the input. hlhen the'input goes from 1to 0, the output

momentarily goes to 1, then reverts to 0. The actual circuit configuration and

operating waveforms are shotvn in Figure 6,L2.

vin --l Vout

vx

(b)

a_rFD-' :lD"-.Q = 64 + dB

(c)

., ,ii i]vout ll lL-

-----_-o-

Q:64 Q: 6A* e

Figure 6.12: (a) The capacit'ively coupled gate

( b ) 'i ts operati ng waveforms

and (c) its synhrolic representati0n.

The length of the output pulse is determined by the capacitance C, and

will be written in the logic diagram (see Fjgure 6.7?c) alongside the capac'itor

as T microseconds. The three forms shovln in Figure 6.1.2c a1l appear in sub-

sequent circujt diagrams. The iogic statement 6X is taken to mean a G'l

transjt'ion af X, i.e,, Q=6A impf ies that Q 'is a 1 for a G'l transition of A

and a 0 at al I other times.

6.53 A Detailed tjescriptjon of the Programmer Operation

In the descript'ion of the programming unit it rvill be necessary to refer

to the output states of specific logic elements. If the output of the specified

element is not a labelled system output, then jt will be referred to by the

reference code for that element, shown on the relevant d'iagram (e.g., Gro refers

to the output of gate Groi the Q output of flip-f1op Ds vrill be referred to as

Ds, the Q output as Du).

Page 145: 2-Whole-digital Data Processing in Radio Astronomy

138.

C LOCKIN

SAMPLElN(

cil,,

ciz

st,se

Do

Figure 6.13: The control wavefornt generator for the

analogue-to-digital converter programming logic'

Figure 6.15 shorvs the timing diagram for the programming logic (Figure 6.14)

and jts control waveform generator (figure 6.13). The vrord-length switch is

taken to be in the seven bit position; s'ix bit reso'lution is required of the

programming logic-dig'ital-to-analogue decoder system, the remaining bit being

supplied by the sign deternrination unit. The input voltage Vu is assumed to

be such that the fina'l digital output, excluding the sign bit is 011010'

i.e., vi = -4x (26/oq t I/na)

The timing of the system is controlled by a 100KHz square wave clock (see

Figures 6.13 and 6.15). This is used to generate two internal clock waveforms,

CAt and Cgr. Cp, is a 100 KHz repetition period lusec pulse waveform with

a rising edge corrbsponding to that of the input waveform. C,Z is a 100KHz

square wave r.lith a rising edge corresponding to the fal'l'ing edge of the input

waveform; the rising edge of cgz occurs 5psec after the rising edge ?t.tqt'

Cgt is supplied to the trigger inputs of the eight J-K flip-flops r'rhich form

the data register (Rr*8in F'igure 6.14). These fl"ip-f1ops contajn the output

digitai word at the end of the conversion. Data appearing at the J and K inputs

of these flip-flops during the lusec high period of Cpi wi1'l be transferred to

the outputs tthen Cp1 returns to 0. CgZis supplied to the trigger inputs of

the eight t.vpe D fl;p-f1ops (Dr*a in Figure 6.14) wh'ich form the strobing

register. Data appearing at the D inputs prior to the G>l transition of CgZ

will be transferred to the outputs duling this transition.

Page 146: 2-Whole-digital Data Processing in Radio Astronomy

139.

c.9

>ytob!ccouJo

E-l-tl!

a,CL

F ()ln('lo-ooq- o)

l-.3 .=El!E(U

,-t !c'to!o(Dfrd3l.(u

c..ot,

=-i +rtr.'r (t)

.Fx.Yao +tInc)o-5o (ttnotr

cL(d

t!.!

:<Er-- t-

olot

E rrlr.ol

I

olr-l5lctl.rl

LLI

IhtrJz

I

EttlooJ

oF

IaF-

ILF

oI

I

I

I

I

I

I

friu'l

= anF)o-F

oJ

F

0o

.rs,;Lro6.d:

ILooEoU

(Dtti,J

I

I

I

I

I

I

I

I

:.&,o=

GT

=t(n

ooE-(J (4

Page 147: 2-Whole-digital Data Processing in Radio Astronomy

14{.

Glocklnput

cg,

ct,

SompteInput

Grc

st sz

Do

Ccmpor-qtorr

R1

D1

D€

G,

End ofConn

Tirne

,1 rI

II

If

III

tI

R2

o2

R3

03

&

D4

ts5

Ds

Rc

06

loIItI

t5 tg' t1 t1 t2 t3 t4 t5 tA tv

Figure. F,15: Tfrning diagnam f,or.the_analoEue-to-digitalcon;r/erter programming logi c.

l!

Page 148: 2-Whole-digital Data Processing in Radio Astronomy

141.

A conversion is initiated by a &nl transitjon at the sample input (Figure

6.13). When this transjtion occurs, the RS flip-flop formed by Grz dnd Grs is

set, and the sample instruction js stored unt'il the next G'1 transition of Cgt.

Grr is then reset to 0, and a 2Usec reset pulse Sr, Sz is generated by the

monostable multivibrator G:s, Grs. At this same instant the RS flip'f'lop formed

by Gre dnd Gzo is set, making Do a 1. If the sample instruction occurs during

the lusec interval when Cgl is high, then the instruction is not stored and the

reset pu'lse and Do are generated immediately,

Referring now to Figures 6.14 and 6.15, a sample instruction is received

at time tr. 0n the next G'1 transition of CgI, at time to, a reset pu'lse

Sr, Sz is generated setting flip-flops R2 to Re and Dr to De all to 0, and Rr

to 1. The Q outputs of Rr to Re are suppiied to the ladder slitches, and as R1

is the m.s.b., the ladder input is 10000000. The resultant ladder output of 2

volts is greater than -Vi, and after a short de'lay the comparator output goes

from its initial 1 to a 0, indicating that the ladder voltage is too h'igh. At

time t*,Susec after to, the clock Cp2 goes high transferrjng the 1 on Do to Dr,

and at the same instant, Do is returned to zero (tfre RS flip-floP Gre, Gzo in

Figure 6.13)

The J and K inputs to the data reg'ister flip-f1ops must now be examined.

Ignoring the presence of the word length control gates G2 and Gi, the J input

of Rn, where 2:n1B is Jn = Dn_l, and J1 is 0. The K input of Rn, where

1:n18 is l..n = Gr.Dn. At this time (t*<tctr) Rr and Dr dr€ 1's, R2*s and D2*6

are all 0. Gr, the inverted coniparator output, is L. The cument J and K states

are then

Jr = Jz = 1i Jr*, = 01 Kr = Kr*. = 0.

At time t1, Cp1 goes to 1 and lusec later returns to 0. As a result of this'with the J and K inputs given above, Rr Ftill return to 0, Rz will become 1, and

R.*, wi'|1 remain at zero. The ladder input js n0w 01000000 and as the resultant

voltage is less than -Vi, after a short delay the conrparator output goes from

0 to 1, ind'icating that the ladder voltage is too low. Susec after tr, a 0+l'

transition of C* occurso transferring the 1 at Dr to Dz, and returning Dr to

zero. At thjs time Gr js 0 and the J and K states are

Jr, Jz = 0; Js = 1; Ju+, = 0;

and Kr*, = 0'

Page 149: 2-Whole-digital Data Processing in Radio Astronomy

L42.

At time t2 another lusec pulse of C^ occurs, and as a result, with the J

and K inputs given, R3 go€s to 1, and al'l other R's remain in their Previous

states, i.€., R1 , Ra-+6 = 0 and Rz = 1. The digita'l input to the ladder switches

is now 01100000 and the resultant ladder voltage is st'il'l less than -Vt. The

comparator output rema jns at a 1 indicating th'is condition. 5psec after tz 'another G+l transition of C* transfers the 1at D2 to De, returning Dz to 0.

Gr is still 0, and the J and K states are

Jr*, = o; Jo = 1; Js*B =

Kr*. = 0.

Jr=Gr=Do=

and

After the next Lusec pulse of Cpt at time tg, dll R's remain at theirprevious states except R,, vrhich goes to a L. The ladder input is now 01110000'

and the comparatgr output goes to 0 indicating that the ladder voltage is too

high. Another G'1 transition of CgZ occurs 5psec after ten transferring the 1

at D3 to D,, and returning D3 to 0.

The word length control line Wr js 0, so G+ = 1 and Gz = Dq. As Gr is now

I, the J and K states are

and

Jr*u = 0i

Kr*, = 0; Ku=Do Gl=

Ja*, = o

Ku*, = 0.

t,,n R1+3 dld R.*, remain at

to 1. The ladder inPut isjndicatjng that the ladder

transfers the 1 at D+ to Ds

[' states are

As a resu'lt of the lusec pu'lse of Cgt at time

the'ir previous stateS, R,, returns to 0, and R5 $oes

now 01101000 and the comparator output returtrs to 1

voltage is again too low. A 0*1 transition of C'92

and D,. returns to zero. Gr is now 0 and the J and

Jr*s = 0; J, = D, = 1; JrJ,=o

After the next f.irsec

previous states except R5

comparator output goes to

the G'l transition of CgZ

to Ds and Ds returns to 0.

and Kr-r, = 0'

pu'lse of Cpf at time ts, allwhr'ch goes to 1. The ladder

0 indicating that the ladder

which occurs 5usec after ts'

R's remain at theirinput 'is 01101100 and the

vol tage i s too hi gh . l^lj th

the 1 at Ds is transfemed

Page 150: 2-Whole-digital Data Processing in Radio Astronomy

The word length

As Gr is now 1, the J

143.

control line l,lz is l so that Gs = 0 and Ga = De 'Go = 0.

and K states are

Jr*e=0(Jz=Gs=0);

Kr*, = 0; K. = 1; Kz, K, = 0.

because of the 1*0 transition of D5. This is taken to

conversion process.

and

As a result of the lusec pu'lse on Cpl at time te, d'll R's remain at theirprev'ious states except Re which returns to 0. The d'igital input to the ladder

network is now 01101000, and the conrparator output returns to 1 indicating that

the resul tant voltage is too snrall. At time tr, Spsecs after tr, 'r,

aga'in

makes a 0-+1 transition. Ds returns to 0 and as the shift regilter phth is

broken by Ga1 D7 f€flldins at 0. HoweVer as [lJ2 is 1, then Gz = De.Wz = De d1d

hence

Ge=6dz+odr+6Da

= 6dz = 6ds

produces an output Pu1 se

indicate the end of the

As the J and K inputs to the data register and the D inputs to the

strobing register are now all 0, the programrner will remain in its present

state (01101000) until the next sample instruction is received, in spite of the

continuous intemogatjon of these reg'isters by their clocks C^ and CQZ'

During the conversion process, after a nev, dig'ital vlord is set by the

falling edge of Cpi, a settling tirne of gusec elapses oefore the resultant com-

parator output is-interrogated by the next CB1 pulse- In view of the 5usec

response time of the comparator, this period'is amp'le to ailow Lhe comparator

to indicate its final state.

A sequential truth table for the fjrst six bits of the data register

throughout the operation iust described is sltown in Table 6.3' From the state

of the comparator and the control register at time tn-, just before the pulse

of Cpt at time tn, the resu'ltant J and K inputs to the data register are cal-

cu'lated. As a result of these inputs, the R states are shovln for time tn+'

iust after the Lusec pulse of Crt at time tn.

If both 14r and lolz (the word length control ljnes) had been 0' then the

conversion prgcess r,rould have contjnued until Re had been set and verified'

Page 151: 2-Whole-digital Data Processing in Radio Astronomy

L44.

q)g

+)(I,-cPg

=o-c.nCo+,16!rr,C, r-looro(U(u-cLP= (t)t-'Fol!iF

rF(uo-oE(o(d{Jl- g)-c .6{J.F-pLP

rtr

.lJ

c)

=C'(uv)

n(o(u

-ordF

i!d.

o@O

>44 (9to u)

DO

o O

c)

O

o

O

o

o

O

o

o

o

O

-l

o

r-l

o

H

o

n&

rattov: ahs

DO

o o

O

O

o

o

o

o

o

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r<

o

r{

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r{

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'oyr(.'

50-) Cf,

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do>l: (5

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c>

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r4

o

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or-l

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F{

o

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ooO

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o-=o(J

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r++,lJ

r+NN

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t+PP

t++)P

r+on+t +-)

t+@@

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Page 152: 2-Whole-digital Data Processing in Radio Astronomy

145.

and the end-of-conversion pulse would have been generated by the 1+0 transition

of D6 (Onr). (R, would have been set to a I as a result of the Crt Pulse at

time te, and the I at Do would have been transferred to Dz).

If l,lr had been l and l,l2 0, then the conversion process would have been

terminated after R,* had been set and verifiecl. The CBt pulse at time t,. "'JoulC

not have set Rr to I as Jq woulcl have been 0. The end-of-conversion pulse vrould

have been generatecl by the 1*0 transition of Da. The resultant digital vrord

would have been 0110C000.

hlith a 100tiHz clock input the converter has an aperture tinre of B0psecs forg-bit resolution, and 60 and 40usecs for 7 and S-bjt resolution respectively.

The r,uximum jnterval bet1een the receipt of a sample command and the despatch

of an end-of-cottversion nlessage is 89Usec,69psec and 49Usec for 9-bit' 7-bit

and 5-bit resolutjon respectively.

As a result of the fjnal operation in the convers.ion process described'

that of setting the sjxth bjt to a 1 and returnjng it to zero, the converter

has determ'ined that the vo'ltage corresponding to the sjx-bit word 0110i1 is

greater than -Vi (Vi js tlre nodjfied input voltage, see section 6.43) and that

the voltage corresponding to 011c10 is less tlran -vi. Thus the final digital

output represents -V.i to t'rirhin +4/64 volts and -0 volts, rather than the

x4/LZB volts predicted. Th'is apparent deviation is a characteristic of any

discrete comparison ana'logue-to-digi tal converter (lloeschele, 1968) .

This devjation has been corrected by setting the comparator switch level

one half quantum level above zero vo'lts. The effective atralogue'input to tlte

comparator is then -(Vi * 97r) vo]ts, and the final ladder input represents

this voltage to within +o or -0 volts, i.e., the ladder vo'ltage represents -VI

to within t97, volts. As the quantum level q changes witlr word'length, the

comection ltas been appljed for tlie nine b'it case only, tnthen Q = 15'6mV' Thjs

has been achieved by connecting the comparator input to the -15 volt supply via

a resistance of 2i4CI.

6.6 The Input Anrpl'if ier

The basjc sensitivity of the converter, at the input to the sign deter-

mination unit, is t4 volts full sca'le. Ampljfication is required to increase

this sensjtjvjty to the specified ranges of t400nV anci r100nrV full scale, i.e.,gains of 10 and 40. The input res'istance of this amplifier must be greater than

100Kn and the drift at the output should be much less than !q/2 (r7'BmV)' Such

Page 153: 2-Whole-digital Data Processing in Radio Astronomy

146.

s,pecifieations are nst easily met by cjrc,uits. u.sing inexpenrsive integrated-

cifcuit, operational amplifiers such as the Metrffi9G available. F:inite input

bias currnents (-XuA) sr input offset cuments are tlle most troub:l,esorne

deviation from the ideal in these amplifiers. The de-'sign of an input amplffier

'based on one of thes,e units req,uires a carefu''l consideration sf the effect of

input offset currents on its perfornance.

6.61 Input 0ffset CurFsnt Consideratlqls

The typical externa'l circuit arrangement sf a

amplifier is shown in Figurre 6.16' witli all input

conditisns the amplifier draurs offset currents of

differrential i nput o;Perational

voltages at zero. Under the'sre

Ir and Ia.

Figure 6.1,6: Externa'l cronnections for a differentialinput oPerationa'l amPl ifien

If the amplifier has an open-'loop voltage gain A then

Vn = A(Vz-Vr) (6.3)

ulhey'e

and Vz = -IzRa

SUbstitr.rting these values of Vr and Vz into equation 6'3, and assuming

A>>l*Rs r., , then/nl

vo + IrRa - IzRa [t - *:]

V1 = RrR'r

RrtRa

fvo

t-, - r,]

(6.4)

thefr effecteqrual to

UsualI;r the inpu,t offset currents are practically equal' and

can be d'lliminated hy making the parallel cornbination of Rr and R3

nrofR, = R, ,t - *tJJ .t

Page 154: 2-Whole-digital Data Processing in Radio Astronomy

147.

5.62 Tlre V,oltege-Follower Csnfiguration

As the amplifier is requirred to be non,-inverting, it was decided to urse an

opeyational amplifier in the voltage follower configurdtion (see Figure ;6.1,7).

This mode ls charaeteri:sed by a very h'igh input impedance and a very low out'put

impedanee.

Figurt 6.171 The voltage follower configuration.

Beferring to Figu,r'e 6.17, the galn of the feedbaek pa,th is -Rr/(Rr+R3},

frorn the basi,c theofV of f€edback amplifiers (fitchen, 1966), provided A>>

[nrtn3]/Rr, the closed-loop gain 46 wi]I be

n.=H=

and the input resistance Rip wlll be

,-fii (6.5)

Rin = Rin(o) [t - *'.J

where, R1p(l0) is the opan-loop input rresistance. For the MC1439G' Rin(0)-100KS]

and A-50,000, which for a gain A* of 40,results in a theonetical valu'e of

Rin = lz5.Mfi, Rin is actually limited to lower values of rnesi,stance by intennal

cottsiderations (Eimbinder, 1969),but is typically greater than 40[&.

, The outpu't resistance in th,is mode, Ro, w'ill be given by

Ro = ##A.

where Ro(g) i,s the open-loop output resistance. The I'1C1439G has a typical o'utput

resistance of 4l$, yielding Ru = 3.20 for a gain As of 40.

Page 155: 2-Whole-digital Data Processing in Radio Astronomy

148.

Provided that the source res'istance r, is much less than Ri;', the vo'ltage

Vz cdh be taken as equal to V' and the gain of the ampiifier is unaffected by

the source resistance.

Flaving estab'lished that the circuit of Figure 6.17 vrjll produce the gain

and input impedance requ'ired, it is pertinent to examine the effect on its per-

formance of the input offset curents. In equation 6.4, Rz is noll ry and ifthe anrplifier is to be used with various source'impedances, then the condition

that

R'=d#

cannot be met. llorlever if Rg is kept constant, the effect of Ir will be to

produce a constant output voltage, which can be accounted for by an offset

voltage applied to the input. If r, is to vary, the on'ly way the resultant

variatjon in Vo can be e1inrinated is to reduce Iz to zero. This can be

achieved by'injecting a constant current equal to Iz into the non-'inverting

input of the amplifier.

6.63 The Des jgn of an Input__.tAtttpl if ier

The input amp'lifier designed to meet the requirements is shorvn in Figure

6.18. Six different gains are available; 1, 2,5, 10,20 and 50' giving a

range of full-scale sensitivjt'ies from t4 volts to t80mV. The input impedance

is set to 1l''10 by the resistor Rr r drd a constant-current source is used to

provide the bias current for the non-inverting'input, making the offset voltage

independent of the source resistance. The feedback resistance R: is kept con-

stant at 10Kfr as the gain is changed by switches S. and S.,making the offset

voltage due to the bias current flovring through this resistance constant' s0

that it can be eliminated by the'input offset voltage control Pr.

Details of the constant current source 15 are shown in Figure 6.19. By

keeping the base resistance small compared with the emitter resistance, the

collector current I, is maintained at a constant value l'lith variations in the

trans j stor parameters .

The values of the ga'in settjng resistances Rz, Rs, Rror Rzo and Rso (pjgure

6.18) are determjned by relriting equation 6.5 as

Rr=uh

Page 156: 2-Whole-digital Data Processing in Radio Astronomy

t49.

s3Rs.

Vout

Figure 5.18: The inPut amPlifien

+ 15v

tsc178

lsl

Figure '6..-19: The constant current sourc€'

The calculatedr vallfues for these resistances iire shown

Is'

in Table 6.4.

GAIN

RESISTANCE

l.

@

2

[0,000

,5

2'500

l0

I,111

50

526

z0

204

Teble 6.4: The Eain-setting resistance values

When drjven from a source of resjstance 30K0' with the gain set at 50, Pr

and P2 canr be adjusted unti'l the zero-leve-l outpllt drifts by only t2mV for

variations, of ternperature in the range l7-.?44C. l,lith these settings sf Pr and

Pz, fon changes in sourEe resistarnce from O'301(0, and for all gain settings'

the ze,rO-le.vel output does- hot vary Outside the range t$mV.

l0Mn

Page 157: 2-Whole-digital Data Processing in Radio Astronomy

150.

6.7 The Digital Output and Display

The parallel djgital output from the data register of the programming logicpersists between samp'les as specified, but is lost at the commencement of the

next sample. In order to provide a persistent output, even when the converter

is sampling continuously, it is necessary to transfer the data from the eight

data flip-f1ops (figure 6.14) and the sign bit into a buffer register on the

receipt of an end-of-conversion tnessage. At this tinre a flag should be set toindicate to the externa'l equipnent that the data is available. t'lhen the data

has been accepted by the external equ'ipment it is assumed that a reset command

will reset this flag to zero. The circuitry for this buffer, including the flagfaci'lity, is sholn in Figure 6.20.

I NPU

OUTPU TS - -

End of

Gga

Figure 6.20: The output buffer circuit.

The end-of-conversion 0*1 pulse from the programming logic is buffered by

Gso, Gsr drd Ggz and fed into the trigger inputs of nine type D flip-flops'Br*r'. This pulse transfers data from the nine inputs to the outputs, and the

outputs remain constant until the next end-of-conversion pulse. The end-of-

conversion pulse also sets the RS f11p-f1op formed by Gsg dnd Ggq, dnd F goes

to 1, and stays at 1 until il, an invented reset line, goes to 0.

If a sample is transferred into the buffer before the previous data has

been accepted, some indication of th'is data overf'low condition is required. A

Page 158: 2-Whole-digital Data Processing in Radio Astronomy

151.

cincuit designed to perfonn this function is shown in Figure 6.21a. If F is 1

(1.e., F is 0.) vrhen an end-of-cornrversion message is received' then 816 $oes to

a 1. As Br.q then goes to 0, Bro will remain at 1whe,n the next, end-of-conversion

occunseven if th,e flag F is 0. Until the 'overflox reset'switc:h S,, is elosed

when a'rr,eRd-of-conversion pulse oqcursn the data overflow indication 0F willpersi st.

0vaFronge

OR

S-g

Fo-o*'sv

(b)

to progrsrnmcrcontrol

. somple oir.lst ructlon

+5v

(cl

(a) The data overflsw indicator'(b) ttre data over ranEe indicatorr(c ) the manual samPl e faci'l i tY.

[* t'

v777'

Figure 6.?1:

and

An over'ra:nge indicaton and a manual sample-f nitiate contro:l have also

been providedn and the circuits of these are shswn in Figure 6.21 b and c.

When the output state 01111XXXX occurs (X can be either tr or' 0) then the RS

flip-f1op Gra, G3g is set, and remains set (0R=1) ur,rti'l the over-range reset

switeh Ss is closed. If 0R is l, then this indicates that at some previous

time the input wAs at 15/1,6 of its positive full'-scale value,

llhen the sample mode switcJt So (Figure 6.21c) is in the external position

Page 159: 2-Whole-digital Data Processing in Radio Astronomy

then the output of the sample

sample input. When Se is inshort l-pu1se occurs when Sz

delivered to the sample inputexternal functions.

152.

control uni t , Gq r fol 'lows exactly the extertla I

the manuai positionn G'.r is normallY 0' but a

is closed (Gu, = 6.Sz). This pulse is also

terminal, and may be used to trigger other

An additional requirement of the ana'logue-to-digita'l converter was for an

i ncandescent I amp di spl ay of the current d'igi ta'l output. Thi s di spl ay i s use-

ful when checking the system, and for ensuring that the dynamic range of the

converter is being utilized to its fullest extent. The discrete component iamp

driver shown in Figure 6.22 is used for this purpose.

Doto

Inhi bi t

+12v

Figure 6.22: The incandescent lamp driver.

Nine of these gates, driven by the outputs of the buffer register (F'igure

6.20) display the current digita'l output of the converter. By connecting the

nine inhibit lines to ground,the lamps are a1l extinguished in spite of the

data input states. Similar lamp drjvers are used to display the data overflow

and over-range states, 0F and 0R (Figure 6.21).

6.8 Mechanical Details of the Analogue-to-Digital Converter

A functional diagram of the completed converter is shown in Fjgure 6.23.

Details of its construction can be seen in Plate 2. The unit measures 7" high

x 4r4" wide x 12" deep, and occup'ies part of a 7" hi.gh standard 19" rack drawer.

The analogue input and the sanple input are available on the front panel,

together with the various control switches (Sr*z) and the incandescent display-

In add'ition, connections for monitoring the comparator output (serial digital

word), the s'ign b'it, the end-of-conversion pulse, the reference voltage and the

output of the input amplifier are avajlable on the front pane'|. The digitaloutput is via a 16-contact connector located on the rear panel. Power supply

connections, and the 100KHz clock input connector are also located on the rear

panel .

Page 160: 2-Whole-digital Data Processing in Radio Astronomy

153.

10Kn

1KnAnclogue

Input

oigitotOut pu t

Ftog

Sompte Input

C tock Inpu t

F'igure 6.23: The analogue-to-dig'ital converter.

Key: AS = analogue switch; C = comparator; A = amplifier.

The progranrning logic and digital-to-analogue decoder are contained on

two separate printed-circuit boards which are connected together by lateral

connecting pins to form a s'ing1e plug-'in unjt (Plate 2b). All of the analogue

circuitry,'including the reference voltage supply, except the input ampljfier'

is contajned on the decoder board. Two more plug-in printed-circuit cards con-

tain the output buffer register and the lamp drivers. The input amplifjer

circuit is mounted on a sntall printed-cjrcuit board alongside the gain srvitch

and the coaxial input connector.

Rr=

R:

Progromming

ond ControtLog ic

Page 161: 2-Whole-digital Data Processing in Radio Astronomy

I 54.

uc')og)

=to!ct)oLo.

^o-ct -s

-cr

Egro

og^|r'Lao,-POC-ovL

lFlo!Ec,o+, L'to(u€

sc,o=,g|uro.Fc.r tUEnl.e C)'gPtlO-+, ctIP

O.e5 ttl9)'FOE|l'Ttgg16CtOa.ELFO'gaCttt=

e ? iqt cfro f colne

ol s#

'i,

#ss

fro#fr

o.

5-o-vtllI

fto

-g-

.ttr lrlFJCL

C'

oo2f,1| Tt

{l::?:1:

Page 162: 2-Whole-digital Data Processing in Radio Astronomy

155.

6.9

The overall performance of the converter is best demonstrated by a measure-

ment of its'linearity. The threshold voltage for each of the 512 output states

was measured, and lvith a maximum and minimuni ordinate for each state, the zero-

based straight line of least mean-square-error was fitted to the resultant

staircase (see Figure 6.24).

Anologw

Input

Besl Fit stroightLine

Digitot0utput

o Meosured Ttreshotd Votucs

Figure 6.24: Ana'logue-to-digital accuracy measurements.

The mean quantizer step Qp was found to be 15.6953mV and the maximum

deviations of the measured staircase from the straight line were +12 and -10mV.

The overall accuracy of the converter is then +.3% to -.25/', not significantlyfan from the inherent quantizer error of x.2%.

REFERENCES

EIMBINDER, J. (ed.1, (1969): "Designing with Linear Integrated Circuits".(Wiley, New York).

FITCHEN, F.C. (1966): "Transistor Circuit Analysis and Design". (Van Nostrand'

New Jersey).

HEESCHEN, D.S. (1961): "Observations of Radio Sources at Four Frequencies".

Ap.J., 133 pp. 322-334.

-1

Page 163: 2-Whole-digital Data Processing in Radio Astronomy

156.

IISESCHELE, D.F. (fsu8): "Analogue-to-Eigital/D-igital-to-Analogue Osnversion

Techniques" . (t'li lelr, New York) .

LIM, J.C, (lgES): "Non-Uniformly Spaced amal/s of Directlonal Elements".

Ph.D" Thesis, Unive-rsity of Auckland

l,lANI{, R. (1968):,'An Integrated-circuit High-speed Analogue-to-Digital

,Gonverterl' . (te,x.as insttnuments Appl i cati'on Note') .

MgLAUGHLI'N, J.C. (1962):. "A Data DfgitizinE and Pro:cessing System for a Radio

Telescope". M.Sc. Thesis, Ohio State Univers'itJ'

MSLLARD, (tgOB): I'Integrated Logic Circuit Applieations, MuIla,rd FJ Ra'nge".

(t*'tutlard, London).

yARRALL, J.g. (lgOA): "A 42wt!z Radjometer Using t4etall 0xlde Field-Etfect

Transistors an-d trntegrated-Circuits"- M.E. Thesi's, Universlty o'f

Au:ckl and.

Page 164: 2-Whole-digital Data Processing in Radio Astronomy

157.

CHAPTER 7

The Generation of Solar and Sidereal T'ime Coordinates

For the majority of observations of objects outside the solar system'

sidereal time i s the rnost meani ngful coord'inate. The rel ati onsh j p bettleen the

position of a radiating source and the output of an interferometer as a function

of sidereal tjnre has been establjshed in Chapter 3. Hovrever for observations of

objects near at hand (€.g., the sun), the output of an interferometer has more

meaning if considered a function of universal or solar tinte. In Chapter 4 itwas specified that both solar and sidereal time should be available for storage

as coordinates to the interferometer output data, and that it should be possible

to control the acquisition process from either of these tirnes. The generat'ion

of time coord'inates is perhaps the nrost important requirement of the entire

system.

As the time coordinates are required in digital form for storage, and in

view of the present state-of-the-art of electronic digital clocks (Fisher and

Frank, 1965), the choice of a digital clock js obvious for the generatjon of

the coordinates. The numerous clock waveforms available from the dividing

chains of a digital clock would be invaluable jn the generation of the control

functions for the system.

preci se I ocal time-keepi ng uti 1 i z'i ng di gi tal techn-iques i nvol ves (1) a

standard frequency osci'llator, (2) some means of converting the oscillatorfrequency into the desired time indication, and (3) the use of standard time

signals (e.g., those broadcast by I'll,,lV and l,lWVH) to calibrate this indicator

(fisher and Frank,1965). These three functions will be specified by respect'ive-

1y the stabjlity, resolution, and absolute accuracy required of the coordinates.

7.1 Resolution, Stability and Accurac uirements of the Coordinates

It has been shovln that it is not necessary to record the tinre coord'inate

w1th every sample of the interferometer output, but only once wjth each block

of data, where a block is a set of a predetermjned number of samples- Hovtever

this block size will vary from one experiment to another, and may be as small

as one sample. For this limiting case the resolution required of the coordinates

would be determined by the sarnple interval . l,lith the sample interva'l specified'

7.5 seconds, a resolutjon of 0.1 seconds will be adequate.

Page 165: 2-Whole-digital Data Processing in Radio Astronomy

158.

One of the primary reasons for the development of the data processing

system is for use in averaging data obtajned over long periods of t'ime

(typically of the order of months) to produce considerable improvement in

signal-to-noise ratio. If, as specified, each of these sets of data'is to

correspond point for po'int to each other, then the clock must be stable over

the entire duration of the observations, or be ca'librated at sufficientlyfrequent intervals to ensure that any drift does not marr the results. Solar

or universal time can of course be caljbrated direct'ly from standard time

broadcasts, but sidereal time is not so readi'ly calibrated, and any ca'libration

must be made from a solar standard, the corresponding sidereal time being

obtained by ca'lculation. For this reason it was specified that the drift in

the sidereal clock should be sufficiently small that the clock does not require

calibrating more frequently than at monthly 'intervals.

The stability requirement of the sidereal clock js that the maximum

accumulated error over an interval of one month be of the order of one second.

This can be expressed as a'long-term stability requjrement of approx'imately7

t3 parts in 10 Although the stability requirements of the solar clock are

not as great, it is anticipated that jt wilt be of a similar design, and hence

of a similar stabilitY.

The absolute accuracy required of the time coordinates is not nearly so

stringent as the stability. Pos'itions of sources can be determined only

to within the resolution of the interferometer itself, and thus the absolute

accuracy need only be of the same order as the reso'lution of the clocks

(i.e., 10.1 seconds).

7.2 The Generatjon of Solar and Sidereal T'ime Inlg1yais

As a sidereal day'is 3m 56s shorter than a solar day, a digital clock to

give siderea'l time must be based on a frequency 0.27379% higher than the

frequency which would give solar tjme from the same system. Aithough the

obvjous method of obtain'ing this sidereal frequency vrou'ld be to use a specially

ground crystal (Co'|e,1968; Grimsley,1967), two sepanate high stabilityoscillators would be required for the generation of the solar and s'idereal

frequencies. An alternative method which requ'ires only a single oscillator'is to feed a reference solar-based frequency into two separate dividjng chains,

one of vrhich divides the input by 100,000 to give a basic solar interval, and

the other r.rh'ich divides by 99,727 to give a basic sidereal 'interval , accurate

to within 4 parts in 107 (see Chapter 3). If the reference frequency was lMHz'

both solar and siciereal time intervals would be available to a resolut'ion of

Page 166: 2-Whole-digital Data Processing in Radio Astronomy

159.

0.1s. As the sidereal frequency is actually 0.00004?i slow, the addition of an

extra 0.L sec pulse every 64 hours would improve the accuracy to 1 part in 10e

(Cole and Shimmins, 1971).

7.3 The Development of a Standard Frequency Oscillator

At the present state-of-the-art, frequency stabil'ities of up to 1. part in108 can be achieved with quartz crystal oscillators (Stratemeyer, 1964).

Available for use in this project was an obsolete l4arconj TME-Z frequency

measuring instrument which conta'ined a 5l4Hz BT quartz crystal unit in a con-

trolled,temperature oven. It was decided that if the desired frequency stability'(t3x10-t) could be achieved with this un'it, then it should be converted to

solid-state contro'l and used as the standard frequency oscillator.

7.31 Factors Affecting the Frequency of Quartz Crystal 0scillators

Factors affectjng the frequency of quartz crystal oscillators can be divided

into tvlo groups:- long-term and short-term effects. These effects may be caused

by inherent properties of the crystal itself, or by the associated electronic

circuits. Long-term frequency varjation in the crystal can be attributed to

aging and temperature variation. Aging is the result of temperature grad'ients,

structura'l changes, clranges of mass and stress relief . For vacuum encloseci BT

crystals, normally used in standard frequency oscillators, there is an initialaging rate of about 1 part in 108/day, falling off to less than I part in l0e/day

after a period of weeks.

Temperature affects the frequency of oscillations in that the natura'l

frequency js a function of tenrperature. For a BT crystal this function is para-

bolic in nature, with a positive maximunr, and hence a zero temperature coeffj-cient, at a temperature which can be placed practically anywhere in the usable

range, depending on the orientation of the quartz plate with respect to the

crystallographic axis (Gerber and Sykes, 1966). l,lithin t5oc of the turning

point in the characteristic, the grad'ient is typically

- tzxro-7 loC.

In addition to th'is steady-state temperature-frequency characteristjc,

crysta'l un'its shovr a great sens'itivity to temperature gradients. As well as

contrjbuting to the aging rate, temperature gradjents within a crystal, created

during transient temperature variations, cause frequency fluctuations much

greater than'indicated by the temperature coeffjc'ient. Typ'ica1 fluctuations

|,arl[jru*

Page 167: 2-Whole-digital Data Processing in Radio Astronomy

during trans'ient temperature varjat'ions are (Pustarfi, 1966)

160.

Lf _ z.5xL0-e/oc/hr.a-

L.J J.lr I vlttl

Considerations of frequency fluctuations arising from thermal noise and

driving cupent noise are not real'ly necessary un'less stability over very short

periods (<lms) is of interest. Hor^rever, as the aging rate of a crystal isincreased at high driving currents (Gerber and Sykes,1966) and similarly the

driving current noise (si2), and the thermal noise is inversely proportional

to driving 1evel, jt has been found that driving currents of the order of 50uA

lead to the best compromise (Gerber and Sykes,1966; Pustarfi, 1966; Felch and

Israel,1955). At this level the thermal noise arising in the crysta'l over a

period of 0.ls (the shor"test period of interest) gives rjse to fluctuations of

the order of Aflf = 10-12. A variat'ion of driving level of 1dB at 50uA pro-

duces a fluctuation of Lf/f - 5x10-10 (Stratenleyer, 1964).

Variations in oscillator load can also produce frequency fluctuatjcns in

crystal oscillators, even when isolation between the crystal and the load is

high. These effects are caused primarily by pick-up of the output current in

the oscillator circuit. If the induced voltage and the oscillator vo]tage are

not ejther exactly in phase or in antiphase, then changes in the output current

will produce a phase shift in the circuit which must be offset by a shift infrequency. tlith 4OdB of isolation between the output and the oscillator this

effect can produce frequency fluctuations of up to 0.5x10-8 for large load

variations (Stratemeyer, 1964).

For a stability of 3x10-7/month, the specificatjon resulting from these

considerations can be summarized as follows:

1. The effect of aging should not be significant if it is kept to its expected

value of 1 in l0s/day.

?.

3.

The temperature of the crystal wi'11

at a temperature within soC of the

frequency characteristic (-60oc) .

have to be maintained to within tl.5oC

turning point in 'its temperature-

The maximum rate of change of temperature within this environment should

not exceed 1oc/min.

4. The driving current should,be of the order of 50uA, and should be maintained

to vlithin tldB of this level.

Page 168: 2-Whole-digital Data Processing in Radio Astronomy

5.

161.

Isolation betlveen the oscillator and the output should be at'least 40dB'

even though the unit will normally be operating into a constant load'

TME-Z oscillator in its opiginal form had a stabifity of i part'in

decided to convert it for use in th'is proiect.As

10', i tthe

was

The TME-2 oscillator is based on a SMHz BT cut plate supported in an

evacuated glass bulb by four springs attached at the points of least motion.

The temperature-frequency characteristic of this crystal has a maximum in the

vicinity of 600C. The crystal, together w'ith a circuit for coarse frequency

control, is contained in an oven which consists of two heavy metal cylindricalpots bolted together end-to-end and heated by a 1000CI non-inductive winding on

the outer surface. The temperature of the oven is sensed by a copper-eureka

bridge. When the oven is at its correct temperature the brjdge is balanced;

when the temperature falls slightly, the resistance of the copper arm fallso

while that of the eureka arm rema'ins practical'ly constant. In the original

system the error voltage from the bridge was antplified and used to trigger a

thyration, rvhich controlled the heating element in an on-off fashion.

7.32 The Temperature Control System

Because of the rather lrigh temperature gradients and inherent fluctuations

of on-off temperature controllers (Kenreny and 0lthoff, 1968), it was decided to

convert the oven to a proportional control systern. 0n1y the original sensing

bridge and heater element have been used jn this nrodified system.

Measurements conducted on the oven shoyred it to have a single dominant pole

with an associated time constant of 180 ntinutes. The therrnal resistance of the

oven's insulatjon was found to be 2.96oc/watt. The input porver Ps requ'ired to

maintain the oven at TooC when the ambient temperatu:e is TuoC'is then

Po = *# watts

For To = 600C and Tu = 20oC, a steady-state po\,/er input of 13.5 rvatts is

then required, or for the 10004 heater element, a voltage of 116V rms.

If the oven is equipped rvith a proportjona'l temperature contro'l system with

a ga'in of K vratts/oC, i.e., the powelinput to the oven iS P = Po -KAT' where

ATo is the deviation in oven temperature from To, then for a step variation of

ambient tentperature ATu, the resultant time variation of tlte oven tenperature

vrill be

Page 169: 2-Whole-digital Data Processing in Radio Astronomy

tr.]

162.

(7.1)mo(t) = ,flg* [r-.-(t+z'gor)

where t is the oven time constant.

Measurements taken in the laboratory environment, where the equipment isto be used, over a number of weeks shor,led variations of temperature to be inthe range 20t5o0. However, in the design of the system a variation of tl0ocwas used as a $torst figure, in order to take into account extremes which may

occur during heating failures, or in mid-summer. For these variations it t,ras

decided that the crystal temperature should be kept to within 10.Loc of itssetbmperature, in order to keep variations to a minimum. For these conditions,the gain required of the system is

K > 33.4 rvatts/oC

A simplified diagram of the control system designed to meet these requ'ire-ments is shown in Figure 7.1.

ForwordRegutotion

Steody-StoteOffsct

f zgo" ton,

Figure 7.1: The temperature contro'l system for the

crysta'l oven.

The sensing bridge is supp'lied with a mains derived 50Hz 2.5V r.m.s.voltage, and the resultant emor signa1 , 1.625nrV/0C, is amp'lified by amplifierA and rectified in a phase-sensitive detector. This type of detection isnecessary in order to establish the sign of the error (Sigdelt, 1968). The

\

-5v

nsrt rveTrigger

Page 170: 2-Whole-digital Data Processing in Radio Astronomy

163.

ortprt is positive when the oven temperature is'lovl, and negatjve when the

temperature is high. This control voltage is then added to a 50Hz ramp signal,

together with an offset voltage and a forward regu'lation signa'I. The resultant

sum, which is an offset ramp, is used to trigger a Schmitt trigger circuit, the

output of rvhich controls the gate of a silicon=controlled rectifier. This

s.c.r.applies a 220Y r.m.s. 50Hz vo'ltage to the oven heater for a portion of

a half cycle. Representative waveforms are shown in Figure 7.2.

Romp

Qrtput

Adder

0utput

Triggcr

0utput

Heotcr

Vottoge

Figure 7.2: Temperature controller waveforms

The resultant poler delivered to

Px=

the heater for a trigger ang'le x is

(n-x + ]'"sinZx) 0.r)v2'rms2riR

heater.where R is the resistance of the The maxjrnum power input to the heater

Page 171: 2-Whole-digital Data Processing in Radio Astronomy

is then 24.2 watts and under steady-state conditions (Ta = ZOoC) the oven willbe running at approximately half power. Figure 7.3 shows the relationship

between heater power P and trigger ang'le x. Because a linear ramp is used to

generate the trigger signal, x is proportional to the control s'ignal, and

Figure 7.3 also shows the relationship betureen error temperature and power

delivered to the heater.

Figure 7.3: The relationsh'ip between the trigger angle

and the output power for an s.c.r.

Schemes have been suggested for the removal of the non-linearity from this

relationship (Nalesani,1969) but as the normal operating point is near the

centre of the range (x + gOo) where the relatjonship is essentially linear'this non-linearity is not considered detrirnental to the operation of the system.

164.

limit the rise ofa manufacturer's

The function of the inductor L (lmH)'in Figure 7.1 iscurrent in the heater. The choice of this value was based

design figure (Zinder, 1967).

to

on

As both the eryor voltage and the heater vo'ltage are mains derived, fluc-

tuations in the mains voltage will have a two-fold effect. The error voltage is

proportional to the mains voltage, and for a particular error voltage the error

input power AP js proportional to the square of the mains voltage. Thus the

gain K of the system can be cons'idered to vary as the cube of the mains voltage.

These variations rvill not be significant provided the error is small. The

second effect of mains voltage fluctuations is that on the steady-state power Po.

Page 172: 2-Whole-digital Data Processing in Radio Astronomy

165.

As this is derived from a constant voltage input to the adder, its variations

are proportional to the square of the ntains voltage. A change APo'in Pe willproduce a change ATo in the steady state temperature of

^T - APoa'o - *

To offset this effect, forward regulation has been used (Kemeny and 0lthoff'

1968). A sma'll negative voltage proportiona'l to the mains voltage is obtained

from the bridge supply and added to the control voltage (see Fjgure 7.1). A

drop in mains voltage will then be accornpan'ied by an increase in control voltage'

and by careful adiustment of potentjometer Pz, the heater power for zero error

(po) can be made to remain essentjally constant for mains variat'ions of t10%'

A gain switch on the error amplifier enables the gain of the system to be

set to Z00f{/0C , Z}ll/oc and 2l,l/oC. it was found that it was necessary to use low

ga'ins when starting the oven from cold because the large error signals tend to

saturate the system. In addjtion, the switch S.,, (Fjgure 7.1) enables the full

cycle of the 220V signai to be applied to the heater (-SO vratts) for rapid

heating from cold. A fourth posit'ion of the gain switch al'lovrs the amplifier

emor input to be set to zero,'in order that P1 dhd P2 may be adiusted for the

steady-state condi ti on.

A meter M, calibrated in oC deviatjon,phase-sensitive detector. Thjs meter has a

i s connected to the outPut of the

full scale deflection of t0.05oC

when the ampl ifier is set to maximum gain (200t'l/oc).

As the oscillator has been des'igned for stability over periods of months'

and as the present power failure rate in the laboratory environment is less than

l/year, provision of an emergency power supp'ly to take over in the event of a

power failure vras deemed unnecessary. Design of an emergency supply would have

been complicated by the fact that the system is dependent on 50Hz voltages'

7 .33 The Oscillator and Automatic Gajn lqtolIn the nrodificatjon of the oscillator circuit, no attempt vtas made to alter

the conf.iguration of the orig'ina'l feedback network, wlt'ich contains the crystal

and coarse and fine frequency controls. The crystal and coarse frequency control

are conta'ined'inside the oven, the remainder of the feedback netvrork being

located jn a solid rnetal box adjacent to the oven. The vacuum-tube amplifjer'

which together vrith this feedback netvrork formed the original oscillator c'ircuit'

Page 173: 2-Whole-digital Data Processing in Radio Astronomy

166.

has been replaced by an integrated circuit cascode-configuration amp'lifier with

automatic gain control facility (see F'igure 7.4)

5 MHz0utput

Figure 7.4: The 5MHz osci I I ator.

The oscillator signal is ampfified in two stages. The output from the firststage is rectified and used to control the gain in the osc'i'llator, maintaining

a constant drive level of 60uA in the crystal. The second ampfifier stage'is

an output buffer, which also has automatic ga'in control to provide a constant

output level for a rnride range of 'loads. The output voltage is approximately

2 volts peak-to-peak.

7.34 T.he Performance of the Standard frequency 0scillator

The completed 51.'lHz oscil'lator unit, shown in Plate 3, is contained in an

B" h'igh, 12" deep, standard 19" rack-nourrt dravler. The door in the centre of

the front panel provides access to the coarse frequency control, and also to

a recess jn the overr wall into rvhjch a thermocouple nray be fitted for monitoring

the tempenature. The temperature emor meter and control switches occupy the

space to the right of the door, and the control circuitry and pol{er supplies are

located behind this meter. 0n the left-hand side of the oven'is the oscillatorunit and fine frequency control, whjch may be adjusted from the frontpanel with

the aid of a key. The 5MHz output'is availab1e at both the front and rear

panel s.

After an initial rvarm-up and aging period of tlvo weeks, the aging rate

fr . afJ

16 5-tJ

f inefreq.

cont rot

is less than 1 part in 108 per vreek, and random variations are less than t2 parts

Page 174: 2-Whole-digital Data Processing in Radio Astronomy

t67.

]'

.ti

,6,e

Lo+tG'

uthoagocroLEL.qEgtr6Poo

.G+trFo(l,gG'CL

+tgoL||o.8

;1lrJ I

EIdl

u

'E$E.nEt =iO

t.fll.'_tb

;Ifri

ilH9rtJt ;5;I sii, o

n

tll

0

rf-ti

Page 175: 2-Whole-digital Data Processing in Radio Astronomy

168.

in 10s. These measurements lvere made r,r'ith a Hervlett-Packard HP5245L counter'

which has an accuracy of 1 part in 10e after 36 hours; all measurelnents vrere

averaged over a ten second period. llithjn four hours of sw'itching on from

cold, the oven is stabilized to rvithin t0.010C of its set temperature for

variations in environment of up to t4oC.

The coarse frequencY

750H2; the fine frequency

for L80o rotation.

controlallows adjustments to be made over a range of

control al'lows for adiustntents over a range of 75Hz

7.4 Jhe Solar/Sidereal Digital Clock

The primary requirements of the time keeping system are that both solar

and sidereal times be available, in dig'ital form, to a r'esolution of 0.1' seconds.

The absolute accuracy requirements of these times (t0.ls) can be satisfied by a

direct comparison I'rjth locally received sjgnals of the standard time trans-

missions from t,lhrV. Additional requ'irements of this system are for a d'isplay of

the current sidereal and/or solar time (these displays can be combined ifdesired) and that the system should be capable of contro'l'ling the acquisition

process. For calibrating the tinre coordinates, a display of the instantaneous

time is essential (f isher and Frank, 1965). llol,rever because of the rapid changes

in an indicator of tenths-of-seconds, a visua'l disp'ld.v to a resolution of 0.1

seconds is not vrarranted, and a disp'lay of liours, minutes and seconds will be

adequate.

It has been established that the sanrpfing of the interferometer output must

be control'led by the timing circuits whjch generate the coordjnates. These

timing circuits must also control the storage of the quant'ized samples and the

storage of a time coordinate at the end of each block of data.

Because of man-made interference and the strong signals received from the

active sun, jt is unlike'ly that observations will often be made during daylight

hours with the present system. l,lhen making repeated observations of a particular

source, 'it would be des'irable to have some facility to automatically init'iate the

acqu1sition process, and to stop it again after the source has passed. This too

could be provjded by the timing circu'its, as the times of interest would be

determined by the coordinates of the source. Additionally, such operations as

the'injection of calibration sjgnals at set intervals (Yang and Srvenson, 1967)

could be control'led by the time-keepi ng systent.

The c'ircuits for the generation of the two coordjnates required, solar and

Page 176: 2-Whole-digital Data Processing in Radio Astronomy

169.

sidereal time, have been combined jn a sing'le unit. A block diagram of this

solar/sidereal digital clock js shown jn Figure 7.5. The 5l4Hz output of the

standard frequency oscillator is shaped and divided by fjve to give a basic

lMHz reference signal. This lMHz signaf is fed into two separate frequency

divjder chains whjch produce outputs of 10Hz solar and 10Hz sidereal. These

10Hz signals are supplied to two jdentical time-keeping chains wltich give

binary-coded-decjmal (b.c.d.) outputs of tenths-of-seconds, seconCsn m'inutes

and hours. The seconds, minutes and hours outputs of each of these chains are

connected via a tvrenty-channel tvro-way multiplexer to a six digit nixie-tube

display. This display can be switched to show either solar or sidereal t'ime,

and the djgi ta'l outputs of both cl ocks are avai I ab1e simul taneously to a

reso'luti on of 0. 1 seconds .

There are seven controJ functions which can be operated on either or both

of the t;o clocks; start, stop, advance by 0.1 seconds, retard by 0.1 seconds'

set, reset to zero, and synchronization with external time signals. These

functjons can be actjviated by depr"essing an appropriate push-button together

with either the solar or sidereal'interlock button, or by an external pu1se.

At the time construction of the digital clock was begun, r.t.l. (resistor-

transistor-logic) integrated-circuits were 'less expensive and available in

greater abundance in this country than the t.t.l. devices later used in the

analogue-to-digital converter (Chapter 6). For th'is reason, except in the

sjdereal d'iv'ider for whjch no suitable r.t.l. devices l'tere available, r.t.l.has been used throughout the clock with its associated negative logic convention

(1=lovr levej -0.4 volts;O=hjgh 1eve1 *2 volts). flolever the output buffers

supply the necessary invers'i0n for jnterfacing directly vrjth t.t.l. circuits.

7.5 The So]ar and Sidereal frequency dividers

A discrete-component Schmitt trjgger circuit is used to convert the input

2 volt peak-to-peak SllHz sine wave into a Gl2 volt square vrave suitable for

triggering the r.t.l. devices. The d'ivide-by-five circujt (Fjgure 7.6a) is a

modified rjng counter of three J-K flip-f1ops r'rhich vljll alvrays regroup to a

valid sequence if a spurious count should appear (there are eight possible cont-

binations of wh'ich only f ive are used).

An inverting buffer (Gr) supplies t,he lMHz rectangu'lar wave (;') to an

external connector, and the jntenral ll'lHz clock for the solar and sidereal

dividers is derived djrectiy from the Q output of C1.

Page 177: 2-Whole-digital Data Processing in Radio Astronomy

1,70.

20 pote 2 posi tiorr rnultiplerer

F=igure 7'5; The solar/sidereal digital cloek.

l- 5 c'Ycte-s

I

I

l"_- I cfg{g

{b}

T

c1

%

caInput

0u'tprts

Figurre 7,6; (a) The divide-by-five cit'cuJt, and (b). its vraveforms.

Page 178: 2-Whole-digital Data Processing in Radio Astronomy

171.

7.51 The Solar Divider

The solar divider (figure 7.7) consists of a string of five integrated-

circujt decade counters which divide the input 1t4Hz frequency by 100'000 to

g'ive tenths-of-solar seconds. Buffered outputs of 100KHz, LOKHz, LKHz' 100H2

and 10Hz are available for external use (e.g., the 100KHz output supplies the

clock waveform for the analogue-to-digital converter). An RS flip-f1op (Gt,Gt)

gates the 10Hz output of the divider through Ge for the solar time-keeping cir-cuits. This provides the start/stop facifity for the solar clock. The control

inputs are shown as START and STOP because they require inverted logic levejs.

ext. l 0Hz

int. l0 Hz

Figure 7.7: The solar frequency divjder

Details of the CuL9958 decade counter used in the d'igital clock are shown

in Figure 7.8. The'logic diagram has inversion symbols shot'tn on the reset and

tpigger inputs (ft anA i) to convey that these are operated by inverted levels.

The outputs are 'in negat'ive logic b.c.d. format and are labelled Zr,72, Zr+ and

7s respectively. Correct counting occurs if each successive decade is

triggered d'irectly from the Zs output of tlre preceding one.

7 .5? The Sidereal D'ivider

The sidereal divider (Fjgure 7.9) er.rp'lo-vs five decade counters connected

in a similar fashion, but gating'is provided to reset all five decades to zero

when the count 99,727 appears, i.e., they count 273 short of 100,000, producing

the necessary 0.274% h'igher frequency tenths-of-sidereal seconds. The count

99,727 is decoded by gates Gr, Gz and Ga, dfld triggers a 500 nanosecond mono-

stable multivibrator formed by G,-, G5, and Ge . This titultjvibrator drives the

reset-to-zero termina]s of the five decades. The monostable is necessary

because the count 99777 vrhich triggers the reset pulse disappears as soon as

G8

Page 179: 2-Whole-digital Data Processing in Radio Astronomy

172,

R trasct to zcro'l

FiguTe 7,r8: Sytnbo'lic represe,ntat{on of the

integ'rated-ci'rcuit, decade csunter.

zo

10 Hz0ulputs

G7 I

t/^ in t.oB

MF

Figu,re 7.9: The sideneal frequency dlvlder.

any of the dreeades reset, and they may not all reset'simultaneously. This

reset pulse must be less than one microsecond or the ncxt trtgge.r pulse willbe lsst, d,nd the unit will div'ide by 9'9128, The divider actually uses t't,l.deeadgrs which do no-t trave an inverted reset input; the CuL9958 deead:e could

not be reset in the short time available.

The gate G:r B.rrovides a buffered 1,0ttz output for external use, and Gr, Gg

and Gro Fro\ride the startlstop facility for the sidereal eloek.

7 .6 Timq.$'eepiryg an{ Diispt qy ,Cfi!^cui ts

The' identJca'l Solar and si:d'el^eal: tirne-lkeep'ing circuits e'ach provi'de b'G'"d'

T-igg,et )

Page 180: 2-Whole-digital Data Processing in Radio Astronomy

173.

outputs (negative logic) of tenths-of-seconds, seconds, minutes and hours, as

shown in Figure 7.5. The tenths-of-seconds counter is an integrated-circuitdecade connected to provicle the advance and retard control functions discussed

in the next section. The seconds and minutes counters each consist of an

integrated-circuit decade fo1lorved by three J-K flip-flops connected as a

modulo-6 b.c.d. counter (figure 7.10).

lHz

To Minu tcsCounter

Input

4 ZzZcZa\--\,/---l

bsd. seconds

Figure 7.10: The seconds counter

The inv€Ft€f Gr is necessary to supply a G'l transition trigger to C+ vlhen

a L+0 transition of Zs occurs. The hours counter (figure 7.11) employs an

integrated-circuit decade counter followed by a two stage binary counter (two

J-K ffip-flops connected in toggle mode) rvith the two counters gated to reset-

to-zero when the count 24 appears. A one millisecond monostable multivibratorMr ensures that each counter resets before the command is lost.

z4

10 x minutesGz

4 7z TaZa\---v--J

b-cd. hoursz't 22 lmsec

\--v-------l

b.cd. 10 x hours

Fiqure 7.II: The hours counter

The twenty-four outputs from each clock are buffered

output connectors, either of which may be connected to the

These buffers, which are unloaded r.t.l. glates, supply the

and taken to two

tape punch system.

correct polarity

bsd. 10x seconds

Page 181: 2-Whole-digital Data Processing in Radio Astronomy

174.

logic at the correct vo]tages for interconnection with the t.t.l. circuits used

in the remainder of the sYstem.

The twenty b'its represent'ing seconds, minutes and hours from each clock are

gated through twenty AND-$R switch circuits (figure 7.I2) and the outputs of

these drive sjx integrated-circuit decoder-drivers, lvhich in turn drive the six

digit nixje disp'lay.

4'II

Decoder-Dr i ver

N ixicTube

1iI

I

i

zt̂oi

SotorI nputs "-. Sidereol'Inputs

G5

S2

Figure 7.12: One dig'it of the nixie tube display.

When the sidereal push-buttor Sr is mornentarily closedr Gr+ goes to I and

G5 goes to 0. The nixie tube then djsplays the number indicated by the four

sidereal input 'lines. l,Jhen the solar push-button Sz is momentarily cl0sedr Gq

goes to 0 and G5 goes to 1. The number indicated by the four solarinput lines

is then displayed.

7.7 Clock Control Circuits

The seven control functions ment'ioned 'in section 7.4 each have assoc'iated

with them a pulse source of the form sholn in Figure 7.13. Each function is

activated by depressing a funct'ion button (Sr), while either the solar or sidereal

interlock button (Sz, Sr) is held dorvn. These slitcheso although on the front

panel of the clocl<, are normally protected by a cover and as an interlock button

must be held dor.rn while a function button'is pressed jt takes very deliberate

operator action to upset the times kept by the clock.

Page 182: 2-Whole-digital Data Processing in Radio Astronomy

L75.

Sotorfuset

ExternoIInputs '-->

* Note that with the negative

coup'led gate_of the forn used

to q = 6A + B for the t.t.1.

logic convention of r.t.lin Figure 7.13 rePresentsqate.

+ lrv

SidereoIInterlock

gates, the caPacitivelY

Q = 6A + B, as opposed

SidereotReset

side?eor rr)i _i( sr

Sotor L---r

Interlock 777r7r

tiggre.Z_l3-: The reset pulse source.

Each funct'ion may also be triggerecl by a negative-going pulse; two

separate 'inputs (solar and sjdereal) are provided for each function. Connec-

tions to these inputs can be made on'ly with the protecting cover removeci' and

when the cover is back'in place both interlock buttons are automatically

depressed, rendering the inputs active.

The driv'ing gates G1 and Gz nornlally have both'inputs high (0) and thus

their outputs are normally low (t). When Sz(Ss) is held down, and Sr depressed'

then Gr (Gz) momentarily goes to 0n then returns to I as the capacitor C

charges.* This positive (1*0) output pulse is of the right form to drive the

start/stop RS flip-f1ops mentioned in sectjons 7.51 and 7.52, and a'lso the set'

reset, advance, retard and synchronize functions discussed in detail in the

following sections.

7.71 Start and StoP Facilities

Either clock can be started or stopped to a resolut'ion of 0.1 seconds by

control functjon push-buttons or external pulses as described in the previous

section. The start/stop RS flip-f1ops, shown in Figures 7.7 and 7'9,gate the

10Hz clock puise at the output of the frequency divfder sectjon, and thus the

external LMHz,100KHz,10KHz, lKHz, l,OOflz and 10Hz solar and 10Hz sidereal out-

Page 183: 2-Whole-digital Data Processing in Radio Astronomy

176.

puts are not affected by the starting

7.72 Set and Reset Facilit'ies

or stopping of the c1ocks.

The set facility allows the visual register (hours, minutes, and seconds)

to be set to any time of day. The appropriate time jn hours, minutes and

seconds is selected on six front-panel-mounted thumbwheel switches, and when

the set function button is depressed together with the desired interlock button'

this time js transferred into the time-keeping counters. The circujt configu-

ration of the thumbvrheel swjtch and djode setting gates is shown jn Fjgure 7.14'

SotorSecondsSet

*i'lii" +t+u

Fiqure 7.14: Circuit for setting the solar seconds

decade counter. Switch position sholvn

will set decade to 0100.

Although the J-K ff ip-f1ops used in the tens-of-seconds, tens-of-minutes,

and tens-of-hours counters are provided r.rith both set and clear inputs which

are activated by positive (1*0) pulses, the integrated-circuit decades used

for the units counters have only a single clearinput. Hot'rever if the decade

is first cleared to zero (all outputs hiqh), the jndividual bits can be'pu1'led'

down to 1.. This setting of the decades can be achjeved by providing four

transistors per decade as shovln'in Fjgure 7.15. For these counters, a diode-

transjstor-logic integrated-circurit expander gate cornbines the diode gate of

Figure 7.14 and the transistor of Fjgure 7.15 jn a single integrated unit.

Page 184: 2-Whole-digital Data Processing in Radio Astronomy

b.qd. 21 22 240utputs

Figure 7.15: The Provision ofi ntegrated-c'i rcu i t

Sett in9Inputs

a setting facilitY for the

decade counters.

177 .

(Figure 7.13)

from 0.1 seconds

decade counters,

be set to a Parti -

z2

z4

z8

The positive pulse generated by the reset pulse source

drives the reset terminals of the ent'ire time-keep'ing chain

upwards. Because of the peculiar faci'lity for setting the

the time-keeping chain must be reset-to-zero before it can

cular time.

7.73 The Tenths of SeconOs Cognters and the Advan

The advance and retard functions allow respectively one count to be added

or one count to be subtracted from the tenths-of-seconds counter, while the

clock is running, for each pulse generated by the function pulse source' Thus

the indicated tinre of either clock can be advanced or retarded by 1/10th of a

second at a time. The c'ircuit of the tenths-of-seconds counter, with the

advance/retard facility, is shown in Figure 7.16'

}lhen the retard function js activated, the trvo J-K flip-f'lops c1 and cz

are reset-to-zero and the triggerinput to Dr, Gz is 1 (low) regardless of the

state of the 10Hz input. 0n the next 1*0 transition of the input' which rvould

have normally triggered Dr, d 0+1 transition of Gr causes Cr to become 1' 0n

the subsequent G'1 transit'ion of the input, cz becomes 1, enabl'ing Gz to follorv

the input once again. One 1*0 transition of the'input has been prevented from

triggering Dr, and so the clock has been retarded by 0.1 seconds'

A positive pu'lse on the advance line sets the RS fliP-floP Gs, Gz and on

Page 185: 2-Whole-digital Data Processing in Radio Astronomy

10.H2lnpui

178.

21 7ZA Zar-r/

bp.d. output

odvonae

l-l-;-br-.-.

.-

(b)

retord

Fiqure 7.16: The tenths-of-seconds counter shovring'the advance

(o)

(e)

c6

E

l,Javeform in the tenths-0f,-seconds counters'(a) normal operatio:n, (b) with retard functioniriggered ani (c) wi[h advance function triggered.

Page 186: 2-Whole-digital Data Processing in Radio Astronomy

179.

the next occurrence of the count 9 jn the decade counter Drn the ntonostable

multivibrator formed by Gu and Gs is triggered, resetting Dr to zero, and also

resetting the RS flip-flop. Dr has then counted short by one count, and as a

result the clock has been advanced by 0.L seconds. The Zr line is capacitively

coupled to G31 pf€Venting the reset pu'lse from being triggered if the advance

function js activated when the count 9 is present.

In Figure 7.17, typical traces of the waveforms in the tenths-of-seconds

counters are shown. Figure 7.17(a) shows a counter operating under normal

conditions. The upper trace is the 10Hz input, and below this are the Zr,7z,Zq and Za outputs of Dr. Log'ic 0 is the high 1evel, and logic f. is the low level

Triggering occurs on the 1*0 transition of the input. Figure 7.17(b) shows the

waveforms at the same terminals when the retard funct'ion is triggered by the 9'0

transition of the counter. The count 0 (0000) then retnains for two periods of

the input waveform before changing to 1. Figure 7.17(c) shovls these same wave-

forms rvhen the advance function is triggered once during each cyc1e. The decade

then recycles directly from B to 0.

7.74 Synchronisat'ion l^lith External time signals

The synchronising function allols the one second 'tick'of either clock to

be synchronised to w'ithin one microsecond of a standard time s'igna1 as received.

The circuit wh1ch performs this function (F'igure 7.18) gates the 1l'lllz input to

the appropriate frequency divider through gates Gs and Gg. tlhen the synchroni-

sing function is activated, the RS flip-floP Gen Gz is set, and the command

stored until the next 1+0 transition of the internal one second waveform- The

Zs output of the tenths-of-second counter whjch produces this waveform, marks

the end of each second with a L*0 transit'ion. When this transition occurs' a

one microsecond pu'lse (56r) sets the RS flip-flop of G,,, Gr. Gs then goes to 0'

and the lMHz clock is cut-off from the divider. 0n the follolving G'1 transjtion

of the standard time signal, a lus pulse 6G, resets botlr RS flip-flopsn return'ing

the system to normal. The clock's jnternal one-per-second ttaveform has been

slowed dovrn so that the end of a one second period coincides with the fallingedge of the external standard. If the clock was original'ly a fraction of a

second slow, it is now exactly one second slow, and can be brought into'line by

depressing the advance button ten times.

A typical osc'illoscope trace demonstrating the action of this function is

shown in Figure 7.19.

Page 187: 2-Whole-digital Data Processing in Radio Astronomy

l.r1sac

180'.

Int,Itr.r

s,ilnC-

J

lMHa ln lMl'lz 0ut

Figyre 7.18: The cireuitry of the synehlnon'izin'g

control functi'on.

Ftgltre Ll9-: The opepation of the synchroniztng' function.

(a) The activatjng 'purlse, (b) the external s;tandard

'tiickrr dhd (c) ttre internal 'tick'.

7.8 0o'ntrg:! qf lhe Acquisili0n Fr0cess

The pno.gr.arnned contnol of the acqnrisitiorr syst'em'is perfo'rnred b,y two

units, a cloc,k3pulse source and, a time interval gener:ator' vlhich are separate

and distinc,t frsm the clock. The clock-puls€ soupc€ is pl',ovided with buffered

outp-u'ts of the lorv frequency clock prirlses from the solf,rlsiderEal clock

Page 188: 2-Whole-digital Data Processing in Radio Astronomy

181.

(tenths-of-seconds, seconds, tens-of-seconds, ntinutes, tens-of-minutes, hours

and days, both solar and sidereal), and also with either the solar or sidereal

b.c.d. hours. At a programmed time (integer hours), clock pulses at one of

these frequencies are supplied to the time interval generator vrhich produces

both sample and block-mark instructions at preset intervals unti1, at a later

time (also progranrned), the clock pulses are stopped by the clock-pulse source-

7.81 The Time Interval Generator

This unit, which generates both sample and b'lock-mark instructions, ispatch-programmed to maintain a certain flexibility. l,lith normal patching itwill generate sample instructions at intervals of I to 99 input pulses (in unit

steps), and at the same time generate block-mark instructions at intervals of

I to 9 samples in unit steps, or 10 to 90 sampies'in decade steps. t,lith alterna-

trve patching it can produce single pulses at intervals of I to 999 input

pulses. A variety of other sequencies can also be programmed.

The unit is based on fourintegrated-circuit decade counters' three of

which are connected'internally to thumbwheel decodjng switches as shown in

Figure 7 .20.

0123t 567 89Cotnct dence

0utput

Thumbwhee I DecodtngSwitch

Figure 7.20:

of the

A progranimable decade counter

time interval generator.

Page 189: 2-Whole-digital Data Processing in Radio Astronomy

182.

The thumbwheel switches give a I output (negative logic) when the state of

the decade counter coincides lvith the number set on the switch. The ind'icated

termina]s (T, R, Za and S) of these three clecades, all functional terminals of

the fourth decade, and input/output connections of severa'l gates and monostable

multivibrators, are connected to a 7x7 terminal patch pane1. Interconnectjons

for the normal ntode mentioned are silown in Figure 7.2I.

Inpu t

C tock

not required i

for block tengths

less thon 10 i

D3 D4

Somp [e

lnstruc tion

Fi gure 7 .21: l,lormal i nterconnecti ons for the time

interval generator.

Btock MorkInstruc tion

By triggering the mcnostable l'1r from the AND combination of the coinci-

dence signa'ls from Dr and Dr, tlre resetting of these two decades occurs only

when both are coincident with their resDect'ive switches, j.e., if the Dr switch

is set to Nr(decimal) and the Dz switch to Nz, then the sample interval will be

NzNr (decimal) periods of the input clock signal. The reset pulse'is pos'itive-

going and of the correct form for the sarnple'instruction to the analogue-to-

d'igital converter. This reset pu'lse also triggers another counter' formed by

Ds a.nd D,*, which generates the block-mark instruct'ion. If the D'+ switclt is set

to N (decimal) then the block length wj11 be N0 (decimal) samples' or if Ds

i s omi tted , mere'ly l,l samp'les .

7.82 The Clock-Pulse Source*

The clock-pu1se

generator and gates

and stopping of the

source suppljes the basic clock pulses to the time interval

these on and off at programmed hours of the day. The starting

acquisition process can also be performed manua'lly. The six

* This unit uses t.t.l. gates and thus a pos'itive logic convention

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183.

lines bearing the b.c.d. hours infornration from one of the clocks are supplied

to t;o 32-way circuit-board connectors (figure 7.22) together their conrplements.

By using progranrming cards to connect a particular combinatjon of these twelve

quant'ities to the sjx inputs of Gr (or Gz), a 0 level wjll occur at the output

at one hour duping the day. Twenty four prewired cards are available, enabling

any two hours during the day to be selected to initiate and terminate the

acquisition of data.

b.cd. InpulsFrom Clock

Progrom Progrom

AB

ProgromA Out

ProgromB Out

Progronr CordSocke ts

Figure 7.22: The start/stop programming faci'lity of the

c'lock-pul se source.*

The circujt vrhjch selects and gates the desired clock pulses to the time

interval generator is shown jn F'igure 7.23. The tr^ro svrjtches Sr and Sz select

one of the fourteen clock frequencies avajlable for use as a basic t'iming

waveform. Gr generates a short positive pulse from the negative-go'ing trattsi-

tion of the waveform, the transition which narks the beginning of a clock

interval when the clock waveforms are in this positive logic form. Gs is con-

trolled by the RS flip-f1op formed by Gr and Gs. When the outputs from the

coincidence gates G1 and Gz (Figure 7.22) are connected to the set and reset

term'inals of thjs flip-f1op, then program A r,rill start the system' and it will

be stopped by program B. At the beginning of any acquisition period, vrhen G+

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184.

is first set to 1, G5 generates a short positive pulse whjch is supp'lied to one

of the patch-pane'l connectors of the time interval generator, and causes all of

the monostables in this unjt to be triggered. The counters are then allinitially reset-to-zero, and as both sample and bloclt-nrark instructions will be

generated, the beginning of the acquis'ition period will be marked by a sampie

and i ts coord'inate.

The acquisition process can also be started and stopped manually by the

trvo push-buttons, S: drd Sq.

t_

I

,*{

t

SolorCtock Put

s----o-------{

-------{#

---------€---4

----o----------€

----------o-----{-------4--{

0.1s

1s

10s

1m

10m

th1d

0.1s

1s

10s

1m'l0m

lh1d

-[-ctoctr Purr.

START Lt \o^7? ttm7T

Reset Time lntervol

,id"r."t fctocr eursesl

i.; Generotor

.sq"l

77V/r

Figure 7.23: The selector and gating portion of

the clock-pulse source.*

In addition, an event marl(er is included in thjs unit, provided primariiy

to produce sjdereal hour marks on the analogue chart record of the interferometer

outpui. This circuit provides a contact closure at the 1*0 (end of clock period)

transition of any one of the fourteen basic clock frequencies.

7..9 Physjcal Characteristics of the Solar/Sidereal Clock

The solar/sidereal digital clock (Plate 4) is housed in a standard 19" vride

rack unit,7" high and 12" deep. The most prom'inent feature on the front panel

is the six djgit in-l'ine nixie tube display of hours, minutes and seconds. At

the right-hand side of the front pane'l are the six thumbvlheel switches used in

STOP

* This unit uses t.t.]. gates and thus a positive logic convention.

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185.

setting the c]ocks. The only other controls normal'ly exposed are the

disp] ay-select slitches (St and Sz, Figure 7 .tZ), wh'ich together with their

indicator lamps are located betvreen the dispiay and the setting switches. Also

on the front panel are the two recorder connection larnps, which indjcate which

of the two c'locks currently has its b.c.d. output connected to the tape punch

systern, and three mjniature sockets, two of r.lhich give outputs of the solar and

sidereal one second 'ticks', the third being the input for the standard time

signal required by the synchronjzing function.

The controls vrhich affect the clocks'accumulated times, shown exposed in

Plate 4, are normally protected by a cover p1ate. These controls are the solar

and sidereal interlock buttons, the seven control function buttons, and an

aux'iliary pulse source button. This auxiliary pulse source can be used to

manually generate control pulses for other parts of the system' The plate also

covers the solar and sidereal inputs for tlre external triggering of these

functions. Connections to these inputs can be made only with the cover removed,

and when the cover js back in p1ace, the solar and sidereal interlock buttons

are both depressed, rendering the inputs active.

The SMHz input connectiorr, and the 1llHz, 100KHz 10Hz outputs are

available at rear panel coaxial connectors. The tvrenty-four-bit b.c.d. outputs

of each clock and the fourteen basic lorv frequency block waveforms supp'lied to

the clock pulse source are also available at the rear pane1. The power supply

connectjons,4 volts for the logic circuits and 200V for the display tubes' are

on the rear pane'l .

The djsplay and control unjts are accessed from the front of the clock;

the front pane'l can be h'inged forlard. The dispiay unit (Plate 5a) consists

of a single plug-in printed circuit board vrhich contains the t|enty AND-0R

gates of the display-se'lect slitch, and the six decoder-drivers for the nixje

tubes, the sockets of which are attached to the board. The control function

pu]se generator circuits are mounted on small printed circuit boards attached

directly to the rear of the control subpane'I, and this entire unit can also be

removed from the main frame.

The rema'inden of the clocks'circuits are contained on twelve p'lug-in

circuit boards r.rhich can be reached from the rear pane1. The connectors for

these boards are readily accessible from the front pane'l when the display and

control units are rentoved.

Page 193: 2-Whole-digital Data Processing in Radio Astronomy

186.

';(Jo()

G'+J

o)T'

G'(l,LoEan

LG'

otn

c,+,rFoq,g.uCL

+tgoLlFq,.CF

+1lrJ I

klJIcLl

C;o

i

.. -r-H#idilr,i..rJil[L'.i . -

i

X Orl:8;

i{; ti,C,O,'i* aH

Grlft,tur,*.;

,lt.!ilpi

..t!D

.o

:

slo

Page 194: 2-Whole-digital Data Processing in Radio Astronomy

187.

(a)

rr ! c.rs

r} rs

rf ros

r! rr

O I O rf.ron

#* r? rx

r! ro

soL srD

;

ototoIlryl ,.1.

C ol

,_.,sk

cr||f*]aot'.onJE

€a

PLATE 5:

and

-l{},}{tOr,ro-

f

(c)

digital clock display board,time interval generator front panel,clock-pulse source front panel.

b)

Thethethe

(a(u(c

Page 195: 2-Whole-digital Data Processing in Radio Astronomy

1BB.

Plate 5b and c shovrs the front panels;of the tjme interval generator and

the clock-pulse source. The time interval generator occupies a portjon of the

7" high frame r,rhich contains the analogue-to-digital converter. The gates and

counters rvhich make up thjs unjt have all their funct'ional connections brought

out to the 49 socket patch-pane'|, and are clearly labelled. The clock-puise

source occupies part of a 5%" high unit which l'li'll later accomtnodate a recejver

for standard time signals. The programming card sockets are on the right, and

on the left are the selector switches and the start/stop unit. The indjcator

lamp below the start and stop controls indicates vrhen the unit is actually

transmitting clock pu'lses to the time interval generator.

7'10 The Performance of the solar/sidereal Ditt'ital clock

With the observed drift rate of the crysta'l oscillator (1 part in 108/week)

the solar clock vrould take fifteen weeks to accuntulate an error of 0.1 seconds.

The sjdereal divisor of 99 ,727 gives an approximation to sidereal frequency

accurate to 4 parts in 107. No provision has been made to correct this error

which amounts to 0.1 seconds every 70 hoursn houtever by advanc'ing the sidereal

clock by 0.1 seconds every three days, th;'s systematic error can be removed.

REFEREIICES

CSLE, D.J. (1968): "Solar and S'idereal Time from a Single Crystal". Electron'ics

Aust. , 30 P. 77 .

c0LE, D.J., and SHII"IMINS, A.J. (197i): "A Time and Frequency system for use at

the Australian Nat'ional Radio Astronomy 0bsei vatory". Proc. I.R.E.E.

Aust., 32 PP. 12-L6.

FELCll, E.p., and ISRAEL, J.0. (1955): "A Simp'le Circuit for Frequency Standards

Employino 0vertone Crysta] s". Proc. I.R.E. , 43 pp' 596-603'

FISHER, D.0., and FRANK, R.lJ. (1965): "A Nerv Approach to Precision Time l'leasure-

ments". G.R. Experinrenter, 39, llo. 2 and 3, pp. 3-13'

GERBER, E.A., and SYKES, R.A. (1OOO; : "State of the Art-Quartz Crysta'l Un'its

and Oscillators". Proc. I.E.E.E., 54 pp. 103-116.

GRIMSLEY, S.1,,l. (tgOZ ) : "A Transi stori zed l'lean Trrle to S jdereal Tirne Converter" .

Proc. I.R.E.E. Aust.,28 PP. 92'95.

Page 196: 2-Whole-digital Data Processing in Radio Astronomy

189.

KEl,lEl\tyr G.r 8n 0LTtt0FF, l|l.. (rsggl: n'Tanperature con,trollen with small Dead-

Time and High Resolutio,n"' Conttrolt !9 pB' 786-790'

MALESANtr' L. (1g6g1: f,ImpnOved Delay: eircuit for" Thyristor" Linear Powe,n 0ontrolil'

Electronic Eng., 4i PP. 84-89.

PUSTARFI, H.S. (1966): "An Irrproved 5l'trHz Reference oscillator for Time and

Frsquency Sta,ndard Applicatr'ons". Trans, I.E.E.E", tr$,-tri! pp" l'96-202'

SIeDELL, J.E. (1968): "A New Simple PhaSe Dependent Detector". I.E.E.E' J' of

Sorlid State CIircuits, SC-3 pp, Z$L-ZQZ.

STRATEMEyER, H.p. (Xg64)- rrJftq Stability of Standard Frequency 0scil']ators"

Q.R. ExperJmentet^n 3,8-, No. 6, pp- 1-8'

YANG, K..S,n and S}lENsoNl G,.lil. ('1967): ''The IIJi'nois 400ft Radig Teleseopei

Fer formano€ dhd Electronic Egulpment". Radio Sci., 2 pp. 147-159'

ZINDER, D.R. (1967): i'suppressing R,F.L in Thyristo'r Cit'cuits"' (Motono'la

APPI i eatl on Note. Al'l-295 ) .

Page 197: 2-Whole-digital Data Processing in Radio Astronomy

190.

CHAPTER B

The Paper TaPe Record'in(l SYstent

From the generai specification developed in Chapter 4, the function of the

paper tape recorrling system can be split into tvro parts; a un'it vlhich accepts

data to be punchecl and groups this into ejght-bit bytes, and a unit which

punches each of these bytes on to paper tape as a sing'le tape character' The

development of a djgital multiplexer and a paper tane punch unit to perform

these functions js discussecl in this chapter, together with the phi'losophy

behind their design.

8.1 Requirements of the Multiplexing Systent

Data from one sample of the interferometer output will occupy nine binary

digits anci cannot be acconmodated in a single tape character of eight bits'

The sample data must thus be grouped into at'least tvto tape characters, and in

any sequence of such characters appearing on the paper tape, each pa'ir must be

distinct. Similariy the data from a time coordinate occup'ies tnenty-four bits,

and will require at least three tape characters. Again the data must be grouped

into these cltaracters and in any sequence of tape characters, the order must be

obvious, and the tirne coordinate data must be distjnguishable from the pairs of

sample data characters.

The unjt which groups the input data into eight-bit bytes and controls the

sequential punching of these tape characters is the digital multiplexer' The

characteristics of this unjt are completely specified by the requirentents of

the input data to Lre punched and the characteristics of the output unit' the

paper tape punch.

8.11 Characteristjcs of the Paper Tape Punch

An I|IVAC P-135-20 paper tape punch lvas nnde available for use in this

system. Th'is punch can be operatecl asynchronously at speeds of up to ttuenty

characters per seconcl. It punches one-jnch wicle, eight channel paper tape to

specifications cor]laatible with those of the 1134 tape reader of the IBM 1130

computer. 0f the fifty m'illiseconds required to punch one character, the punch

actjon involves on'ly eleven millisecottds, tlte remajnder of the period being

taken up by tape trarrsport action-

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191.

B.I2 General Requirenrents of the Input Data

When a sample of the interferometer output has been taken and the nine-bit

vrord transferred into the buffer register of the ana'logue'to-dig'ita1 converter,

tlre instruct.ion to the recording system that the data should be punched rvill be

conveyed by the end-of-conversion nressage, or'flag', mentioned in Chapter 6.

l.lhen the data has been punched this flag shoulcl be reset by a'data punched'

instruction from the tape punch unit. l',lhen a block is declared and the t'ime

coordinate is to be recorded, the block-mark instruction from the tirne interval

generator (section 7.81) will convey this informatjon to the recordittg systent

and set a 'block-flag', vrhich will be reset vrhen the coord'inate data lras been

punched.

8.13 Specjal Requirerlents of the Coordjnate Data

As three tape characters can cnly just acconntodate the tvrenty-four bits of

coordinate data, jt is 1ike1y that more than three characters will be required

for tSis data in order tlrat identity and sequence can be established. At least

200 milliseccncls w'ijl then be requirecl for the punch'ing of this cjata, attd as the

data will change during this period, a buffer register rvil1 be required to hold

the coordinate data durjng the punch operation.

Noting that vrhen a block is declared it will be declared sitttu'ltaneously

with a sample instruction, and as there r.till be a delay of at least eighty

microseconds betvreen the sample instruction and the end-of-conversion message'

then the request that the coordinate be punched rvi11 be received before the

request to punch the sarnple to r,rhich it refers. If it is desired that the

coordinate data aDpear on the tape inmecliately after the data to which it refers,

then a delay nrust be incorporated 'in the 'block-flag' ttressage.

8.14 Indexjng of Paper Tape Files

The output from the acquis'it'ion system will be a series of lengths of

punched paper tape, or paper tape fi1es. It is proposed that each of these

files should begin with sorne ident'ifjcation of the data contained on the tape'

to prevent confusion of data during analysis. A standard lreading format has

been developeci (Ciscussed later in the description of the software systenr)

which includes a fjle number and infornrat'ion pertaining to the conditions under

vrhich the data r,ras recorded. In aclclition to the provision of a manual data

entry faciljty (a switch-register), add'itional cltaracter identification must

be allocated for this heading data.

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r92.

B.1s@In view of the inherent unreljability of mechanical paper tape equ'ipment'

was decided to generate and punch a parity b'it rvith each tape character. Data

once in the computer could then be checked for errors occurring in e'ither the

punch or the reader. One of the available eight tape channels must therefore

be set aside for use as a panity-check channel.

8.2 Grouping of the Data jnto Eight-Bit Bytes

From the requirenrents enumerated or implied jn section 8.1, it is obvious

that some standard tape character format must be developed. The paper tape is

primari]y intended as a recording medium for data from the interferoneter and

its coordinates. Ho1evelif parity checking is to be jncluded in the computer

analysis, and if more than one kind of character is to be punclted (a firstsample data clraracter, a second sample data character, etc.), then some of the

data area on the tape must be sacr'ificed for identification and parity bits.

In the preceding discussion, three types of clata have been ment'ioned; sample

data, coordinate data, arrd heacling data. If each of these types of data is tobe distinctll, jdentifjedn then three djfferent jdentificatjon codes vrill be

required. Thjs inrnlies that tvro bits'in each tape character must be set aside

folidentificati0n purposes, and if one further bit js to be used for parity

checl<ing, only five bi'ts jn each character vtill be ava'ilable for data. The tape

channel allocation devisecl to meet these requirentents is sholn jn F'igure 8.1".

Tope Chonnels1

2

3

sprocke tlr

5

6

7

I

1

2

3 Dotq Chonnets

t,

5

Pt

2

Pority Chonnel

Identif rcot ion Chonnets

___=->Tope Motion

Figure 8.1: Tape channel allocation

II

i)

iI)

If only five b'its in each taPe

sar,rple of the jnterferonteter output

and each coord j nate (24 b j ts) wi'll

entry is to be five bits at a time,

character are available for data, then each

(g Uits) vrill occupy two tape characters'

occupy five tape characters. If manual data

then eight different kinds of character

o ooo ooooooooooooooo

oooooo ooo ooo oo oo o

Page 200: 2-Whole-digital Data Processing in Radio Astronomy

193.

vlill be encountered. In order to retain dist'inction betvleen the first character

of a set and the remaining characters, the identification code appropriate to

the data is used only vrith the first character, and the renraining characters

are identified by a continuation code, the fourth combination of the two

identificatjon bits. The allocation of the input data into eight eight-bit bytes

is shown jn Figure 8.2

tiioRDa 7 ht 4 nJ 2 {'I

1 1 o

F]t'lz-(()

itHH

P{

:1Jn 27A

2" 2s 21 I)

L/DT'\fn^vntll

z \J?

2" 22 21 2a n

e 0 I MA}IUAL DATA E};TRY

4 1 1Z2

L0xhZ1

|. 0:<rZs

1 r:hZa

1-xhZ2

1:rh

tv!UUA

DATA

ra U 0ul

1xhLt,

lCxn2

C:rm

'L1

lf)vrZ6

1x;i

0 UZa

.t.,-J. /|..Ll

Z2t -.^.

Z1

J. ..'- lu

ZaI Cxs

Z2L0r s

7 Ll o Z1

l'0xsrjL8

1vcZt

1xsz2

1xsZ1

1 >:s

B 0z8

1xsZa

. 1xgz2

1r:sz1

r I IJ

r. D. T\ l'n tl-rtl J. jt

Figure 8.2: The allocation of the input data into eight-bit bytes

l,lhen data from paper tape is read into the computer, channel I is regarded

as the least signifjcant bit of each character. For this reason the data has

been allocated to channels 1 to 5, wjth the nost significant bit of each five-bit data byte in channel 5. The identification codes have been set at 01 for

heading data, 1.0 for sample data, and 11 for coordinate data. The code 00 is

used to indicate continuation.

Each input data r.,ord has been split'into five-bit bytes vrjthout concern forgrouping (e.g., the tlrree most significant bits of the b.c.d. unit hours inform-

ation are contained in the fourth character, and the least significant bit of

this group appears in the next character). This is in accordance with the

requirement for hjgh data packing density vrithout consjderation of complexity'in

decodjng the information.

Page 201: 2-Whole-digital Data Processing in Radio Astronomy

194.

8.3 The Development of the Digital Multjplexer

The functjon of the digital nrult'iplexer can be best established by

observing the action required. This can be described as follols.

When the sample 'f1ag' is set, the unit should provide the five data bits'

two identificatjon bits, and parity bit of t'lord 1 (Fjgure B'2) to the tape

punch, and transmit a 'punch'signai. l/hen the punch replies to this signal

with a 'data punched'message, the unit should supply the eight b'its of Word 2

to the tape punch, and once again transmit a 'punch' jnstruction' 0n the

receipt of the follotving 'data punched'ntessage from the tape punch the unjt

should reset the sarnple'f1ag'to 0, and then return to a qu'iescent state until

the next 'fl ag' occurs.

If the nlanual data entrY 'f l ag '

punch the f i ve sw j tch-regj ster bi ts ,

parity b'its (tlord 3), and transmjt a

the 'data punched' message tlte 'f1ag'

to i ts qu'iescent state .

A seven-pole eight-Positionbi ts and trvo i denti f i cati on

is set, the unit should provide to the

and the appropriate identification and

'punch' instruction. 0n the receipt of

should be reset to 0 and the un'it return

srvjtch to select the appropriate five data

bi ts,

Similarly if the block'f'lag'is set, l'lord 4 should be first provided to

the punch and tlre 'punch' jnstruction transnrjtted. tJhen the 'data punched'

message is received, l'.iord 5 should be supplied to the punch and tlte process

repeated, until with l'lord 8 supplied to the punch the'data punched'message

is received, vrhen the bloclt'flag'should be reset to 0 and the unit return t0

its quiescent state

If tvro or more flags are set simultaneously, the unit should provide each

word concerned to the punch in strict numerical sequence, resetting each flag

when all words from that source have been punched, and returning to itsquiescent state only after al'l flags have been reset to 0. To avoid interrup-

tion of the vrord sequence, after any f]ags have been set, further flags should

be ignored until all data perta'ining to the original flags has been punched'

The multiplexer cjrcuitry clesigned to perform these functions can be cate-

gor i sed i nto the fol I ol'ri ng u n'i ts .

1.

Page 202: 2-Whole-digital Data Processing in Radio Astronomy

?,

4.

195.

a seven-input parity-bit generator, to supply the eighth b'it to the punch

as a result of the seven data bits selected,

3. ,f1ag, circuits for each of the three data sources, and,

a switch-drive system to respond to these flags and instructjons from the

punch system, and to select the appropriate data and identification via

the seven-pole eight-position switch.

In addition, from section 8.1, d tvrenty-four-bjt parallef input buffer

register is required for the coordinate data, and a five-bit switch-reg'ister for

manually entering data on to the tape must be prov'ided'

The development of these circujts is discussed in the following sections.

8.31 The Seven-Pole Eight-Posit'ion Switcll

One bank of the seven-po1e eight-pos'ition switch is shovtn in Figure 8.3.

Each switch bank comprises an eight x ?-input AllD-OR network. When the srv'itch

select l'ine n is 1, and all others are 0, the output is l'ln' Thus each of the

eight.inputs can be indivjdually selectecl by making the appropriate switch line

hjgh. The switch select lines are drjven by the sr,r'itch-drive circuit descrjbed

in sectjon 8.34. There are seven banks of the fornt of Figure B'3, one for each

of the five data channels and two for the identification channels.

8.32 The Parity-Bit Generator

From the seven outputs of the eight-position switch, the parity-bit generator

produces the eighth bit of the tape character as one which makes the total

number of 1's in any tape character an even number, i.e., the tape characters

have'even parity'. The circuit used to generate this bit (Figure 8'4)

utjlizessixexclus.ive-orqatestoproducetheleast-sjgnifjcant-bitofthesum of the seven binary inputs. If thjs bit is 0, then the sum of the bits'is

even, and hence the parity bit should also be 0. If thjs bjt is 1, then the sum

of the bits is odd, and the parity bit should also be 1 -'i'e, the output is

in the correct form to produce 'even parity' tape characters'

8.33 The Flaq Circuits and the Clock Buflg1

data flag is included jn the analogue-to-dig'ita1 converter

So only the circuits for the block and ntanual data entry flags

The twenty-four-bit buffer register for the coordinate data

The samp'le

buffer cjrcuit,are requi red.

Page 203: 2-Whole-digital Data Processing in Radio Astronomy

wl

,116

w3

vr{

Ilb

196.

Chqnnel 1 InpqtsFrom EEch Word

Chonnel, 'l

Out To Punch

r23.4S678 ,

Swirtch Setsct Lines

Fjgu.re, 8,.3,; One bank of t,he- seven-pole eig:ht,-position stlitch

lvlu,tti;p lcrcr Outputs

1

7

3

l.

5

T.

I

Porlty Ei't ,0ur

( Chonnel 6 )

Fisure €.4,: The parity,-bit generatotn

consist€, of six rcluad ilatch'ci,rculits Wtnich can each be consider€d as fbun

type D flip-flops (s,ee Ohapter 6) eontained in a si,ng;tre package with a,comlon

Page 204: 2-Whole-digital Data Processing in Radio Astronomy

clock input and only the Q outputs available.

on a positive (G'1) transition of the clock.

The circuit vlhich suppljes the clock pulse to

mark instruction, and a'lso acts as the block flag'The capacitive coupfing betrveen G, and G2 produces

t97.

Data is read into these latches

this buffer from the block-

is shown in Figure 8.5a.

the short clock Pulse of

--' r-BtockMork

B u fferTri gger

BlockFtog

Btock Ftog

Resst

BtockMork

q

G2

G3

F-.' Tt

(b)(o)

Figure 8.5: The b'lock flag circuit (a) and its v/aveforms (b)

length T1 for the buffer circuit. Because Gz is also capacitively coupled to

the flag RS flip-f1op Ge, G4, the flag is set by the fal'ling edge of the clock

pu1se, and is thus delayed by tir",re Tr fronr the block-mark instruction. This

delay is set to 100 microseconds to ensure that the b'lock flag is always set

after the comesponding sanrp'le f1ag. The waveforms of this circujt are shown

in Figure 8.5b.

The manual data entry flag (F'igure 8.6) can be set either electrically by

an externa] pu1se, or manually by the sr.ritch Sr. A similar delay circuit tothat used in the block-mark flag has been provided for the external input.

This de'lay has been included in order that the flag may be set by a sample

instruction yet the correct character sequence be nraintained.

ExternqlFtog

FLAG

Reset

9rn9te con t I nuou5

Figure 8.6: The manual data entry flag circuit

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198.

The flag may be set manually in two different klays. If Sr is closed to

the left (position 1) then a short pu'lse sets the f1ag, which is reset afterthe switch-register data has been punched. If Sr is closed to the right(position 2) then the flag is set and remains set, even after a reset pu1se,

unti'l the switch is opened and a reset pulse occurs. This continuous flag can

be used for punching blank leader and trailer tapes. If the switch register

and its identification bjts are all set to 0 and Sr held in position 2, then

the punch r,ril1 produce blank tape (sprocket punching on'ly) at its maximum speed

(20 characters/second) untjl Sr is opened.

8.34 The Multiplexer Svritch-Drive

The most important function of the recording system, that of grouping the

data into eight-b'it bytes and arranging these bytes on to paper tape, is con-

trolled by the mu'ltiplexer sr'ritch-drive. Briefly, fts operat'ion can be des-

cribed as folIols.

When data is ready for punching, a flag bit is set for each character con-

cerned. These flag b'its are continuous'ly interrogated and read into an eight-

bit memory in the unit, 1000 times/second. When a 1 is read into a memory

location, the interrogation ceases, and the lowest indexed vtord of vthich the

f'lag-memory is a l is written by the punch. I,lhen a 'data punched'signal is

received from the punch, that menlory location is reset to 0 and the next lowest

indexed word of which the flag-memory is I is written, and so on. 0n1y when

all f'lag-memories are 0 does the f'lag.interrogat'ion recommence' so that ajlcharacters of which the flags were set at one instant are punched in numerical

sequence and subsequently set flags are not acknovrledged until all of that data

has been punched.

The circuit which controls this operation is sholn in Figure B.B' Before

its operation can be described in detail it r.lill be necessary to establislr the

functfon of the gates Ay*6 in delaying the inverted outputs of the memory fiip-glop:, Dr*.. Consider the circuit shovrn in Figure 8.7a vlith Q initially at 0

and Q at 1. If thjs state has persisted for some time then X will be at 1 and

Y(=d.X) will be I (see waveforms, Figure B.7b). Novl assume that the ffip-f1opis triggered with D a 1, and thus Q goes to 1 and d to t..o. As X is unaffected'

Y will follow Q and go to 0. At some'later t'ime assume that the fl'ip-flop is

triggered rvith D a 0, so that Q returns to 0 and d to t. The input X momentariiy

fo1lows Q to 0, returning to I after an interval T. Y then becomes a 1, and

thus the G>l transition of 0 has been delayed by an interval T.

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(o)

Figure 8.7: The

Referring now to Figure

logical expressions for each

a delay circuit (a) and its waveforms (b)

8.8, after any transient delays have passed, the

of the switch-drive lines Sr*, can be written

It is assumed of the paper tape punch that a punch action will be initiated

by a 'punch enable, ljne becoming a L, and jf this line is stil'l 1 at the end

of a punch cycle, another will be init'iated. The 'data punched' signal is

transmitted after the punch action but before the punch cycle is comp'lete'

199.

(8.1)

will be reset

(8.2)

Sn=Dn.Dn-r.Dn-, .Dl

as the output of gate An (11n<8) it q. Thus

switch drive Iine corresponding to the. -'lowest

high, and all others wi]l be lovt.

where 'E represents

bV Nn becoming a 1,

if any of the D's are 1, the

indexed D which is a 1 will be

The resetting'lines N,*, of the eight flag-memories can be expressed as

Nn = Sn.E, (1:n<B)

the 'data punched' I ine, and as the fl ip-f 'lops

this can be better written as

4- = sn'E

Thus, when a 'data punched' pulse occurs, the memory locatjon corresponding

to the currently selected svlitch line will be reset to 0, and from equation 8"1

the next lovrest indexed word for r'rhich D is a l wil] then be selected. However'

because An does not become a L immed'iately that {So.t to a 1, the next switch-

drjve is not selected'immediately that Dn is returned to 0, but after a de'lay T'

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200.

SwitchDriveLines ^+)lSomple

F tog

Sompte FtogRese t

MsnuolEntry Ftog

Monuol FlogReset

BtockFtog

Btock FResct

PunchEnoble

Ctock Enoble

Figure 8.8: The multiplexer switch-drive unit.

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201.

ensuring that the resetting signal E has returned to 0.

and the outPut of gate A,

1ine, isAs the output of gate A, is D,

6-e, then the outPut of gate l'lg, the

.02 . \, 1S

'punch enab'l e'

(s.3)

and the'output of Gate N1s, the 'clock enable' line' is

Nro = Ng = t)-r.D'.Dr .D't (8'4)

Thus if a'll D's are 0, the 'punch enable' line Ng is 0 and the 'clock

enable''line is 1, al]owing the interrogation of the three flag inputs by the

lKHz clock. If any D goes to t, i:hen lle becomes a ]. and Nro a 0' The interro-

gation then ceases because the clock'is inhibited, and a punch action is initj-ated by the 3.+1 transition of Ne. No delay is assocjat,ed t'rith this action' as

only 1-r0 transitions of the D's are 'involved (see Figure B.7b).

Consider the unjt initially in its quiescent state (continuous'interrogation)

and the samp'le f'lag suddenly becomes 1. 0n the next 0+1 transitjon of the lKHz

clock, both Dr and Dz wil] go to 1. As a result of tltis, from equation B.l''

51 goes to 1 and all other S's remain 0. From equations 8.3 and B'4' Nro 90€5

to 0, inhjbiting the clock, and Ne goeg to L, starting a punch action' At some

'later time a short 0*1 pulse r,ri'll occur on the 'data punched' line, indicating

that Word t has been punched. Fron equation 8.2, this will cause Dr to be reset

to 0 (Sr vril'l also fall to 0), and after a deldY T, from equation B'1, Sz willgo to 1. As D2 is still a 1, l{g and tlls Femdin in their present states, and at

the end of the first punch cyc1e, a second will commence. l.lhen the 0+l'

transjtion of tlre'data punched' ljne occurs indicating that I'lord 2 has been

punchbcl, from equation 8.2, Dz will be reset to 0, and also the sample flag as

it also is connected to Nz. lJhen Dz is reset to 0, Sz will also return to 0'

After an'interval T, ilg w'ill return to 0 and llro to 1, allorving the flag

interrogation to recommence. tlhen the second punch cycle ends, aS Ng is'0' no

new cycle will be initiated until further flags are read into the memory'

8.35 Provision For Reduced tJord Length

As the analogue-to-dig'ita1 converter rvord length can be shortened to five

bits, provisjon has been made to ounch only l^lord l vthen a samp'le flag occurs'

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202.

should a reduced resolution be desired. Sirnilarly if samples are taken at

integer seconds jt jS not necessary to punch l{ord B when a block flag occurs'

as this word conveys only fractional-second information. If samples are taken

at integer minutes, then trlord 7 also is not required' as it conveys only second

informatjon. The circuits which provide for these reduced word lengths are

shown in Figure 8.9.

Seconds 0.1 x Seconds

SompteFtog

5 bit

7,9 bitr---_->

01 InPut

D2 InPut

Do,Ds'De.)

07 ),nou,,ID8 -,'

N6

N7

frln

an

outN1

N27,9 bit* q %tNs

(b)

Figure8.9:Theprovjsionforreducedwordlength.(a) ffre sample data circuit, and (b) the clock data circuit'

When five-bjt sample resolution'is used, the sample flag sets only D1'

and the flag is reset from flr trhen Dr is reset (see Figure 8'9a)' l'Jhe seconds

coordinate resolution is used, the block flag sets only D+, Ds, De and Dz (see

Figure B.9b) and the flag is reset from l'lz vthen Dz is reset' If mjnutes

resolution'is used, the block flag sets on'ly D,*, Ds dhd Ds, dfld the flag is

reset from lle when Do is reset.

8.4

The Dig.ital Mult.iplexer (Plate 6) occupies the remain'ing B" of front panel

space.in the 7,,high,19" wide frame which houses the analogue-to-digjtal con-

verter and the time interval generator. In addition to the sw'itches St' Szn Sa

(Figure 8.9) for reduc'ing the sample and coordjnate vrord lengths, switches are

jncluded which allow the identification codes of lrlords 1 and 4 to be supplied

from an external source. This facility rvas included for tlord l in partjcular'

to enable different identification codes to be used for the sample data if the

input analogue signal was mul tiplexed

(o)

The seven-bit switch-register allorvs for

and also enables the identificat'ion of l'lord 3

the manual entry of f ive data b'its'

to be programmed. The centre-off

Characteri sti cs

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203.

#* eDIGITAL MUlTIPtEXTR

A/D DATA

ooI.O LINGTH FIAG

CTOCX OATA

oooI.O. LENGTH FLAG

rr:r,:,lll,f, ;.ir,::f,tlO;stc 0.1 sEcoa

,trililf,m|f,r

ooo

oo-to.-

AUX DATA

oooooDATA _

oINT

ocoirr.

(a) Thewith the

(b)

digital multiplexer front pane1, and (b) a viewside panel removed.

PLATE 6:

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2A4.

swjtch to the right of the switch-register provides a single flag setting in the

upward position and a continuous flag setting in the downward position (Sr

Figure 8.6). Data from an external source can also be entered to Word 3 via

the seven input sockets below the switch-register. The eighth switch on the

right-hand end of the register selects data from ejther the switch-register or

the iriput sockets (see Figure 8.10). When in the external pos'ition the switch-

register is disabled and its setting does not affect the input data.

t.o. _*tF s*ii.r,.f- Doto Swttches

Figure 8.1.0: The swi tch-reg'ister for manual data entry.

The three indicator lamps are illuminated vrhen their respective flags are

set to shovr from which source data'is being punched. As a flag may be set fot:

as little as ten milliseconds before be'ing reset, a monostable circuit has

been incorporated in the lamp drivers to ensure that the lamps stay on for at

least 200 mi'll iseconds, the nrinimum period requ'ired for adequate indication.

The input connections from the analogue-to-digita'l converter and from the

digital clock are located on the rear pane1. The lKHz'f1ag interrogate'signal

which is obtained from the lKHz output of the clock, js also connected via a

rear panel B.N.C. connector. The various circuits of the multiplexer are con-

tained on ten plug-in plinted-circuit boards' arranged in two rows as shown in

plate 6b. Access to the circuit board connectors can be obtained from the

front, by hinging the front panel forward, and frorn the side by removing the

side panel as in Plate 6b.

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205.

8.5 The Requirements of the Tape Punch Un'it

The INVAC P-135-20 paper tape punch, briefly described in section 8.11,

was purchased as a basic unjt, without control and driving circuits, power

supplies or tape-spooling equipment. The requirements of these units will be

specified by the characteristics of the signals from the digjtal multiplexer'and the requirements of the punch itself.

8.51 The Requirements of the Control and Dniving Circujts

The P-135-20 js a solenoid-actuated e'ight-channe'l tape perforator. Thirteen

solenoids are used to operate the unit, eight for the data channe'ls and one to

punch the sprocket hole (the'punch'action), tlo for retracting the punch pins

from the die (the 'bail'action) and two for advancing the tape by one character

(the'transport'action). Each solenoid has a resistance of 23CI, and requires

a twenty-seven volt pulse to actuate it (INVAC,1965). The inductance of these

solenoids has been measured as approx'imately 20 mjllihenrys.

The timing requ'irements for the punch action are shown in Figure 8.11.

LJhen a punch action is required, a 27t2 volt pulse of 10.5t.5 milljseconds

duration must be applied to the appropriate data solenoids and the sprocket hole

solenoid. After this pulse, an 11.5r0.5 rnillisecond 27tZ volt pu]se is app'lied

to the bail soleno'ids, retracting the punch pins from the die. This is followed

by a further ?7tZ volt pulse of 12.510.5 m'illiseconds duratjon applied to the

transport solenojds, moving the tape forward by 0.1 inches. A further punch

cycie cannot be initiated until at least fifty milliseconds have elapsed since'

the previous action began (lNVAC, 1965).

of PunchAction

50 mittisecondsmlntrnum

Sorocket ondDoto Sotenoids

Tronsport Solenotds

B4rnnrng*

11-12ms

Figure 8.11: T'iming requirements of the P-135-20 punch.

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206.

A circuit will be required to control this punch cycle jn accordance with

the requirements of the multiplexer. These requirements are (1) tfrat a punch

cycle should be initiated by the'punch enable'line becom'ing a 1 or by the

end of the prev'ious punch cycle (50 mjlliseconds after it started) if the 'punch

enable'line is already a 1, and (Z) tfrat a'data punched'signal should be

transmitted as soon as the input data has been punched, j.€., at the end of the

first 10.5 mi I I i second pul se.

In'addition, interface circuits will be requ'ired to convert the G'5 voltlogic levels of the multiplexer's t.t.l. integrated-circuits to the 27 volt,1.2 amp signa'ls required by the data solenoids. The outputs of the controlling

circuit for the sprocket, bail and transport solenoids will also need to be at

this 27 volt level, and 2.4 amps will be required of both the bail and transport

pul ses .

8.52 Power Supply Requirements

The power supp'ly requirements can be estimated from the punch cycle des-

cribed in section 8.51. Taking the maximum load conditions, when al'l channels

are punched at the maximum rate, and noting that the time constant t of the

solenoids (=L/R) is approximately one millisecond, the variation of load current

with time is shovrn in Figure 8.12a. The power supply will be required to

deliver a maximum current of 10.6 amps, and a max'imum average current of 3.1

amps. The maximum current will never be drawn for periods longer than 10.5

milliseconds.

Assuming that all comb'inations of the eight inputs are equally probable'

only four data channe'ls will be punched on the average, and thus the average

maximum variation of loari current with time will be as shown in Figure 8.12b.

The 'average average' current required from the supply will then be 2.2 amps

when the punch is operating at 'its maximum speed.

From the punch manufacturers' spec'ification, (INVAC, 1965), voltage

variations in the range 27xZ uolts are perm'issible, although this js the voltage

across the solenoids, and voltage drops across the switches must be taken into

cons i dera ti on .

8.53 The Provision of Tape Spooling Equipment

As it is envisaged that the acquisitjon system should be able to run for

weeks r.rithout attentjon, and as approximate'ly forty feet of tape may be punched

Page 214: 2-Whole-digital Data Processing in Radio Astronomy

Figure 8,12: Punch power supply toaa r.equirenents.(a) Peak maximum requirements, and(b) averaEe mttximum requirements.

z.zc'qel_ _

206a.

t(mil,liscconds)

5o (mittiscconds)

inhibit the

Jam in front of

per day (six hours' acquisition at one sample in ten seqonds' thirty samples

pen block)o s,ome provision fon the autornatic sfiooli'nE o,f this tape should be

provld,ed. Under the conditions des,cribed, the l.ate o tape flow would be

e.r'ratic fon a preriod o'f six hoursn and no tape at all would flow for eiEhteen

hoursn so it wils ptoposed that some fonn ofon-off ta(e-up mstor would be used

rather than one incorporating a slipping clutch.

In this spooling unit should also be fncluderd facilitJ topunch action dnd produce a fauTt lndtcatjon if the taFe:sttould

the punch, or if'the end of the tape. is encou'ntered.

--++--:--

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207.

8.6 The Develooment of a Punch Control Unit

From the control s'ignals available at the multip'lexer, the spec'ification

of a sequencer to control the punch cycle is as follows. When the'punch

enable'line becomes a 1, the sequencer should generate a'punch'pulse of

10.5 milliseconds duration, which gates the eight data inputs from the multi-

plexer into buffer circuits, applying 27 volts to the data solenoids. This

pu'lse should also drive the sprocket punch solenoid through a similar buffer

circuit.. Following the 'punch' pu'lse, a second pulse of 11.5 mill'iseconds

duration should be generated to drive the bail solenojds. This pulse should be

follovred by yet another of 12.5 mill'iseconds duration which drives the transport

solenoids. 15.5 milliseconds after the end of this pulse, if the'punch enable'

line is a 1, the cycle should recommence with another 10.5 millisecond'punch'

pulse. If the ,punch enab'le' line js 0 after the 15.5 millisecond period, the

sequencer should remain dormant until a Grl transition occurs on thjs line'

8.61 The Punch Sequencer Unit

The punch sequencer unit (F'igure 8.13) js based on four monostable multi-

vibrator circuits which sequentially generate periods of 10.5 ms,11.5 ms,

12.5 ms and 15.5 nts, for the punch, bail, transport and rest periods' This

asynchronous system of sequencing the pUnch operat'ion l,\las chosen in preference

to a c'lock-based synchronous system because of jts simplicjty' The FCK1Oi

monostable units used have a dual I'lAllD input, and are triggered by a negative

going (1*0) transitjon at either of the- inputs. Timing'is controlled by an

external capacitor and resistor; variable resistors have been used to provide

fine adjustment of the monostable pepiod. The pulse outputs of the punch, bail

and transport periods are at pos'itive logic t.t.1. levels, enabling similar

buffer circuits to be used for all of the solenoids.

PunchEnoble

G7

Punch Doto BorlPunched

Fi gure 8.13: The punch sequencer circuit.

Tronsport

Rest

Page 216: 2-Whole-digital Data Processing in Radio Astronomy

208.

0n a G'l transjtion of the'punch enable''line, Gz is set to a 1 and

stays there regardless of the future of the'punch enable'line. At the same

time a L-rO transition occurs at the output of G,*, and this triggers the mono-

stable l4r, causing the output'punch' to become L for a period of 10.5 milli-seconds. At the end of this period Mr returns to 0, and Mz is triggered by

thjs l+0 transition. The'bail'output then becomes L for a period of 11.5

milliseconds. At the same time Gz goes momentarily to 1, then returns to 0,

generating the 'data punched' signal . l'lhen t{2 returns to 0, l'la is triggered'

and the 'transport'output goes to 1 for 12.5 milliseconds. The 1*0 transition

of M3 at the end of this period in turn triggers Mq whjch causes the 'rest'line to go to 1 for a period of 15.5 milliseconds. If the 'punch enab1e' line

is 0 at the end of this period, the 1-+0 transition resets the Gz, Gg RS flip-flop, and the circuit becomes dormant until another G>l transition of the

,punch enable'line causes the cycle to reconrnence. If the'punch enable'line

is 1 at the end of the rest pepiod, then Gz, Gr will not be reset, but the

negative (t*O) transition wj'll be conveyed through Gs and Ge to trigger Mr ollce

again, causing the cYcle to rePeat.

The purpose of the RS flip fioP Gz, Gg, is to prevent G>l' transitjons on

the'punch enable'ljne from triggeping l{1 trhen a cycle is in progress' This

circuit effectively locks out the punch enable line during the 50 millisecond

cycl e.

The punch, bail, transpor! and r.it wuu.forms are Shown

The 500 nanosecond'data punched'pulse js too short to show

trace.

1n

up

Figure 8.14.

on this low-speed

Figure 8.14: Osci1 loscope tracesand rest Dulses.

of the punch, bai1, transPort

Page 217: 2-Whole-digital Data Processing in Radio Astronomy

209.

8.6? The Solenoid Drive Circuits

Eleven solenoid drivers are required for the punch; nine to drive the

punch solenojds (27 vo1ts,1.2 amps each) and one each for the bail and

transport so1enoid pairs (27 volts, 2.4 amps per pair). All of these must be

operated from t,t.'1. iogic levels. The eight data solenoids are required to

have a dual AND input, 'in order that the sequencer 'puncH pulse may gate the

data outputs from the multiplexer. In addition, a means of inhibiting al'l of

the punch actions from a logic signal is requ'ired in case of mechanical faults

(see section 8.53).

The drjver circuit developed to satisfy these requirements is shown in

Figure g.15. Each driver uses a three-jnput t.t.l. gate to provide the necessary

gating of the data, control pulse and inhibit signals. 0nly two inputs are

used on the sprocket, bail and transport drivers as no data input'is requ'ired.

When a'll three

supplies 100mA base

will draw at least

i nputs are L, the 2N706 does not conduct, and the 2N697

current to the 40310 output transistor, ensuring that it2.5 amps collector current (B*rn+ZS for Ic = 2A)'

The diode D and res'istance R form a trans'ient suppression network which

prevents reverse-biased-second-breakdown from occuring in the output transistor

(Lochern lg70). As the solenoid tjme constant is -L millisecond, after a ten

+27v

lr.7KN

iRi Sotenoid

dqto

con t 40310innioit

.Figure 8.15: The solenoid-drive circuit.

Page 218: 2-Whole-digital Data Processing in Radio Astronomy

2lo.

mjllisecond 'on'period the load current will have practically reached itssteady-state value IO., and when the transistor turns off this current willcontjnue to flow through the inductor. If no a1ternative path is provided for

this current, the collector voltage of the output transistor wi'll rise to the

collector-emitter breakdown voltage VCE', and the stored energy in the inductor

will be dissipated in the transistor. If the inductor current is high' this

can lead to reverse-biased-second-breakdown (Locher, 1970).

The diode D and resistance R provide an alternative path for this current,

which then decays with a time constant t' = L/(R+R'), and hence the'larger the

value of R, the more quickly the current decays. The removal of this current

is important for the rapid operation of the punch. When the transistor turns

off, the collector vo'ltage (see Figure 8.16) is g'iven by

v.. = zl + vD* Id. Re-t/T' (8.5)

where VO is the forward voltage drop across the diode.

Figure 8.16: (a) The vo'ltage waveform at the collector of the

output transistor, and (b) the current through the so'lenoid.

The maximum vajue of R which may be used will be determ'ined by the collector-

emitter breakdown voltage VCE' of the transistor. For the 40310, if the collector

voltage is not to exceed the collector-enritter breakdown voltage (VCSO = 35 volts)

then Rru* = 5.96e for the punch solenoids and 2.980 for the bail and transport

so'lenoid pairs assuming a forward voltage drop VO across the diode of L volt.

Page 219: 2-Whole-digital Data Processing in Radio Astronomy

zLL.

The average povler diss'ipationsin these resistances when the punch is operating

at its maximum speed are 0.05 and 0.1 watts respectively. Preferred value

resistances of 5.6Q and 2.7a at )-" watt rating vtere used in these networks'

The requirements of the diodes, that they r+ithstand a peak current of L.2

amps (or 2.4 arnps for the bajl and transport solenoid pa'irs) and ihat they carry

a mean current of B.3mA (or 33.2mA for the bail and transport solenojd pairs),

were readi'ly nret by the MB03 diodes used.

8,7 The Tape Punch Power SuPPIY

The design of voltage regu'lator c'ircuits is t'rell covered in the literature,

but the specification of transformers, rectifiers and'i'jlters to supp'ly the input

to such units is not (Pownall,1969). The requirements of thjs supply are that

it provide currents of up to 10.5 amps for periods of 10 mjlliseconds, and a

maxjmum average current of 3.1 amps. These requirements introduce unusual

features to the design of both the unregulated supply and the vo]tage regulator.

8.71 The Design of the Unregulated Suppl.v

The typical circujt of a full wave rectifier unregu'lated supp'ly is shown

in Figure 8.17. The transformer winding has been assumed to be lossless, all

voltage drops be'ing accounted for by the resistance R.

u*l

F'igure 8.17: The unregul ated supply

The requirements of this regulator were determined by the diodes available

(40110) and the transistor to be used in the regulator (2N2773). As this

transistor has a maximum dissipat'ion of 150 utatts, the output voltage of the

unregulated supply should never exceed 42 volts (27+15). The regulator will

requ.ire some vo]tage droo across it in order to function, and it lvas specified

that the output voltage should never fall below 32 volts (Zt+S). These require-

AI

Page 220: 2-Whole-digital Data Processing in Radio Astronomy

ments are satisfied by a 30-0-30 volt r.m.s. transformer winding and

tance C of 10,000UF. The total rvinding resistance R, jn order that

surge cument of the diodes (t40 amps) is not exceeded, should be at

2L2.

a capac'r -the peak

least 0.3n.

A model of this unregu'tated supply was constructed (both voitage and.current

were scaled) in order to evaluate the r.m.s. transformer cument. The maxjmum

load conditions of Figure 8.12a were sjmulated, and the fol'lovring voltages and

cunents determi ned:

Average ful'l -l oad output vol tage:

Mi nimum ful I -'l oad output vol tage:

r.m.s. transformer current (through centre-tap) :

Average transformer current:Peak repetitive diode cument:

35 volts32 volts6.5 amps

3 amps

23 amps

amps is well within the 40 amPs

current in the transformer calls

8.72 The Voltage Regulator

The vo'ltage regulator (Figure 8.18) uses a conventjonal series regulator

circuit with a pre-regulator constant-current source. The transistor Tr forms

the pre-regulator, supplying a constant current to the control transistor Tz.

The error current is amplified through-Ta, Tu and Ts and applied to the load.

The peak repetitive diode current of 23

maximum of the 40110, and the 6.5 amps r.m.s.

for a transformer with a 200 watt rating.

Unregu totedInput

R2

o.105nRl

o.o7n27 Yolt OutPut

lOpF

T1 ; 40319

TzJ:,TaIz t 10314

To ; 40310

T5;2N2773

3.3O-O1pF

lKn3.3Kn

Figure 8.18: The 27 volt regulator circuit

Page 221: 2-Whole-digital Data Processing in Radio Astronomy

213.

The unusual feature of this requlator is the time dependent overload pro-

tectjon prov'iclr:d by transjstors To and Tz.. The unregulated supply and the

output transjstor T, have been designed to supply a maximum average current of

3.1 amps, Vet they must also supply up to 10.5 amps for intervals of 10 milli-seconds. Transistors T6 and T7 €flSUfe that these conditions are not exceeded.

If the instantaneous load js such that the maximum rating of 10.5 amps is

exceeded, then the voltage deve'loped across resjstanc€ R1 causes Tz to turn on,

reducing the output voltage and converting the supply to a constant current

source of 10.5 arnps. Holever if the load is slight]y less than this, say 10 amps'

then T, does not turn on, but the voltage devetoped across Rr+Rz (t.ZS volts)

will charge the capacftor Cr through resistance Rg, and after approximately 13

mil'liseconds, transistor Te will turn on. This will cause the output vo'ltage to

drop, and the supp'ly to change to a constant current source of 4 amps. In the

first case vrhere the instantaneous current rating was exceeded, after about 10

milliseconds, the constant currenI source would drop from 10.5 amps to 4 amps'

as Cr was charged.

Transisior Tz thus prevents the instantaneous current from exceeding 10.5

amps, and T5 prevents the s'beady-state current from exceeding 4 amps. The

duration for rvhich a current greater than 4 amps w'i11 be supplied is inversely

proportional to the extent by which it exceeds 4 amps.

As the reference voltage supply is obtained from the regulator output, ifunder overload condjtions the output vo-ltage fa'lls below this reference voltage

(15v) then the reguiator will shut dovrn, and will not restart even when the

over'load cond'ition is removed. To reset the regulator from this state, switch

Sr has been included to apply a short cument pulse to the zener d'iode from the

unregulated supply.

8.73 The Perfornrance of the Punch Porver Supply

The following characterjst'ics of the power supply have been measured:

0utput impedance (loads of up to 10A):

Input regulation under full load conditions(3.1A, mains variations t10%):

No-l oad ri pp1 e:

Full-load ripple:

0 .05n

2%

<2mV pk-pk

SnrV pk-pk

Page 222: 2-Whole-digital Data Processing in Radio Astronomy

2t4.

The operation of the overload protection circuits is shown in Figure 8.19.

The lower trace shor^rs the load current (5A/division) and the upper trace the

load voltage variation (10 volts/djvision). The horizontal sensitivity is

l0msec/division. l,lhen a load of 2.70 is connected across the regulator itinitial'ly supp'lies 10A witir no appreciable vo'ltage drop, but after 16 mil'li-seconds the output voltage begins to drop as T5 (Figure B.1S) begins to conduct.

After a further 10 rnilliseconds the voltage has dropped by 16 volts, and the

cument has reached its limiting value of 4 amps.

Figure 8.19: The operation of the overload protection circuit.(a) fne load voltage variation (tov/aivision)

(b) The load current variation (sA/division)

Horizontal sens'it'ivjty is lOmsec/division

8.8 Tape Punch Mechanical Details

I .81 The Ta pe Spool i ng Equ i P!'Len!

The tape hand]ing unit developed to satisfy the requirements listed in

section 8.53 is shown in Plate 7. It occupies 10%" of front panel space 19"

wide, The punch control electron'ics are contained behjnd the front panel. The

supply drawer (1) on the left of the un'it is designed to accommodate an eight-

inch diameter 1000 foot reel of unpunched tape. The tape passes out through the

bottom of thjs drar.rer and over the 'tape tjght' arm (2), before entering the

punch. If the tape jams in the supp'ly drawer, this arm actuates a microswitch

vrlrich inhib'its the punch act'ion and iJlunrinates the'tape t'ight'indicator(top right). The'end of tape' switch (3) is part of the punch unit; this

inhibits the nunch actjon and illuminates the 'end of tape' ind'icator when only

(o)

(b)

Page 223: 2-Whole-digital Data Processing in Radio Astronomy

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2" of unpunched tape remain in front of the punch head (4).

The punched tape passes over the two capstans (5) and under the tension

arrn (O) before being wound on to the take-up spool (7). l^lhen the tension arm

arrives at the bottom of its travel it actuates a microsvlitch which starts the

take-up motor. As the tape is wound in, the tension arm travels upwards untilit reaches the top of its travel and actuates another microswitch which stops

the take-up motor. The 5-inch diameter take-up spool has a standard 2-inch

diameter hub, and can accommodate 350 feet of punched tape. It is driven by a

governor-control'led gramaphone motor wh'ich has its peed adiusted to be suffi-ciently fast to cope with the maximum tape speed (2"/sec) when the take-up spool

is empty

If there is no tape tension then the tension arm falls to the bottom of itstravel, and does not rjse vrhen the take-up motor starts. To prevent the motor

from running continously under this 'tape break' condition, a further microswitch

stops the motor if the tcnsion arm does not commence to rise when the take-up

motor starts. As this condition sometjmes occurs when a new tape is being

threaded, an override button is prov'ided vrhich keeps the motor go'ing until the

slack tape is taken up.

The tape punchings accumulate in the chad drarver (8).

The circuit details of the tape handler unit are given in Appendix 9. The

circuits associated with the motor control are mounted inunediately behind the

motor, along with the self-locking relay which starts and stops the motor. Arc

suppressors have been provided on all breaking contacts to prevent the generation

of str:ay pulses'in the'logic circu'itry. The circuits associated with the control

of the punch, i.e., the'tape tight'and'end of tape'c'ircuits, are contained

in the punch control unit, d'iscussed in the next section. When either of these

faultS occurs, the 'punch inhibit' line (see section 8.6) falls to a logical 0'

and no energy'is suppiied to the solenoids of the punch.

B.BZ The Punch Control Electronics

The punch control electron'ics (Plate 8a),1ocated at the rear of the tape

handler unit, contain the punch sequencer circuit, the solenoid drjve bufferst

and the punch control circu'its associated with the tape handler. These circu'its

are contained on six plug-'in printed-circujt boards. The eleven output transis-

tors of the solenoid drive buffers are ntounted on a common heat sink which forms

Page 225: 2-Whole-digital Data Processing in Radio Astronomy

217.

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Page 226: 2-Whole-digital Data Processing in Radio Astronomy

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the base of the unit. Connections froln the 27 volt and 5 volt power suppfies

are made to this pane'I, together with the eight data inputs from the multiplexer'

connection to the punch is nrade vja a Z8-rvjre cable and l,r'inchester connector.

The eight-way connector on the left hand side of the unit provides the control

functions from the tape handler.

The outputs of the punch, bail, transport and rest monostables in the

sequencer can be monjtored at the four sockets located on the left hand side of

the unit. l,lith the multip'lexer disconnected the punch can be tested by

depressing the punch activate button. The toggle swjtch allows the unit to be

turned on when disconnected from the handler and the front panel on-off switch'

8.83 The Punch Porver SUPPIY

The punch power supp'ly (Plate Bb) occupies a T" vlidth of an B-3/4',high'

l.9,,wide rack mounted dravter. The clock power supply and genera'l 1ogjc power

supply (see Chapter 9 and Appendix 9) occupy the remajnder of this drat'rer'

The outout transistor (Ts, Figure B.18) and its driver (To) are mounted on an

extruded aluminjum heat sink which fonns tire rear pane'l of the unit' The

connec^uion to the punch is located on th'is rear panel' Access to the adjustment

potentiometer (Ru, Fjgure 8.18)'is obtained through a hole in the front panel'

and two sockets are avajlable on the front panel for monjtoring the output

vol tage.

REFEdENCES

INVAC, (fgOs): "TaPe Punch Model

1e65) .

P-135 Instruction Manual ". (Massachusetts '

pj 1[ P,or'ler Trans i stors" .LOCHER, R.E. (1970): "0n Switching

' Trans. I.E.E.E. ' IECi-17

Inductive Loads

pp. 256-262.

P0I^JNALL, M.J. (1969) : "A Data Processi ng System

M.E. Thesis, University of Auckland'

for a Rotating Interferometer"'

Page 227: 2-Whole-digital Data Processing in Radio Astronomy

2L9.

CHAPTER 9

A General Description of the Data Acquisition System

In the previous three chapters the developnrent of the three basic elements

of the acquisition portion of a digital data processing system for a radio

telescope has been described. The elements are an analogue-to-digital con-

version unjt, for digitizing the input analogue signal, a solar/sidereal

digital clock, to provide coordinates for the digitized data, and a paper tape

recording system which stores the digitized data and jts coordinates on a machine

readable medium. These elements form a system which prepares the input analogue

data for conrputer analysis. In this chapter the coordinatjon of these three

elements and the operation of the resu'ltant system are described.

9.1 The Complete Acquisition System

The block diagram of Figure 9.1 shows the relationships between the three

basic elements and their ancillary units. The digital clock simultaneously

produces both solar and sidereal times in b.c.d. format. Between two programmed

hours of the day clock pulses at one of the availab'le periods (0.1s to 1 day)

are fed into the time interval generator. This unit produces sample instructions

at a programmed multiple of the input clock period, and block-mark instructionsat a programmed multiple of the sample period. Sample instructions cause the

anaiogue-to-digital converter to take a sample of the input analogue voltage and

transmit a 'f1ag'message to the digital multiplexer indicating that data isready to be recorded. The block-mark instructions resu'lt in the digital output

of one of the clocks (either solar or sidereal) being transferred into a buffer

register, and a 'flag'message is transmitted to the multiplexer indicating that

a coordi nate i s ready to be recorded

When a flag is received by the multiplexer, the input digital data concerned

is divided up into five-bit bytes which are punched together with two identifica-tion bits and a parity bit as one eight-bit character on the paper tape. These

groups of data are punched in a preferred sequence, and when all of the data

from one source has been punched, the f'tag concerned is reset. A seven-bit

switch-register can be used to enter data manua'l1y on to the tape.

The operation can be programmed to start and stop at any tvro hours during

the day. Samples can be taken at 100 millisecond to 99 day periods. The time

Page 228: 2-Whole-digital Data Processing in Radio Astronomy

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coordinate can be recorded with 1

a resolution of nine bits for the

0.1 second resolution. The input

coordinate resolution to 1 minute

2?1.

to 90 sample groups. The system normally has

data 'input, and coordinates can be recorded to

resolution can be reduced to five bits and the

if desired.

9 .2 The Operati on of the Acqui si ti q!__f5_teq

A description of the typical operation of the acquisitjon system is best

divided into two parts; the operation of the clock-pu1se source-time intervalgenerator system, which actua'lly controls the acquisition process, and the opera-

tion of the multip'lexer-tape punch system which responds to the requirements of

the former.

9.?L The 0peration of the Clgck-Pulse Source and Time Interval Generator

The circuit diagram of the clock-pu1se source (Figure 7.23) has been

reproduced in Figure 9.2 for reference. The inputs to the selector switches Si

and Sz are the positive logic, most-significant-bit outputs of each of the

counters in the time-keeping circuits of the clock. The timing information is

actually contai.ned in the falling edge (1*0 transition) of these waveforms.

s1

SotorCtockPulses

0.1s

1s

10s

lm'l0m

th1d

0.1s

1s

10s

lm

10m

th

ld

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$0P

t

t

Ctock Putse0ut

START

- ResetIn tervot

ilmeGcnero tor

Si dereolCtockPu lses

iHl*-J'1 nln'

Figure 9.2: The clock-pu1se source

In Figure 9.3, typical control vraveforms at the beginning of an acquisitjon

period are shovrn. The sample interval is set to four clock periods, and the

block interval to five sample'iqtervals. At time trr coincidence occurs in the

Page 230: 2-Whole-digital Data Processing in Radio Astronomy

?22.

start program (Figure 7.22) and as a result the RS fl'ip-flop formed by G2 and

Gg (Figure 9.2) is set. Gr then starts generating clock pulses from the fallingedge of the selected clock pu'lse. Hovlever when Gz is set to 1, Gu generates a

positive reset pulse, which resets both the sample and block counters to zero,

and generates both sarnpie and block-mark instructions. This pu'lse also prevents

the first clock pulse out of G1 from entering the counters. 0n the fourth clock

pulse after the reset pulse from G,*, the samp'le interval counter resets and

generates another sample instruction, as it continues to do every fourth clock

pulse after this until at some later time cojncidence occurs in the stop program

(Figure 7.?2) and Gz returns to zero.

Informo t ront1

Clock PutseOut FromS;

Timc

l,

G2

Gl

G4

SompleInstruct

Btock MorkInstruct ion

Figure 9.3: Contro'l waveforms at the beginning

of an acquisition period.

Each sample instruction, as well as being suppljed to the analogue-to-

digital converter, is fed jnto the block interval counter. 0n the fifth samp'le

after the reset pulse from Gq, the block jnterval counter resets and generates

a block-mark instruction, as it continues to do every fifth sample instructionafter this unti'l Gz returns to zero.

tJhen cojncidence does occur in the stop program and Gz Feturns t0 zero'

the acquisjtion process stops merely because no further sample or block-mark

instructions are generated.

9.22 The 0peration of the Multiplexer and Punch

Typical multip'lexer and punch waveforms during an acquisition period are

Page 231: 2-Whole-digital Data Processing in Radio Astronomy

223.

shown in Figure 9.4. Initially the three flags (sample, manual data entry, and

block) are at 0, jmplying that no data is waiting to be punched, and thus the

flags are bejng continuously'interrogated by the lKHz clock. At time t1 hovrever,

the manual data entry f'lag is set, indjcating that the data at present showing

in the switch register should be punched. 0n the follorvjng rising edge of the

'flag interrogate's'igna1, this flag js transferred into flip-f1oP Ds, (Figure

S.S) with three immediate direct results; the'svritch-drjve 3'line becomes a

1, the ,punch enable'line becomes a 1, and the'clock enable' line goes to 0.

thus preventing further flag interrogation. As a result of the'punch enable'

line becoming a 1, the first monostable of the punch sequence generator (Ml,

Figure 8.13) is triggered, initiating a punch cycle. As 'switch-drive 3' is 1',

the data from the switch register is gated through the multiplexer sw'itch, and

by the ,punch'pulse, into the solenoids of the punch. At the end of the'punch'

pulse, a 'data punched'pulse is generated which resets both flip-f1op Da and

the manual data entry f'lag. D3 returning to 0 results in the 'switch-drive 3'

and'pun6h enable'lines returning to zero, and the'clock enable'line returning

to L, restarting the 'f1ag interrogate' signal. The system has now returned to

its initjal quiescent state although the'bail','transport'and'rest'periodscontinue in the punch, and at the end of the'rest'period, as the'punch enable'

line is 0, the sequencer also ceases to cycle.

At a later time tz, both the sample and b'lock flags are set simultaneously'

and on the next positive transition of the'f1ag interrogate'ljne flip-f1ops

Dr, Dz, D,,, Ds, De, Dz dhd Da are all set to 1. As a direct result of this'the'switch-drjve 1'and'punch enable'lines both go to 1, and the'clock

enable, line goes to 0, preventing further flag interrogation. As a result of

the'punch enable'line becoming a 1, a punch cycle is initiated, and because

'switch drive L' is a 1, data from Word I (Figure 8.2) is punched. At the end

of the 10.5 mi'llisecond'punch'period, a'data punched'pulse resets flip-f1op

Dr, dfld as a result, 'switch-drive 1' returns to 0, and 'sr'litch-drive 2' becomes

I. The ,bai'l','transport'and 'rest' periods continue in the punch sequencer'

and at the end of the'rest'period, as the 'punch enable' line is still a 1'

another punch cycle is initiated. At this time'switch-drive 2' is a 1, so itis data from l^lord 2 which is punched. At the end of this 10.5 millisecond,punch'period, the'data punched'pulse resets both Dz and the sample flag'

and as a result, 'switch drive 2'falls to 0, and'swjtch drive 4'goes to 1.

The'punch enable'line remajns at 1, and at the end of the'rest'period, a

further punch cycle is initiated whjch punches the data fr^orn l'lord 4. The system

continues to cycle in this manner, punching Words 5,6,7 and B.

Page 232: 2-Whole-digital Data Processing in Radio Astronomy

lr

F togInterrogote

Somptc DotoFtog

Monuot DotqFtog

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0l

02

q

D4

D5

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o7

%

g,vitch l)rivc I

2

3

I

5

6

7

I

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Page 233: 2-Whole-digital Data Processing in Radio Astronomy

225.

When the'data punched' pulse occurs fol'lowing the punching of Word 8 (at

time ta), D. is reset to 0, as well as the b'lock flag, and as all of the D's

are now 0, the 'punch enable'line falls to 0 and the 'clock enable' line

returns to 1, restarting the f'lag interrogation. At some previous time tg the

sample flag had been set, but as the 'f1ag interrogate'signal was inhibited'

this was not recognized by the system. However on the first rising edge of the

,flag interrogate'signa1, thjs f'lag is transferred into fljp-flops Dr and Dz'

and the ,punch enable'line returns to 1. 'switch-drive 1'also becomes 1' and

once again the 'f1ag 'interrogate' signal is inhibited.

At the end of the 'rest' period following the punching of Word 8' as the

'punch enab]e' line is still 1, another punch cycle is injtiated' and Word 1

is again punched. Another cycle js initiated at the end of the 'resf period'

and word 2 i s punched . The ,data punched' s'igna] fol I owj ng the punchi ng of

l,lord 2 resets both D2 and the sample flag, and as no further D's are 1' the

'punch enable' line falls to 0, and the flag interrogation recommences' At

the end of the 'rest' period follow'ing the punching of l-lord 2' as the 'punch

enable' line is 0, the punch cycling ceases, and the unit reverts to its

quiescent state.

At time ts another

next positive transitioninto Dr and Dz, and once

Above the Power suppl'ies

paper tape hand'ler and Punch'

sample is taken, and the sample flag is set' 0n the

of the 'f'lag interrogate' signal , this f]ag is read

again Words I and 2 are Punched'

are the 5l4Hz standard frequency oscillator' the

and the rack containing the time interval

9.3 sical Characteristics of lhg isition SYstem

The complete data acqu'isitjon system occupies 4'-6" 0f a 6' high standard

Lg,,rack.cabinet (see PIate 9). The bottom rack unit contains the three povrer

supplies; from left to pight the clock supply, the general power supply' and

the 27 vo'lt punch power supply. The clock supply provides 4 volts' 2 amps

regulated for the r.t.l. circuits of the clocK' and 200 volts unregulated for

the nixje tube drsplay. Tne general po\{er supply prov'ides 5 Vo1ts' 2 amps

regulated for the t.t.l. circuits of the multiplexer' analogue-to'digital con-

verter and punch, and t15 volts 250mA regulated for the operat'ional amplifjers

used jn the analogue-to-digita] converter. The punch supp'ly prov'i des 27 volts

10.5 amps for the punch solenoids. Cjrcu'it details of these power supplies are

given in ApPendix 9.

Page 234: 2-Whole-digital Data Processing in Radio Astronomy

226.

O .--**iir

._a

A

;a

rr

aii

.. o 1i'fAo-aIFw

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I

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tl

PLATE 9: Front and rear views of the data acquisition system.

Page 235: 2-Whole-digital Data Processing in Radio Astronomy

,?27,

generator, analogue-to-digltal convErt€r, and digital multiplexer^. Above these

are a rack containing the elock pulse source and a space fsir a reeeiver f.str

standard ti,me slglalsn and at the top, the solarlsidereal diEital clock.

All iRterconnections internal to the system, (power supply eonnections'

parallel digital data connectlons, clock pulse connections, etc.} apart frbm

those cohcerred with the progratnming of the system (connection's between the

clsck prrlse gource, t,frrne interval genefatof , d,Ird multiplexer) afe csntair'red

,lnside the rear door of the cab'inet, The input to the anal0Eile=to-digital cor-

verter, and all control and monit'otinE facilitfes.are available on the frontpanel

The 230 v6rtt malns s;upplS to the cabinet i's filtered to remove transients

at the poiffi where it enters the cab{n,et, on the left-hand side. It is conhec-

ted to the varlous pohrer supp'lies, the punch motor and the crystal oven unitvia a distr^ihutis.n board in_the bottsm of the eabinet. Atl units are earthed

ts ah" diameter copper bus wtrJch runs the full length of the cabinet.

A spectficatioh o,f the complete acQrlisition system is 'giiv-en in Appondlx l.

Page 236: 2-Whole-digital Data Processing in Radio Astronomy

228.

CHAPTER 1O

The Data AnalYsis System

In Chapter 4 it was shown that the data processing system can be convenient'ly

divided into two distinct sections; the data acquisition section which presents

the interferometer output on punched paper tape, and the data analysis section'

or software, which processes this clata in a digita'l computer to produce the

desired systenr output. The analysis system can be specified in three sections;

storage, analysis and output. The data on the tape is coded in a rather

unorthodox format (see Chapter B) and as large quantities of data vlill generally

be required in the ana'lysis process, the storage system ntust decode the paper

tape data and store it vlithin the computer in an easily manageable format. The

analysis required jnitially extends only as far as averaging collateral data'

and filtering th'is data digjtally. Output is required in three forms; (1) a

tabulation of the sampled data (many systems'in fact use a printer on-line

coupled to the recorcling device to perform this funct'ion) and of the processed

data, (2) a computer printed chart conrparable with that produced by an analogue

chart recorder, and (3) the original and processed data reproduced on punched

cards, a more permanent and more rapidly reacl storage ntedium than punched paper

tape. The requirements of these three sections constituting the analysis system

are establ 'ished i n thi s chaPter.

10.1 Storaqe Requjrenrents

In order to spec'ify the detajls of the storage system, it is necessary to

investigate the characteristics both of the input data and the storage system of

the IBM 1130 conrputer in which the analysis is to be performed. Additional

requirements placed on tlre storage system are that the storage operat'ion be con-

trolled by special control characters punched on the tape, and that an index be

kept of the data stored at any particular time.

10.11 Characterjstics of the Input Data

In Chapter 6 it was estabjjshed that w'ith the present interferometer con-

figuration, an RC filter w'ith a 12 second time constant should be used and

samples should be taken at 7.5 second jntervals in order to keep both the

reflected noise and distortion'in the s'ignal spectrum dovrn to l'%. Ho|ever if a

twenty second t'ime constant'is used, and the output sampled every ten seconds,

the reflected no'ise is less than 1% and the distortjon is still only ?%.

Alternatjveiy a ten second sanrple jnterval could be used with a tlvelve second

t

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time constant, keeping the distortion down to 1.%, and the reflected no'ise is

only 1.8%. The advantage of a ten second sample interval is that all tjme

coordinates can be kept in un'its of dekaseconds. Thjs is a much nlore manage-

ab'le quantity than seconds'in a computer wjth a basjc word length of sixteenL:r^ 1+327671 ^-b'its \4ri6!) as there are 86400 seconds in a day.

Because of this convenience, it was decided to base the softt^tare system on

a ten second sample interval. If the present interferometer baseline is extended,

then the signal frequency will be higher, however a ten second sample interval

could still be used in conjunctjon with a second-order filter for baselines up

to three times the present length with on'ly L% reflected noise and l% distortion.

Dekasecond resolution implies that only four tape characters need be punched for

a time coordinate (tlords 4,5,6 and 7 Figure 8.2). A typical input tape to the

analysis system will then consist of tvro characters for each sarnple (ident'ifica'

tion codes 10,00) and four characters for each coordinate (ident'ification codes

11 ,00,00 ,00) . The sampl e data i s coded 'in the tvro's compl ement natural bi nary

code used within the computer, and thus will only require regrouping. The block

data ho;ever is in five groups of binary-coded-decirnal characters (fO x hours,

hours,10 x mirrutes, minutes and 10 x seconds), and each group will have to be

separated, multipiied, and summed to the others to fonr the coordinate in deka-

seconds, an integer number betuteen 0 and 8,639.

10.12 Heading and Control Characters on the Tape

As mentjoned in section 8.14 it'is proposed to head each tape file with an

index number and infornratjon pertinent to the data. In addition, it is required

that the storage of the data be controlled almost entire'ly by the tape itself'obviating the necessity for control inforrnation to be punched on cards for each

tape. The switch register (see Chapter B) is to be used to enter specified con-

trol characters on the tape. Using tlre one identification code available for

manually entered data, a system of standard control characters and a standard

heading format have been developed.

The paper tape contrgl conmands (PTCC) each consjst of a sequence of two

characters. Sjxteen different commands are available and the present system

uses on'ly five of these. The basic format uses a 0l- identification in the firstcharacter, r.rith channel 5 always 1, and a four-bit jnstruction punched jn the

remaining four channels. The second character is always blank. A table of the

five valid comnrands is shown in Table 10.i.

The START jnstruction (1i11 or Frs) appears at the beginning of a tape,

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at the end of the leader (blank) and indjcates the beginning of the data. Thjs

will be folloured by several characters of heading data (see next paragraph),

at the end of which the END 0F HEADING code (0010 or 2ro) indicates the

beginning of the sanrple data, The STOP conmand (0000 or 0re) indicates to

the storage system that the end of a tape fjle has been neached. If a tape fileis too long to be accommodated on a single'length of tape (the take up reel of

the handler in the acquisjtion system has a 350-foot capacity) then the PAUSE

instruction (0001 or 110) will cause the storage system to pause and wait for

a new tape to be placed in the reader. I'lhen the program js restarted th'is tape

wjll be scanned until a CONTINUE code (1000 or Bro) is encountered' when the

storage process wi 1 i recommence.

The heading information is coded into nurnbers in the range -129 1s +I?7

(eight bits, two's complernent). Each of these numbers is punched in two tape

characters, four bits per character. The standard format uses a 01 identifica-tion for the first character, ancl a 00 (continuation) identification for the

second character. To distinguish this data from the paper tape control commands

of Table 10.1, channel fjve is a'lways punched as 0. The four most significant

bits of the Cata are punched in the last four channels of the first character'

the four least significant bits are punclred in the second character.

l{ormally the heading vli1l consist of from eight to e'ighteen of these sets.

The first will be a file nunrber, by wh'ich the tape r.ril1 be referenced. This is

followed by the block iength'in samples, the sample length in seconds, the gain

setting of the a/d converter, and the pointing angle of the antenna amay. The

sixth quantity'is the number of scans per day appearing on the tape. Facilityhas been prov'ided in the analysis systern for six scans' but this r'lill normally

be one, although special start/stop progranrming boards can be wired to prov'ide

for more than one. Following this appear the start times and stop times (in

hours) of the scans, the number of rvhich has been specified. The heading data

will always end r,rith the paper tape control command 0010 as shown in Table 10.1'

10.13 Characteristics of the Computer Storage

The IBM 1130 computer at the Univers'ity of Auckland uses a sixteen-bit basic

rvord length and has 16,000 words of core storage, with an additional 1'000,000

words avajlable on two magnetic disks. As the sanrpled data is normally nine bits

long, only one sample can be conveniently stored in each computer word. lrJith

dekasecond sanrpling, 360 samples are taken every hour, and 27,000 words of

storage would be required for 75 hours data (25 scans, each 3 hours long). As itis desired that the data be stored with some permanence, then obviously the disk

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storage should be used.

Table 10.1: Paper tape control commands (PTCC)

The type 2315 disk cartridge used on the IBM 1130 computer has two sur-

faces (top and bottom), each of which is divided into two hundred tracks.

Each track is sub-divided into four sectors of 320 words (Louclen, 1967).

Fortran jnstructions are available for both the read and write operations, the

smallest unit that can be transferred being one disk record. Named data filescan be defined on a disk of a specified record length, and of a specified

number of records. The record length must not exceed 320 words, as no overlap

of records across sectors is pernritted. Records of lengths greater than 160

words but considerably less than 320 words result'in large unused areas of disk

storage, as only one record can be accommodated per sector. However as most of

the time required for a data transfer operat'ion is taken up'in the positioning

of the read/wrjte heads over the appropriate track, the more data read in one

operation (i.e., the longer the record'length) ttre more economjcal of computer

time.

As the acquisition process can be started or stopped only on the hour, the

shortest block of interest is the data from a t hour interval. This will nor-

ma'lly be 360 sarnples, and cannot be accommodated jn a single disk record. Record

lengths of 30 minutes data (tBO words) and fjfteen minutes data (90 words) are

both rather uneconornical of storage area, and it r,ras decjded to define the data

TAPE CHANNELS

COMMAND8 7 6 5 4 3 ? 1

00

00

00

00

00

I0

1

0

I0

1

0

I0

00

I0

00

1

0

I0

1

0

1

0

1

0

1

0

1

0

1

0

00

00

00

1

0

1

0

00

00

00

00

1

0

1

0

00

00

00

1

0

00

00

1

0

00

srART (Fro)

END oF /2 \HEADI NG "l6'

sroP (016)

PAUSE ( 1re)

C0NTTNUE (q6)

I denti fi cati on PAR. I nstructi on

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file with a record length of 60 words, sufficient storage for ten minutes data.

Five of these records w'ill be accomnrodated in a sector, only 20 words bejng

unused in each sector. The smallest unit of interest, the data front one hour,

consists of s.ix of these records and this has been defined as one page of data.

Although the data will be handled as records rvjthin the computer, all externa'l

references vrill be by page.

10.14 Indexing of Disl< Fjles

Some provision must be made to keep an up-to-date record of the data stored

in the systenr files. As the data is to be handled externally by pages (1 page

contains I hour's data), then index entries need only be nnde otte per page. The

index information wjll be of the sane form as the heading data of the tape con-

cerned, and in addition, the tinre of cornmencement of the page will be required,

and some indjcation of the extent to vrhich the page has been processed. The

time of commencement of the page w'i1'l be the on'ly coordinate required for a whole

page of data, provided that data which through some hardt4/are effor has been lost'is represented by blank storage areas. All coordinates will then be implied by

the relative position of the data.

10.15 Checking of Data for Hardware Errors

The data as it appears on tape should have an initjal sample fol'lowed by a

coordinate, and then a series of blocks of data, each of a'block-]engtlr'ofsamples folloled by a coordinate. If for some reason a block does not contain

the coryect number of samples, or the coordinate does not taliy with the block

length, then obviously an error has occurred somewhere in the system, and the

entire blocl< of data concerned must be discarded. When clata is discarded in

this fashion it nrust be represented irr the systent disk file by b'lank storage

area in order to rnaintain the irnpljecl coord'inates. However some means of identi-

fying discarded data as djstinct fronr zero samples must be provided.

lloting that each sanrp'le occupies oniy nine bits of each sixteen-b'it word,

it was dec'ided to use the remaining seven bits as a flag rrrord' Each sixteen-

bit r^rord can then be split into two bytes, one of seven bits and one of nine

bits (see Figure 10.1). If the flag word is zero, then the data corresponding

to that location has been d'iscarded. If the flag word is one, then the data is

valid. l,lhen the data is the average of several collatera'l samples, then the

f'lag word is used to represent the number of samples that have been averaged to

form that particular vlord. if this averaged daL,a is to be averaged still fur-

ther with other averaged data, then the fiag word g'ives the correct vreight for

each averaged sample.

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bit m's

wordstoroge

7-bit f tog 9-brt dq to

word word

Figure 10.1: The distribution of a sample and its flagjn one word of computer storage

10.2 Analysis Requirements

As previously nrentioned, it was the aim of this project to extend the

software system on'ly to the point where the requirements of individual experi-

ments would diverge. The process'ing to be performed on the samp'led data to

bring it to this level can be divi'led jnto three parts; (1) ttre checking of

the input data for occasions of obvious interference, and the rejection of such

data, (2) the averaging of a number of scans vlhjch have been checked in this

manner,and (3) fjltering the averaged data using a digital filter to produce

the optimunt signal-to-noise ratio githout distorting the signal.

70.2L Reiection of Data Marred by Extraordinary No'ise

From a visual inspection of the interferometer output (see Figure 4.8) itis apparent that from time to tinre there occur extraordinary noise bursts' or

interference spikes of quite short duration (-1 mjn).* If records are to be

summed to form an average, then provided that tltese no'ise bursts are not

stat'ionary jn s'idereal time, the average would be better formed by discard'ing

the noisy samples in each record, even though this would result in fewer points

to be averaged.

A criterion for the reject'ion of one doubtful observat'ion from a number of

observations to be averaged has been given by Chauvenet (Smart,1958). This

criterion'is based on the likelihood of a particular sample falling a certain

distance from the mean, assuming that the samples are normally distributed about

the mean. If the average of m samples is i, and the standard deviation is o,

then the probability of a deviat'ion from the mean being greater than e (= l*-il)js ltt - N(qJf where N(t) is the nonlal distribution functjon. If the proba-

* These have been traced to a network of radio telephones on an image frequency

of the receiver.

----|

in

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bility of a sample falling a certain distance from the ntean is less than one-

half for the given number of sanrples, then such samples should be reiected. The

limit for the rejection of one cloubtful santple can then be expressed as

N (;) _ 4m-1- -4m (10. 1)

Beers (tgSZ) gives a similar criterion, but questions the severity of

Chauvenet's method, suggesting that for rejection, the probability of occurrence

should be set at some lesser level.

An alternatjve method for the inrpartial detection of noise spikes has been

used in the preparation of the Ohio 1415MHz sky survey (Djxon and Kraus' 1968).

This involves the calculabion of the standard deviation over s'ix sequential data

points (a one m'inute jnterval) of indivjdual scans. If this exceeds a pre-

determined level, then the data is assumed to contain a noise spike, and is

rejected. This standard deviation 'is calculated in a 'moving-windovt' fashion

along the entire length of each scan. Assuming that the signal variation is

small over the one-minute interval of interest, then the standard deviation

calculated js actually a measure of the r.m.s. noise level over that period.

However, the disadvantage of this technique in rejecting sp'ikes caused by

terrestrial sources is that if the d'isturbance lasts for a significant period,

and levels off at its peak, then the ent'ire spike is not reiected,.but on'ly the

transi ti ons .

These two teihniques are described in detajl in Chapter I?, and programs

developed to perform this function.

L0.22 Averag'ing Col'latel^al Data

0nce the data from several scans has been stored'in the computer, and has

been checked both for errors in the hardvlare system and spurious noise spikes'

then to improve the signal-to-noise ratio, collateral data points from each

scan should be summed to form an averaged scan. The flag words of this averaged

scan should be set to the number of data points summed for each particular point'

so that if further averaging is to be performed, the correct weighting can be

appljed to this data. In addition, index entries for an averaged scan should

indicate the number of scans which contributed to it.

10.23 Filterinq the Data

It was sho;n in Chapter 5 that the best s'igna'l-to-noise ratio could be

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obtained wjthout distorting the signal by only lightly filtering the data prior

to samp'ling, and then applying digital filtering techniques during the computer

analysis. The twenty second time constant RC fjlter currently used with the

system produces a maximum djstortjon of the signal spectrum of less than 2%'

The noise reflected by the sampling process on to the signal spectrum can be

reduced to less than 1% by fjltering the data vrith a near ideal low-pass filterwith a cut-off frequency of .003H2. A general digital filter program should be

developed so that the effectjVeness of different weighting functions can be

eval uated .

It should be notecl that the output of a digital filter of 2N+1 weights cannot

be evaluated for the first N or last N points of a set of data, if the weighting

function is symmetrical about the point of interest' l'lartin (1959) has suggested

altering the vreighting function jn order to evaluate these points' but as the

data at the extremities of a scan will probab'ly not conta'in any signals of

interest, a more sinrple nrethod is to assLlme that the data is constant for N

points prior to the scan atrd for N po'ints follolving the scan'

10.3 0utput Requirements

Three forms of data output have been specified for the software system'

These are (1) the output of raw or processed data on to punched cards for

future reference by the computer, (2) a tabulation of raw or processed data'

and (3) a computer ppinted chart whjch can be used to compare the data at various

stages of the processing rvith the original analogue chart record' Each of these

will be required to operate in units of one page of data (360 words)'

10.31 Storage of Data on Cards

Since data dumped on cards'is intended solely forre-useby the computer' it

does not have to be in an intelligible forn, and thus can be dunrped exact'ly as

it is stored, wjth data and flag words combjned in a single sixteen-bit word

lllith each page of data durnped on to cards, the appropriate'index entries should

al so be dumped for reference when re-readi ng the data.

The disk ut.ility program (nup) on the IBM 1i30 allows for the dumping of

data from a disk file directly on to cards without code conversion' In this

way f.ifty-four sixteen-bit words can be accornmodated on a sing]e eighty-column

card, and only seven cards would be requjred for each page of data' However

th.is DUMPDATA operat'ion is not select'ive and the entjre named fjle must be

dumped, or a portion (in vlho'le sectors) starting from the beginnjng of the file'

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For this reason, although it is much'less economical of both cards and computer

time, for selective dumping the information vrjll have to be read fronr the disk

file into a core storage array, and punched on to cards using the Fortran WRITE

statement. This produces an output in IBM card code, one decimal digit per card

cotumn. Each sixteen-bit word (t7l3l) thus requires six card columns, and a

maxjmum of thirteen data words can be punched per card. The output from one page

of data then occupies twenty-eight cards, and takes tvrenty-eight seconds to punch

by the 1442 card reader/punch.

10.32 Tabulation of the Digital Data

As the tabulated data js intended to be'interpreted manually, the data and

flag words nust be written separately. A heading derived from the index entry

shou'ld a'lso be wrjtten for each (disk) page printed. The flag word is always

taken to be positive, and thus lies between 0 and 1.27; the data word lies

between -256 and +257. If these numbers are to be tabulated then spacing must

be provided between each column, and each flag and data word pair will t'equire

nine printer columns. The 1403 line printer has a L20 character line' and can

accommodate thirteen of these number pairs, so thatilenty-ejght lines wi'll be

printed per disk page of data.

10.33 The Computer Printed Chart

As the University conrputer is not equipped with a graph'ical output unit,

the only way to produce a graph'ica'l record of the data is to use the printer to

p'lot characters such as * or + whose positions on the paper are proportional to

the numbers they represent. The printed page of the 1403 printer consists of

sixty lines spaced six per inch each of one hundred and twenty characters spaced

ten per inch. As time resolution is obviously more critical than amplitude

resolution for this visual representation it was decided to produce a chart vtith

the time axis running across the Pd9e, even though this requ'ires complex

reorganisation to make aniplitude the independent vapiable.

If each sample is plotted in one character position, then three pages of

printout will be produced per d'isk page of data. A more compact time scale is

required for comparison with the ana'logue chart record (3cm/hour) and it was

dec.ided to combjne 3 samp'les in each character position, producing only one page

of printout per disk page of data. It was found that the best simulation of the

continuous trace characterjstic of a pen recorcler could be achieved by plotting

in each character position a vertical line extending from the maximum to the

minimum amplitudes of the three samples to be represented, rather than by plotting

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a single point corresponding to their average.

10.4 A General Descriptjon of the An.alysis System

A flow chart representation of the analysis system is shown in F'igure 10.2.

Because of the large quant'ities of data to be handled at any stage by the system'

each section operates on only a small portion of the data at any one tjme, and

the processed data is re-stored on the clisk before more data is read to be pro-

cessed. In addition to the paper tape input, facil'ity has been included to

store data from cards punched by the output system, but no checking is required

by this process, and the storage is performed directly without decoding. At any

stage during the analysis any of the three output fonns can be produced.

The progranrs developed to perform the functions of the analysis system are

described in the next two chapters. All of the operations are performed by

calling Fortran subroutines, the calling parameters usually being page refer-

ences. Decoding is performed by assenbler subroutines but the user requires

access to these only via the Fortran routines. To store a tape file and perform

an analysjs of the data requires a short main-line progrant consisting entirely

of CALL statements to the subroutines of the softlare system.

REFERENCES

BEERS, Y. (1957): "Introduction to the Theory of Error"

Massachusetts).

(Addi son-l,lesl ey,

DIXoN, R.S., and KRAUS, J.D. (1968): "A High Sensitivity 1415MHz Survey at

North Decljnations Between 19o and 37o". Astrononr. J., 73 pp' 381-407'

LgUDEN, R. K. (1967) : "Programnri ng the IBI'1 1130 and 1800" . (Prentice-Hal I 'New Jersey).

MARTIN, M.A. (1959): "Frequency Domain Applications to Data Processing", Trans.

I.R.E., SET-5 pP. 33-41.

SMART, ll.M. (1958): "Combination of 0bservations". (C.U.P., Cambridge)

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(a) The storage process

(b) The analysis Process

(c) The outPut Pt"ocess

Eigufe t0',2: Analysis system flow e.hart'

DIGITAL

Fl LTER

CIECO;0E &

R.EORGANIZE

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CHAPTER 11

The AnalYsjs System Input/Output

This chapter describes the computer programs developed to perform the

storage and output functions specified jn Figure 10.2. The storage process is

performed by tvro Fortran subprograms, STOPT rvhich stores data from paper tape

on to disk, and ST6CD which stores data previousiy punched on to cards by the

output system. The tabular and card outputs are performed by a single sub-

program DSCAN, the output device (printer or card punch) be'ing defined by a

calling parameter. The graphical output is produced by a subprogram entitled

CHART.

A 540 x 60 word record data file, RSTAR, has been defined on the disk

allocated for this work, for use by the processing systenr. The fjle can be

extended at any time jf required. In its present form it allows for up to ninety

pages of data (one page will accommodate the data from a one hour period) to be

stored at any one time. An index file INDX, consisting of 90 ten-word records

permits up to ten djfferent index quant'ities to be defined for each page. A

subroutine DUMPX is provided which prints out the index entries of those pages

in which data is currentlY stored.

11.1 The Paper Tape Storage Process

A sinrplified f'lor^r-chart of the paper tape storage subprogram ST0PT is shown

in Figure 11.1. Characters from the tape are read wjthout code conversion into

a Fortran array JDATA by the IBM program PAPTB. This is an overlapped

interrupt service subroutine which after an injtial call TCALL PAPTB(0'C0UNT'

AREA)l sets out to fill and maintain an allocated buffer Ithe Fortran array AREA

(C6UNT)l allowino the computer to continue processing the cal'ling program'

.interrupting its operat'ion only when a character from the reader is ready to be

transferred'into the buffer. Tape characters are packed tvro per t^lord into this

buffer, whicS has a capacity of 2 x C0UNT characters. 0n subsequent calls to

the subroutine tCALL PAPTB(l,NUt,tgR,PLACE,ERROR)1, characters are transferred from

the buffer into a second Fortran affay, PLACE(NUMBR), one character per word plus

a parity bit. The ERROR pararneter is used as an'indicator that the end of a

tape has been reached or that the reader has not been made ready. I'lhen characters

have been tra nsf eryed to PLACE , PAPTB conti nues to ma i nta'i n the a'l l ocated buff er 'interrupting the operation of the cornputer every time a character is read' ST0PT

allocates a buffer IBUFR (1000) which has a capac'ity of 2000 characters. Data

is transferred from this buffer 500 characters at a time into an array JDATA'

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Reod 500 Chorocter!Into orn Arroy J,D-ATA

Reqd a ChorqeterSet Frorn J DAI'A

Reod Anothci 500

C'tloroc:ters Into JDATA

ir PTccPAUSE ?

it u SomBle,lRaschad \End of JDATA

NO Annotas in\ YES

Stora in on ArroYKDATA With rug I

it PIccSTOP ?

it,s Glock0oto Sel?

Sornptas inimc TottY

WritaKDATA

on Disk

WriteKqATA

on Disk

Write

lndcx EnrYOn 0isk

Eroge s Eloch ofDoto Frorn KOATA

WiiteIndex EntrY

on 'DlEk

Pri ntcr

{,_Vrite

Messoge

Frin tar

Fi.gure 11. 1,: ST0PT florvcharti the paper tape storage routine.

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24L.

Immediately follow'ing the return of 500 characters front PAPTB, a parity

checking routine PARTY is called by STOPT. Each of the 500 characters is

examined in turn, and if its parity is incorrect (characters are punched with

even parity) it is ignored in the subsequent decoding. PARTY is described

in more detai'l in section 11.14.

The tape leaderis then

language subroutine HEAD.

scanned and the headjng data decoded by an assentbler

The heading data is then written on the line printer.

The decoding of the jnterferometer data and its coordinates from the tape

characters in JDATA 'is performed by a second assembler subroutine TREAD.

When TREAD is called, it decodes a sequence of characters corresponding to

either a sample, a coordjnate, or a control command, according to the character

identifications encountered. This data is then returned to STQPT, as the

quantized value if it is a samplen in dekaseconds jf a coordinate, or as the

four-bit instructjon if a control command, together with an indicator which

shows from which of these three sources the data was obtained. If insufficient

characters are available in JDATA to form a valid sei, control is returned to

STQPT, and another 500 characters are transferred jnto JDATA'

If sample data'is returned to ST0PT, then it is combined with a flag word

of 1, in the manner shown in F'igure 10.2 (bits 0-6 flag, bits 7-15 data) by an

assenrbler subroutine PAK, and the resultant word is stored in an array KDATA'

A call is once again made to TREAD, and another cltaracter set decoded.

When coordjnate data js returned to STOPT, a check is made to see if itis equa'l to the previous coordinate ('in dekaseconds) plus the number of valid

samples decoded since the prev'ious coordinate. If the coordinate and block

length correspond, then a check is made of the number of samples presently stored

in KDATA. If this is less than 360 then TREAD is again called. However if360 or more samples are found to be stored in KDATA after a correct coordinate,

then the first 360 of these are w.itten on the assigned page (6 records) of the

disk fjle RSTAR. The coryesponding 'index entry 'is nrade on the file INDX and

a message written on the line printer g'iving details of the page iust stored'

Any samples.in excess of 360 stored'in KDATA are then moved to the lower end

of the array, and once again TREAD is called.

If the coordjnate and block length do not correspond,

examined to see if it marks the beginn'ing of a new scan.

beginn.ing of a ne$/ scan,any data stored at KDATA is first

then the coordinate is

If it does mark the

written on the disk

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and the subsequent data is treated as a new scan. If the coordinate is not the

beginning of a new scan, and if the previous coordinate was correct, then a

flag is set to ind'icate that thjs coordinate was incorrect, and the decoding

process is continued. If however the previous coordinate was jncorrect, and

this will be indicated by the f1ag, then the block of data prior to the firstincorrect coordinate is erased from KDATA, and after setting as'ide the correct

numbei" of vacant locations in thjs erased area, the program contjnuesrassuming

that the first incorrect coordinate was correct. This double check ensures that

it is the number of sanples which is in error, rather than a coordinate being

mi sp'laced .

If a pTCC instruction is returned by TREAD, then the actjon of STOPT

is controlled by the instruction. If the 'pause'. instruction is encountered

then the computer branches into a vra'iting 1oop. l',then the start key'is pressed,

if a new tape has been loaded'into the reader,500 characters are transferred

f rorn thi s tape i nto JDATA and TREAD 'is agai n cal I ed. TREAD ski ps over the

blank tape leader and returns to STOPT when a valid identification sequence

is encountered. If the 'continue' instruciion is returned then decoding resumes

from the point it left off when the 'pause' instructjon was encountered.

If the PTCC 'stop' instructiori occurs, then after any samples stored in

KDATA have been written on the appropriate djsk page, control is returned to

the mainline program.

If any PTCC instruction other

is ignored, and ST0PT continues as

than those mentioned is returned' then itif it had not occurred.

In the following subsections more detailed descriptions of the three

assembler language subroutines HEAD, TREAD and PAK, and the Fortran subroutine

PARTY are g'iven, and some of the assocjated operations of ST0PT are examined

in more detail.

11.11 The Heading Decoding Subroutine

The symboljc assembler subrout'ine HEAD(HDATA,JDATA,INDEX) scans sequentia'l1y

through an array JDATA, starting at JDATA(INDEX), until a PTCC 'start'instruction (01011111/00000000) is encountered. It then decodes the subsequent

tape characters in pairs, taking four bits from each and combining them jnto one

word which is stored at an aray HDATA. l,lhen the PTCC 'end of heading' code

is encounteredn the HDATA aryay js returned to the calling program together

with the current value of INDEX.

Page 251: 2-Whole-digital Data Processing in Radio Astronomy

?43,

A fl orruchart representation of this su'brouti,ne is shown i'n Figure 11.2'

F,tqure 1,1.?: The' tape headi r|g decodi ng subrouti ne IiEAD

In t,he initial sean for t;he 'stait' instr,uctisn, a windsw tuo chanacters

wide is rngved along th,e arrayr,one character at a tiime, until a vali'd instruc-

tion ls f'ound within the wind,ovr.

The procedure for decoding the heading data is itlustrated in Figure 11'3'

Acoording to section 10,.2, ttle heading data words each oecu,py eight bits' and

afe eoded in two's complement form, four of, these hits being punched in each of

trrro t:aper cha,racte'rs, In or.der to preserve the inforrration when these b.ytes are

converte.d into 16-bit mach'ine words, the most signiftcant bit of the eight-b'it

groupr Br [the two,s complement sign bit) must be reproduced in the eight unused

most-signifi cant pos i ti ons .

Reod JIIATA( INDEX),

it PTCeSTAR]T ?

IN0EX <- INDEX + 1

INDEX.-lNIDEX * 2

Retrd J0ATA ( lFlOEX)

snd JDATA(lNOE:X+1)

Store ot l-tDATA(N)INDEX._TNDEX + 2

Page 252: 2-Whole-digital Data Processing in Radio Astronomy

Figure 11.3: Detail of decoding of the tape

headi ng data

l-lhen the first 500 characters are read into JDATA, STOPT calls HEAD

with INDEX=I. The 500 characters are then scanned through from the beginning

of the tape, and as INDEX is incrernented with every operation' on the return

from HEAD, JDATA(INDEX) is the first data word following the heading 'infotrn-

ation. It is assumed that the headjng data will always be found in this first500 character group, and thus the tape leader should never be longer than four

feet (480 characters at 10/inch).

ll.l2 The Data Decoding Subroutine

The interferometer data and its coordinates are decoded fnom the paper tape

characters stored in JDATA by the assembler subroutine TREAD(TYPE' INFo'SPUR'

INDEX,JDATA), the flowchart of which is shown in Fjgure L1.4. l'lhen TREAD is

called, it first transfers INDEX to a local storage location and increments

it by 2. If INDEX then exceeds 500, control is transferred back to the

calling program with TYPE set to 0 and without returning the modified INDEX'

This indicates to SToPT that insufficient characters are available in JDATA

to form a valid set, and that more should be taken from the STOPT buffer IBUFR'

Any unread characters at [he end of JDATA are transferred'into an array

'immediately in front JDATA, which can be considered to represent JDATA for

negative indexes. INDEX is set to INDEX-500 (which may be negative) and a

further 500 characters transferred into JDATA. Tread is then again called'

?44.

JDATA(INDEX) JOATA(INDEX + 1 )

initially jncremented by 2, INDEX does not exceed 500 then the

characters at JDATA(INDEX-2) and JDATA(INDEX-1) are combined

sixteen-bit word at AREA (see Figure 11'5)'

If , vthen

eight-bi t tape

into a single

HDATA( N)

The identification codes of these two characters, ab and ii are separated

Page 253: 2-Whole-digital Data Processing in Radio Astronomy

245.

.Obioin trNDEX Frorn

INOEX *INOEX+ 2

G0UNI.- nINDEX <-INDEX + 1

COUNT+-COLINT + 1

trNOEX > 500

Ggt JDATA (INDEX-z )

ond JIATA (INOEX-I)

TNDEX +- IN0EX + 2s?poi.dte I0 Codes os

o Four-Bit Word

INoEX> 500

TYFE* *1Get JOATA( INDEX-Z )

ond .I0ATA,(INDEX-1)

SEpsr,cite I0 eodcs os

o Foul'-9it Worrd

CoUNT -CoUN][ + 2

T fPf,<- +t

Oecsde Thesa 4 Chrs

Into DekosecondsS,tora ot lNF0

Return INDEX to

Return COUNT toGctling ftograrn

FiEure 11.4: TREAD flopchart; the tape data deeod{ng routine.

Page 254: 2-Whole-digital Data Processing in Radio Astronomy

246.

and combined into a four-bit vrord ID. If this four-bit word is equal to four

(0tOO1 then the two characters form a PTCC instruction set, and €, f, g, and h

are placed'in the four least-sjgnificant-b'its of INFO. TYPE is set to -1 and

a branch is made to a return procedure. This procedure consists of returning

INDEX to the call'ing program, returning the spurious character count (see later)

as SPUR, and then transferring control back to the calling program'

JDATA (INDEX-2 ) JDATA ( INDEX-1 )

F'igure 11.5: Character combinat'ion and identificationseParation Procedures of TREAD

If the four-bit r,rord ID is equal to eight (1000) then the two characters

form a sample data set and are decoded into INFo accord'ing to Figure 11'6'

TYPE is set to +1 and once aga'in a branch is made to the return procedure' In

the decoding of the sample data, the analogue-to-djgital converter sign bit, d,

must be reproduced jn all eight most-significant-bits in order to maintain the

two's complentent sense.

AREA

I NFO

Figure 11.6: Decoding a sample data character Pair

Page 255: 2-Whole-digital Data Processing in Radio Astronomy

?47.

If the four-bit word ID is equal to twelve (rtoo) then the two characters

form the first ha'lf of a coordinate data set, and two more characters must be

read to comp'lete the set. The two characters at AREA are moved to AREA-I and

INDEX is incremented bY 2.

If INDEX is still less than 500 then the new JDATA(INDEX-2) and JDATA

(INDEX-I) are read into AREA, and their identification codes are separated as

shown in Figure 11.5; otherwise a return to STQPT with TYPE=O is made' Ifthe word ID is not zero for the two new characters, then the two original

characters, now at AREA-I are declared invalid (a 11 code not followed by

three continuation codes). A spurious character counter is incremented by 2

and a branch is made back to the original identification check procedure with

the two new characters at AREA. If however the new ID is zero' then the

four characters at AREA-I and AREA form a valid coordinate set and are

decoded into dekaseconds as shown by Figure 11.7. The various steps in this

decoding procedure are a direct result of the coding given to the coordinate

data by the digital multiplexer and shown in Figure 8'2'

AREA AREA

1'/

INFO

-'-I

{*oI

coordinate set of four

the time in dekaseconds

is made to the return Procedure'

Figure 11.7: Decoding a

characters to give

is set equal to +2 and a branch

l1?ortl

b c detrl

00PtI I I

9,n,',' 00Pkrlltmno

I

0 0 PPrll

q rstI I

10xH \A J_l_!,,)h.,ri

,4 \\ .4,t-lln,o,olc d el

lljktmlrl

TYPE

Page 256: 2-Whole-digital Data Processing in Radio Astronomy

248.

If the identification word ID of the two characters first combined at

AREA is neither four, eight or tvrelve, then the first character of the pair

is declared inva'lid (its identification is not 01,10 or 11 foj'lowed by 00 and

thus it does not mark the beginning of a valid set). Both the spurious charac-

ter count and INDEX are incremented by one, and after checking that INDEX

does not exceed 500, the new ,IDATA(I}IDEX-Z) and JDATA(INDEX-I) are combined

at AREA, and the analysis of the identification word ID recommenced'

Thus , when TREAD j s cal I ed , starti ng from JDATA( INDEX) , JDATA 'i s

sequentially scanned until a valid character set is located' This set is

decoded according to its type and the data returned to the calling program'

INDEX is updated so that JDATA(INDEX) always represents the next unread

character. A count of any invalid characters encountered prior to the valid

set is given bY SPUR.

11 .13 Data/Fl ag Combi ni ng Subrouti nes

An assenrbler language subroutine PAK(NUM,DATA) places the seven least

signifjcant bits of NUM in the seven most significant positions of the word

DATA. DATA is returned as the combined f'lag/data woid in the form 'shown in

Figure 10.2. A second assembler subroutine UNPAK(NUM,DATA) reverses this

process, accepting the cotnb'ined word as DATA, and restoring the two's comple-

ment sign bit of the uncoded DATA.

When data is declared inval

assi gned by sett'i ng a 1 I si xteen

id by ST0PT, blank storage al'location is

bits of the conrbined word to zero'

11.14 The Parity Checking Subroutine

l,lhen tape characters are transferred front the PAPTB buffer into the

JDATA array, the eight-bit tape characters occupy bits 8 to 15 of each urord in

JDATA, and a parity-check bit generated by PAPTB occupies bit 7' This bit

is 0 if the character has even parity, and 1 if the character has odd parity'

The subroutine PARTY(IPAR)* checks the entire 500 words of the JDATA

array in one cal], and returns a count of odd parity characters as IPAR' If a

character has even parity (bjt 7=0) then it'is'left untouched' If a character

has odd parity (bit 7=1) then the action depends on the identification code of

the character. If th'is code is not a continuation code (OO), then it 'is changed

to a continuation code by setting the vrord to zero. If the identifjcatjon is a

* JDATA is transfemed to this subroutine by a common storage area'

Page 257: 2-Whole-digital Data Processing in Radio Astronomy

continuation code, then itword to -1. This Procedure

TREAD, the character set toinvalid.

'is changed to a coordinate code (11)

ensures that durjng the decod'ing of

wh i ch thi s character be'l ongs wi 1 'l be

249.

by setting the

the array bY

decl ared

11.15 Page Indexing in the Storage Procedure

blhen data from more than one scan/day'is present on a tape, the data from

each scan is stored adiacent to data from the corresponding scan on other days'

The call.ing sequence for the storage process is CALL ST0PT(IPAGE)' IPAGE is

a six word array indicat'ing the area in the data file where the correspond'ing

scan of the day is to be stored. The first scan of the day wi'll be stored at

page IPAGE(I) and subsequent pages up to IPAGE(II); tlre second scan of the day

will be stored at IPAGE(Z) and subsequent pages up to IPAGE(M)' Data from the

first scan of the seconci day will be stored at IPAGE(tl+t) and subsequent pages

i.e., adjacent to the first scan of the previous day. This is shown diagranuna-

ti cal 'ly i n F'igure 11 .8.

Doto From OaY 2

IGI

zz.o()ana

('l

z(Jo

(\l

z.O(/)

z.(-)a

(Yt

z(-)a

GIz(Ja

zo(/)

I

I

I

I

f7)UJ(Js

sylrJ(9/L

t!(D

Figure 11.8: Storage

areas

of different scans in differentof the data file

An examp'le of the printer output produced by ST0PT during

of a tape is shown in Figure 11.9. For this operation IPAGE(I)

64.

the

was

storage

set to

Doto From DoY 'l

D ATA AS IT APP ARS ON THE nl SK 1

Page 258: 2-Whole-digital Data Processing in Radio Astronomy

250.

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Page 259: 2-Whole-digital Data Processing in Radio Astronomy

251.

The ten word index assjgned to each page of the RSTAR file is used by

STOPT as follows. The first word is used as a flag; it js zero if the page

is unused, and one if the page is usecl' The next five words are taken directly

from the heading data on the tape; these are the tape file nuntber' the start and

stop times of the scan, the pointing angle of the antennas, and the gain setting

of the analogue-to-digital converter. The next word (word 7) is the coordinate

of the first data word on the page (in dekaseconds) and this is followed by a

count of the number of invalid words (flagword=0) on the page' and the nunrber

of scans averaged to produce the page. The tast word is 0 unless the page has

been djgitally filtered in which case it contains a reference number to a parti-

cul ar we'ighti ng funct'ion '

A subroutine DUMPX reads through the index file (INDX) and prints the

index entries of those pages on which clata'is stored. A typical index printout

produced by DUMPX is shown in Figure 11'L0'

sets the index entries of

pages are thett ignored bYAnotherma.intenancesubrout.ineIRASE(PBEG,PLEN)

PLEN pages beginning at page PBEG to zero' These

DUMPX and can be considered as unused'

Lt.?

0utput of data from the data fjle RSTAR, both'in tabular form and on

punched cards, is performed by a Fortran subroutine DSCAN(UNIT'PBEG'PLEN)'

Four forms of output are available. If UNIT is zero' the output is in tabular

form on the f.ine pr.inter. Data and its frags are printed sicre by s'ide, twerve

pairs being printed per 1ine. Data from one page (360 data/flag pairs) occupies

thirty lines of pginted output. Before each page is printed' one line containing

all of the index data for that page is written' DSCAN outputs PLEN disk

pages of data, commencing from page PBEG. An example of thjs form of output is

shown in Figure 11.11.

The second form of output, on punched cards, is produced if UNIT is +1'

As mentjoned in chapter 10, because of the unserective nature of the unfornratted

output produced by a direct dump from the disk, this form is not suited to the

requ.irements of DSCAN. A standard Fortran card I'IRITE statement is used to

punch twelve sixteen-bit combined data/flag words per eighty column card' Thirty

cards are punched per disk page outputted, and each set is preceded by a single

card punched r'l'ith the page index data'

Page 260: 2-Whole-digital Data Processing in Radio Astronomy

252.

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Page 261: 2-Whole-digital Data Processing in Radio Astronomy

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Page 262: 2-Whole-digital Data Processing in Radio Astronomy

?54.

The remaining output forms, procluced when UNIT 'is negative' are reduced

tabular outputs for manual plotting. l'Jhen data has been processed by a d'igital

filter, then its frequency spectrum is greatly reduced and it can be specified

by fevler samples than the ravr data. This is an advantage tthcn plotting records

manually, as plotting s'ix data points per minute can become laborious. l'lithUNIT equal to -1; DSCAN takes one value from each set of three adjacent values,

and produces only twenty data values front each sixty-word record. The f'lag

worcfs are lot outputted under these c.ircumstances. l,J'ith UNIT equal to'2, a

similar form is produced, but the twenty data values printed are the average of

each set of three adjacent values in a record. Twenty data values are written

per ljnen and only s'ix lines are requ'ired for each djsk page of data'

11.3 The Storage of Data from Punched q{ds-

The operation of storing data from cards, previously punched by DSCAN

(1,PBEG,PLEN), on to the disk file RSTAR is much more simple than the storage

of paper tape data, as no check for errors is required. The input'is assutned

to be in thirty-one card sets, the first card of each set containing the index

data. The card storage process is initiated by the call CALL ST0CD(PBEG,PLEN)'

It js assumed that PLEN thirty-one carcl sets wjll be ready in the card reader.

ST0CD reads the data from the first card and stores this as the index file of

page pBEG. The next five cards are then read (60 combined data/flag words)

and are written in the first record of page PBEG. Fjve more five card sets

are then read, one set at a tinre, and the data written in the retnain'ing five

records of page PBEG. Another index card'is then read, and the data stored

at the index file location for page PBEG+I. The next th'irty cards are read

and storecl in the six reconds of page PBEG+I. This process is continued until

PLEN pages of data have been stored.

Before returning to the calling program, ST0CD calls DUMPX to print out

the new data file index.

11.4 The Graphical 0utput Progratn

The Fortran subroutine CHART(PBEG, PLEN,SIZE) produces a graphical output

of the form described in section 10.33. CHART plots PLEN pages of data'

starting from page PBEG,2 data pages being p'lotted per printer page' Each

page of data is plotted with a t'ime axis one hundred and twenty characters long,

and rvith an amplitude resolution of tvrenty-five characters peak-to-peak. The

parameter SIZE in the calling sequence determines the amplitude scale. The

twenty-five character peak-to-peak cleflection of the chart corresponds to JSIZE'

Page 263: 2-Whole-digital Data Processing in Radio Astronomy

255.

Three data points are combined at each position on the tinre axis, and to

simulate the plot produced by an analogue pen recorder, these three po'ints are

represented by a vertical line of asterjsl<s (*) extending fronr the minimum to

the maxirnum of the three data values. CHART also prints a coordinate grid con-

sisting of a zero amp'litude axis (-) and vertical tjme axes (') at ten minute

intervals. The time axes are labelled, and each printer page is headed wjth

data cbtained from the index file. A typical printout from CHART is shown in

Fi gure 11 .12.

The graphical output flovlchart is shown in Fjgure 11'13' l'lhen called' CHART

reads the index data for the first page to be plotted and heads the printer page'

The data from page PBEG (360 words) is then read into an amayn and the combined

data/flag words decoded by UNPAK. The f'lag vrords are not used by CHART and

are discarded. To bring the clata into the range of 25 characters peak to peak

(t12) each data value is multiplied by a factor ll/sl7E. If SIZE has been

inappropriately chosen, and any of the nrodified data falls outside the range

t12, then jt is ljmited to these extreme values' To allocate each data value l

to a printed line posjtion in the range l rlo 25, the modified values are sub-

tracted from thirteen. A data value of +12 rvill then be printed in line 1' and

a value of -12 will be printed in l'ine 25'

After d.ividing the 360 modified data values jnto 120 groups of 3' two

indicator arrays, MAX(120) and MIN(120) are set for each of these groups'

MAX(J) is set to the smallest modjfied value of the 'lth group of three' and

MIN(J) is set to the largest modjfied value of th'is group.

A1.20-wordarrayl'lAP.isusedtoprintthechart.Initia.|ly,theent.ireone hundred and t;enty words are set to the printer code for a blank' except

the 1st, zlst,41st,61st, Blst and 10lst words which are used for the tjme

coordinate grid. These six words are set to the printer code for a period (')'

tlJith LINE equal to L, each of the indicator arrays is then examined' If

LINE=I,|AX(J), MAP(J) is set to the printer code for an asterisk (*) . I'lhen LII'IE=I

then LINE/MIN(J)+1 and after asterisks have been placed jn all those MAP's where

MAX is 1, the l{AP array is printed. An asterisk will be printed in this first

line at all those locatjons where a scaled data value was equal to or greater than

+I2. The sjx vertjcal axes wjll also hre printed'inless they have been overvritten

by an asterisk. LINE is then incremented to 2, and the program branches back

to I (Figure 11.13). Again if LINE=MAX(J) then MAP(J) 'is set to an asterisk'

IfLINE=MIN(J)+IthenMAP(J),whichmusthavebeensettoanasteriskonaprevious ljne, is restored to e'ither a blank' or a period if it corespollds to a

Page 264: 2-Whole-digital Data Processing in Radio Astronomy

256,

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Page 265: 2-Whole-digital Data Processing in Radio Astronomy

257.

t,1AF (J) -

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Fig.ure 11.3: CHART flowchart; the graphica'l output routine'

Page 266: 2-Whole-digital Data Processing in Radio Astronomy

a58.

vertical axis position. $nce agafn FIAP is pr^inted' and iLtrNE incremented'

The proCess conti'nues unljl the MA'P array has been prepared for prrinting' the

thi,rteenth line, the line corresponding to the eero amplitttde axis' Any ef the

120 I4AF'S Which do not conta,in eJthetl an asterisk on a period (i'e" those co-n-

taining blar,rks) are set t0 the printer code for a dash '(-)' MAP is then

p inted, and those MP's containing dashes are restored to blank's' CttART

then regumes in its previous manner to print the tWelve lines corresponding to

the negative amPlitudes.

Af,ter the twenty-fifth line has been written, CHART prints the times

corresponding to the vertical axes. If more data is to be plotted' then cHAR'r

reads another page of data and p]ots this on the sarne printer page as the first.

If a th.ird page of data ls to be plotted then a new prlnter page is headed and

the process continued.

Thisformofotttputwasfoundtogivethebestgrap.hica]representationofthe inte,rferometer data, especia'lly the raw data which is heavily maffed by

noise. when data has been processed (fitter.ed & averaq'ed) then the variation

amongst the t,hr,ee-v$olld sets is much les,s and the output is very sirnilar to that'

Bnoduced by plotting a single astenisk corresponding to the avqrage value of each

group of thv^ee.

Page 267: 2-Whole-digital Data Processing in Radio Astronomy

259.

CHAPTER 1.?

The computer progrants developed to perfornt the analys'is outlined in

chapter 10 (reiection, averaging and filtering) are descrjbed in t'his chapter'

together with details of their developtnent. A Fortran subprogram CHAUV has

been developed to remove data marred by nojse spikes us'ing a nrodifjed form of

Chauvanet's criterion. As it is necessary to average collateral records to

apply this cpiterjon, CHAUV also produces an averaged output' after undesir-

able data has been rejected. Another Fortratt subprogram AVRG can be used

to average several collateral records vrithout performing any reiection' The

alternative form of reiectjon analysis nrentioned in chapter 10, the moving

window calculation of standard deviations, which can operate on a single record

at a tjme, is performed by a subpfogram REJEK. As nO averaging iS performed

by this progl.am, the subprogram AVRG niust be used if several records are to

be averaged after being analysed by REJTK'

The digital filtering of the input data is performed by a Fortran subroutine

FILTR. This program does not use a specifjc weighting funct'ion; th'is is defined

in the catling sequence. A disk file has been allocated for severa'l weighting

functions, any of which may be used by this program'

12.L The Rejection of Datq- t''lgrleg Extraordi na Noi se:

(a) By Consjderation of Collateral. Data Poi nts

Chauvenet's Criterion (Smart,1958), mentionecl in Chapter 10' is based on

the likeljhood of a particular sarnple of some quantity falfing a certain djstance

from the mean of all such samples available, assumjng that these sarnp]es are

normally distr.ibuted about their mean. If the probability of a sarnple fal'ling

a certa'in distance from the nean is less than Lz for the given number of samples'

then such samples should be rejected from the calculation of the mean' This

criterion can be expressed in terms of a maximum deviation e from the mean' as

N(;) = q# (12.1)

where m is the number of samples concerned,

N(t) js the normal distribution funct'ion'

1<ms30 is given in Table 12.1.

o is their standard deviat'ion, and

A tabl e of e1a as a function of m for

I nterferometer

Page 268: 2-Whole-digital Data Processing in Radio Astronomy

260.

mC

; n1 meo

1

2

3

4

5

6

7

B

9

10

.68

1.15

1.38

1 .53

1 .65

r.731.81

1 .86

1 .91

1 .96

11

T2

13

14

15

16

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1B

19

20

2.00

2.04

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2.r52.17

2.?0

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2L

2?

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24

25

26

?7

28

29

30

2.?6

2.28

2.30

2.32

2.33

2.35

2.36

2.38

2.39

2.40

Tabl e 12.1 : The maxinutn perm'i ssi b'le clevi ati on (./o)

according to Chauvenet's criterion, for a

given number of samPles (m).

It must be appreciated in the applicatjon of th'is criterion, that the

inclusion of one discorclant sample in a mean nny shift the mean by such an

extent that the deviations of the renrain'ing satnples are unacceptable. For

this reason, only one sample should ever be reiected in olle application of

the criterion, and this wjll be the sample for vrhich the devjation from the

mean is the greatest. The new ntean and nevr standard deviation corresponding

to the rennining samples should then be calculated, and the criterion reapplied

to these poi nts.

To perform th.is rejection on the interferometer data requires the simulta-

neous consideration of all m Scans to be averaged. For each set of collateral

data points, the nrean and standard deviation must be calculated. If each scan

.is n data points 1ong, then there r.rjll be n sets, each of nt collateral points'

The rnean of each set must then be subtracted from each member of the set, and

the maxjmunr deviation occurring in the set compared rvith tlre standard devjation

for the set rnultiplied by e/o from Table I2.1. If the maximum deviation in the

set is in excess of th'is quantity, the samp'le corresponding to thjs ntaxinum

deviation should be rejected by setting its flag to zero' The new mean and new

standard deviation should then be calcu'lated for the relraining data points of

gre set and gre criterion reappliecl. l,Jhen the criterion has been applied to the

Page 269: 2-Whole-digital Data Processing in Radio Astronomy

26t.

set l,lith no further points rejected, all tvords vrhich have been declared invalid

should be rep.raced by the mean of the renraining points of tlre set (ttreir f'lags

should still remain at zero) and attention should then move to the next collateral

set. l.lhen the process has been completed, the scan formed by the mean of the

acceptab'te points should be r'rritten'in a specifjed area of the data file'

Replacing rejectecl values by the mean of acceptable collateral samples ensures

that a continuous plot of the scan concerned can be made, even though sonre data

values ntaY have been rejected.

The flowchart of the subroutine CHAUV developed to perform this reiection

is shown jn Figure 12.1. The calling parameters are PBEG, PLEN, NSET, and PANS;

all are integer numbers. ctlAuv analyses NSET scans, each PLEN pages long'

the first starting at page PBEG, and wrjtes the average in PLEN pages start'ing

from page PANS. The ntax'imunr deviations of Table 12'1 are contained in an

array ERR0R, vrjth an index m (j.e., ERROR(m) = e/o for m sanrples) ' ChiAUV can

ana'lyse a maxirnunr of thirty collat,eral scans at a t'inre. The interferometer data

is retained in jts integer form in the computer, and the averaged scan is pro-

duced jn a similar form, but to prevent the accumulation of round-off errors'

inte^nediate sums and averages are calculated in floating po'int decjmal form'

Data from the disk file cannot be read in un'its of less than one disk record

(sixty words), and'if all collateral scalls are to be considered simultaneously'

then for thirty scans, 1800 rtorcls of core storage t'til1 be taken up by the data

from a collateral set. The alternative to this, readjng the data one record at

a time, and accuntulating totals for averages and standard deviations' Would

require each record to be read three tinres during each app'l'ication of the

crjterion; once to read the data and calculate the ntean and standard deviatjon'

once to calculate the jnd.ividual deviations, and tlre third to reject the maximum

deviation if it exceedecl the calculated linrit. Because the 1130 contputer has a

large core store avajlable (16,000 words) it vras decided to use the first method'

wh'ich requires only a single disk read/write operation for each record to be

analysed, irrespective of the number of applications of the criterion'

trJhen called, CHAUV first checks that NSET is not greater than 30' then

proceeds to read the fjrst record of each collateral scan'into an array IDATA

(60, ltsET). The first vtord frorn eaclt record (i'e', tlte first collatera'i ciata

set) js then transferyed into a working array IX(NSET)' and the flag words are

separated 'into a second vlork j ng array N0(llSET) ' iX(llSET) j s summed to produce

SUl,l, and the sum of the squares of IX(NSET) is calcuiated as SUI'ISQ' The number

Page 270: 2-Whole-digital Data Processing in Radio Astronomy

262.

NSErr > 30

KJ Fronr J!D;

'Recor'd io lu

K!-K+l

Unpac,& l:,fJllTarL,rrtfut Dqio in lx'(K),i

Flcg ln, ,NO( K)

gul.l

f txtxrnruo r nl16A

l,l0( Kl: 0l

rK-K + I

o.l ]|tft&sor.d.irn Iffi ge,ct

ERii0RtNuM)r ST0V

E:-JPbe[ lXtKl vfithFlco NO,fK! i\n:d Re,-

ptoca r.n IDATS,{LtK

11 JiOAIA(LI -

AV,R'&

I Fsck NUll rvr th J0AtrAt L

Fidure 12.1: CttAUV fJowchart; the# cha.uvenetts el.ite't":ion

rejection routine based ort(cil l,aterai compari son) .

Page 271: 2-Whole-digital Data Processing in Radio Astronomy

263.

of points contributing to these sums, t'lul4, 'is the suntrnat'ion of NO(NSET) . Frotn

these sums, the standard deviation STDV attd mean AVRG are calculated for this

collateral data set. The mean is then subtracted frorn eaclt metnber of the set'

the nnximum deviation from the mean DMAX calculated, and the scan number

(INDEX) at r^rhich it occurs js noted. The permissible dev'iation ADEV is cal-

culated from the standard deviat'ion and the corresponding term in the ERROR

array, and thjs is conlpared vrith the nraxjnrunt devjation DMAX' If DMAX is

greater than ADEV, then the flag of the data concerned IN0(INDEX)1 is set to

zero, and the mean ancl standard dev'iation for the rentaining members of the set

recalculated. 0nce aga'in the maximun <leviation from the mean is calculated and

compared vrith the nel permissible deviation. llhenever a zero flag is encountered

in the calculations the corresponcting data rrorcJ is replaced by the current value

of AVRG.

lr,lhen DMAX, the rnaxirnum dev'iation,'is found to be less than the perm'iss'ible

deviation ADEV, then each of the NSET IX+l{O pairs are recombined and returned

to their posjtions in the IDATA array. The current Value of the mean AVRG

is combined wjth a flag of the valid vrord count for the set, NUM, and sLored

in an array JDATA(60). The next rvord from each record (i.e., the next collateral

data set) is then trattsferred into the urorl<ing array IX(I{SET) and the process

repeated, until all 60 sets have been checked and their average stored in JDATA'

The array IDATA(60,i,lSET) is therr vlritten back on to the disk in the first record

of the relevant scans, and JDATA(60) is written in the first record of the

answer area, specifiect by PANS. The second record from each collateral scan

is then read jnto IDATA(60,NSET) and the entire process repeated'

Wlren six collateral record sets (360 collateral data point sets) have been

treated in this way, the index entries for the corresponding pages are modified

to include the reiected vtord counts, and an jndex entry is wrjtten for the

averaged page. The process is then repeated on the next set of collateral pages'

until all PLEN pages of each collateral scan have been examined, and the

average written in the allocated pages.

This program, using the pernrissible errors Iisted 'in Tabl e 12.L' has been

found to perform satisfactorily when averag'ing more than ten collateral scans,

but to be unreliable, and often too severe jn the rejection of data' when

operating on only a small number of scans. CHAUV depends on there being at

least two rel'iable members in any collateral set, as the deviations of tvlo

points about their mean js a'lvrays equal to thejr standard deviation, and as e/o

Page 272: 2-Whole-digital Data Processing in Radio Astronomy

for m=2 is 1.15, when only two points remain

264.

in a set, neither will be reiected'

Thereasonforthefailureofthecriterion.intheofobservationsobviously]iesinthefactthatsuchai nf i ni te popul ati on does not iust'ify a criter j on based

In an effort to reduce any tendency to severjty of the criterion for a snrall

number of observations, a correction factor for the va'lues of Table I?'L has been

developed by the following reasotting. The dist'ibution of tlte mean i of a sarnpie

of size n taken from an infjnite population of mean U and standard deviation o'

itself is a randonr variable vrjth a mean p and standard deviation ol6 (ptitter

and Freund, 1965). Thus the calculated mean i from a s'ingle set of m samples

will quite likely deviate from the true mean of the infinjte popu'lation front

rvh.ich the samples were taken, by up to 0.68o/ffi'* This inrplies that the devia-

tions calculated for each data po'int nray be in error by up to l0.6$o/ffi frorn the

devjation about the true mean. Ignoring the e'tfect that th'is error nay have on

the calculated standard cleviation' as a first order correction it seems that the

rinriting values of e/o given in Tabr e rz.1 should be increased by 0.68/ffi-to

ensure that data is not erroneously rejected, as this'is the uncertainty in the

ca1 culated deviations.

Themodifiedrejectioncr.iterioncanbeexpressedas

-t(rz.?)

where

and where e' i s the

for m observations.

Tabl e t?..2.

N( t) 4rn-1= ---=-4m

This cpiterjon, vlhen applied to m co]lateral scans by the subroutjne CHAUV

(m>10), has been found generally to result in the rejection of those points

correspondinq to obvious interference spikes on the analogue record' In the case

of less than ten scans, 6HAUV 'is found to be generally conservative in its

rejection of noise spikes, however it very seldom makes an unjustified reiection'

maximum PermissibleA tabl e of e'lo as

case of a smal I numlrer

smal I samPl e from an

on probabilitY.

dev'iat'ion under the modi f i ed cri teri on

a functjon of m for 1<x<30 is given in

. 0.68.t-

fre'o

* This is the range ofl-r, assumi ng that I i s

iforvthichtheprobabilityofoccurrencejsgreaterthannormally distributed about u'

Page 273: 2-Whole-digital Data Processing in Radio Astronomy

265.

zt22

23

24

25

26

27

28

29

30

2.41

2.43

2.44

2.46

?.47

2.48

2.49

2.50

2.51

2.52

11 | 2.21

t2 | z.zq

13 | z.zo

14 | 2.28

15 I 2.30

16 | 2.32

t7 | 2.34

rB | 2.36

le I z.rs20 | ?.40

1 .36

1 .63

1.77

L.87

1 .95

2 .01

2 .06

2.t02.t42.LB

1

?

3

4

5

6

7

B

9

10

Table 12.2: The naximum permissible dev'iation

accordi ng to the rrrocli f i ed cr i teri on for a

given number of samPles m'

(;')

12.2 The Re ection of Data l'larred b Extraord'ina No'ise:

(b) By Consideration of Sequential Data Points

The reiection nrethod used jn the preparation of the 0hio 1415MHz sky

survey (Dixon dnd l.rrauS, l-968; Kraus, Dixon and Fisher, 1966) was to calculate

a running value of the standard deviation for six consecut'ive data points and

to compare this with a predetertn'inecl I inrit. If tlre calculated deviation

exceeded this value, thett the peak li/as assumed tO be spurious and was rejected'

A subroutine REJEK has been developed to perform a reiection analysis of

the interferometer data based on this method. Theprqram is shown in the flow-

chart of Figure 12.2. The ca]1ing paranteters are PBEG' PLEN' NSET and LIMIT'

I{SET scans, each PLEN pages long, stored sequential]y on the disk file starting

at page PBEG, are processed. Those po'ints for which the standard deviation

calculated for that point and the preced'ing five (6 points in all) exceeds the

parameter LIMIT are rejected and replaced with values obta'ined by linear

.interpolation between adiacent data pojnts. There is no linrit on the number of

scans which can be processed by REJEK 'in one call, but if the scan length

exceeds f.ive pages (tive hours of data) then the rejection is discontinuous

across the boundaries of each five-page set from one scan' and if spurious values

occur near these boundaries, they may not be rejected'

Page 274: 2-Whole-digital Data Processing in Radio Astronomy

266.

In additjon to providing continuity for plotting the processed data'

replacing spurjous values by linealinterpolation has been found to produce the

best rnoclified value for use in the calculat'ion of the deviations of subsequent

data points wh'ich involve the spupious value (the next five points). When an

unacceptable standard devirbjon occurs, or if a zero flag'is found r'rhich jndj-

cates data previously declared invaljd in the storage process, then that data

is replaced by f.inearly interpoiating between the last acceptable value and the

next data po'int (it is not known at this stage lvhether the next po'int is

acceptab'le or not). Any other spurious Vaiues prior to this point' yet since

the last acceptable point, are a'lso replaced by this interpolatjon' Eventually

the entjre rejected section is replaced by the straight fine joining the

bordering acceptable values.

when called, REJEK first detennjnes t^lhether 0r not the scan length is

greater than five pages. If PLEN 'is glreater than five then each scan is

broken up into sections of five pages or less, t'tltich are treated as indjvidual

scans. A set of five pages or less (a nrax'imum of 1800 data points) is then read

into an array IX(1800). This array is so arranged that jt can be addressed to

IX(-4) and IX(1s01). The five points before the first data value tIX(-4) to

IX(0)l are set equal to the fjrst value tlX(1)1, and the po'int after the last

.data value is set equal to the last d.rta value. Starting with IIIDEX=I' the

flag word of IX(INDEX) is read. If this is not zero' then the standard devia-

tion of the six data values IX(INDEX-5) to IX(INDEX) is calculated' If this

devjation exceecls LIMIT, olif the flagr^rord r,vas initially found to be zero'

then a counter FLAG, initially zero, is'incremented by 1, and the data values

IX(INDEX-FLA6+1) to IX(I1DEX) are replaced by interpolation betvteen IX(INDEX-

FLAG) and IX(Il,lDEX+l). Each of these values is then packed vlith a f'lag vrord

of zero, INDEX is incremented by 1, and the process repeated for the next data

value. When a valid vrord is encountered and the standard deviation falls with'in

the acceptable l'irnit, the counter FLAG is reset to zero' As each page botrndary

is crossed tIX(A.360)l the index entry for that page is modified to include the

new invalid word count. l,lhen all of the data read'into IX has been processed, itis wrjtten back on to the d.isk and the next set of five pages or less is read and

processed.

REJEK

spi kes frorn

a1 though i n

is accepted

has been foun<l to be very effic'ient'in reiecting extraordjnary no'lse

isolated scans, vrithout requ'iring co'llateral scans for cornparison,

its present fonn, a no'ise spike occurring at the beginn'ing of a scan

at the expense of the rejection of a number of subsequent valid data

Page 275: 2-Whole-digital Data Processing in Radio Astronomy

267.

MAX + $FLEN +4,1 5

NPAf,€

F,I"EN- 5r I MAX,- I I

NrD ts300x P.IP*GE

|t ix( lNDExt

eornEut$ s1&nddr,d OEv-:iiifion, Sf0v' F-o,ri

lN(lNIDEX-.5) totl{INDEX I

S'lfEU >X-l$,1:

NFACE

- 5

FAGE*FB€G. (L - llx

tNtlExL + 360r(K-l )

OfFF+IINl:lN0EXr 1),

-tx{lNoEx-FtA€ )t/lFLAGr 11

Fiqure 72.2: RE'J'[K flcr*archart; the reiection----- seque,ntial comPari son.

trX'.tlNtEX-FLA6* M I

I X( INEIEX.FLAGI

+ M x UIFIF

Ertry fon Fhge

paGE.+ t( - t

Writc NFAGE

Pogis Bsekon Disk ot

routtne,based on

Page 276: 2-Whole-digital Data Processing in Radio Astronomy

268.

points. This js not of vjtal concern, as the extremes of a scan do not normally

contain data of interest. l^lith the present in'Lerferometer configurat'ion, a gain

of twenty at the input to the ana'logue-to-digita'l converter fully ut'il'izes the

dynarnic range of the systent, and with this settillsJ, a linriting standard deviation

of 20 has been found to be a suitable criterion for the rejection of noise sp'ikes'

The operation of the subrou.L'ine REJEK is demonstrated 'in Fjgure 12'3'

The soljd line in Figure 12,3a shows the Orjginal unprocessed data' with a large

noise spike occurrjng at 13h 57m. The standard deviation of this record' ca'lcu-

lated oven six clata points, is plotted in Figure 12'3b' Those points where the

standard dev.iat'ion exceeded the perameter LilllT vrere rejected by FIEJEK and

replaced by'linear interpolation, as shown by the broken line in Figure 12'3a'

l^lhen a large number (tro) of collateral scans are available for comparison'

the subroutine CIIAUV produces simjjar results to REJEK' but jt must be

rernembered that the criter-ion used by CHAUV consiclers the effect of a point on

the average of a number of simjlar points, ancl is thus d'irected towards producing

the best average scan, rather than cotrsideling each scan jndividua'lly'

'In ChaPter 13, the cPerat'ion of

is examjned and a comparison ntade of

the two subroutines, REJEK and CIIAUV'

thejr relative Performance'

l?.3 The Averagi n of Several Colt@

The Fortran subroutine AVRG(pB[G,PLEN,NSET,PANS) shown in the flowchart

of F'igure L2.4 has been developed to average NSEI collateral scans' w'ithout

processing the data in any other way. Its operatjon is practically identical

to theaveraging portion of CHAUV. Each set is assumed to be PLEN pages long

and all sets are assumed stored sequentially in the disk file starting from page

PBEG. The averaged scan 'is written in PLEII pages starting from PANS'

AVRG reads a collateral record from each scan' and sums the 60 collateral

sets jn AVG(60) and their flags in NUM(60). The sixty averages AVG(L)/NUM(L)

are then calculated and packed with NUM(L) as the flag rvord into IDATA(L)'

If NUM(L) is zero (i.e., no valid urords in a collateral set) then IDATA(L) is

set to zero. This affay'is vmitten back on to the disk in the correspond'ing

record of the area set aside for the average' 0n the completion of the averaging

of a set of collateral pages, an'index entry is rnade for the averaged page'

As with CHAUV, AVRG weights each data point according to its flag word'

Page 277: 2-Whole-digital Data Processing in Radio Astronomy

259,

xo

dccgptoble vq[t!e.5

,neieetd vrqtuc,s

reptoccrnent sectton

|N?l') r-.. a(rr /

The operation(a) The data'

in removing d noise spike.the standard deviation.

of RE,IEKand (b)

Figule 1?.3:

Page 278: 2-Whole-digital Data Processing in Radio Astronomy

270.

wr;t? IDAIA{60

ot Jlh Rcrord

in lthPoge of

r-I- -I r ---L-]-_-_____L_._fnii" r;i:,@

/rronr trhn"ccrri /\in lrt'Poge. ct l

\-$:"' J'- -l-fl,i - ,-l_ - -;T-

Figure 12..4: AVRG flotrchart; tfic record averagjng routine.

Page 279: 2-Whole-digital Data Processing in Radio Astronomy

and thus two different but collateral

form a grand average with the comect

produces a result identical with that

all of the original data at once.

12,4 The Digital Filter

It vras shovln in Chapter 5 that ttre filtering of a function U(f), vlhich is

usually consjdered in tlre frequency domajn as the multjplicat'ion by a filtertransfer function H(f), can be perfornred in the time domain by a digital filter'A djgjtal filter produces the convolution'integral of the time varjation u(t)

of the function with the Fourier transform h(t) of the transfer function

(h(t)) is the impulse response of the fjlter). The convo'lution integral can be

considered as a ,moving vrindow rre'ighted average' of the input function u(t) , the

weiglrts being determined by h(t). A zero phase shift digital filter can be

represented mathematical lY bY

N

vo(to) = ol_*uk.v(to+KT6),

Bk = B-k

where yo(to+Kt.) are sanrples of the jnput function taken at intervals TO' and

yo(to) il tt. oitput of the fitter corresponding to the sarnple y(to). tn: values

ni rorm the weighting functjon of the digital filter and can be obtained from

the 'impulse response h(t) bY

Bk = Td.h(KTd)

The effect of truncating the inrpulse response of a filter to produce a

realistic weighting function was stud'ied in Chapter 5, and jt was shown that a

good approxjmation to the ideal low-pass fjlter could be obtained by truncat'ing

its impulse response to tl/fo in order to make it physically real'izable' The

longer the weighting functjon used hovrever, the better the approximation to the

'ideal filter, and the sharper the cut-off .

Two factors are sign'ificant jn the consideration of how long a weighting

function should be. These are (1) the quantjty of data it is convenient to

involve jn a single calculation, determined by the available computer storage

capab'ilities and operating speed, and (2) the quantity of data which can be

defined as the reg.ion of interest. It is this second consideration which places

an upper l.imjt on the wejghting function 'length in thjs appf ication' several

thousand words of computer memory are available for data storage' and thus

27t.

averaged scans can be averaged together to

r,reighting appl ied to each scan. This

vlhich would have been produced by averaging

Page 280: 2-Whole-digital Data Processing in Radio Astronomy

?7?.

rve.ighting functions thousands of words long can be readily accon[nodated, but as

the quantity of data of interest is nornully not much longer than a few hundred

sarnples (1 hour,s data is 360 sarnples), then such long weighting functions are

of 'little value.

In view of the transfer functions calculated for various truncated filters

in Chapter 5, it was decided that the digital filter should be capable of

applyi ng utei ght'i ng funct'ions of up to t:5/f o seconds 1 ong ' l{owever because of

the non-ideal characterjslics of such a fitter, fo should be -50% higher tlian

the highest data frequency. For the specified upper data frequency of 0'003H2'

this nreans a tvei-qhting functjon -11000 seconds'long, and as samples are at

ten-second intervals, the longest rve'ighting function required wjll be 201

wei ghts l ong .

A d.igi ta1 f i I ter j ng subrouti ne FILTR(PBEG,PLEN,PANS ,NI'IATE,LENTH) , descri bed

in the flolvchart of Fjgure 12.5, appl ies a weiglrting funct'ion (2 x LEIITH +1)

weights'long to PLEN pages of data startjng from page PBEG, and writes the

filtered data in PLEN pages startjng from page PANS' Up to twenty different

weighting functions can be acconimodated jn a specially allocated disk fileIIATEF of tr,venty 201-word records. NI'JATE specifies which of these functjons

is to be used by its record number, ancl LENTH determjnes tlte number of weights

i nvol ved .

An array IX(280) 'is used to store the data required by the filter to

produce the output for one record (60 words). After reading three sixty-word

records into IX(101*2g0) and setting IX(r*tO0) equal to IX(101)' FILTR produces

the fjrst output record corresponding to the data at IX(101*160)' To calculate

the output correspond'ing to the fjrst data point the weighting functjon is

applied to data values fronr ix(101-LENTH) to IX(10i+LEl'lTH). (IX(10i)) is the

first input data point), For the second output point, data values from

IX(102-LENTH) to IX(102+LENTH) are jnvolved, and thus in producing one output

record, data values from IX(tot-LrNrH) to Ix(160+LENTH) are required. For the

maximum length filter (tENtH=tO0), values from IX(1) to IX(260) are required.

After vrriting this first record in the specified data area on the disk'

each IX value is shifted 60 places dovttr the array (i.e., IX(L)*IX(L+60) for

L=L,2?0) and the next record is read jnto IX(221+280). Once again the program

produces an output record corresponding to IX(101-+160) and I'Jrites this on the

disk. The program cont'inues in this fashion until the last but two output

Page 281: 2-Whole-digital Data Processing in Radio Astronomy

273.

(.

(

Wri tc 5ti t(n)

o t Recot C

NAIIS

I

I

I

L

,"n\a K: l"lA).tlc, - I

>->, i\ - f i I

tr\ ri te In dcrEn try forPoge Just

lP : PLft'l

Write Me ssogc

on Printa-r

,1,J0 _2.

t-.-

Fi gure 12. 5: FILTR flowchart; the digital filtering rout'ine'

Page 282: 2-Whole-digital Data Processing in Radio Astronomy

274.

record has been P:t"odueed and the data shifted doun the IX a'rray'' The last inrput

record was rea6 on'the previotts o.ccasion and nob, no further data is availabile

for]ocations.IX(221+2,80).Toproducethe.sameeff-ectasatt'hebeginningoft,he s,can,, assuming the ir.rput corrrstant fsr LENTH points prior to the sean!

IX'(2?1+280) are set to Ix(220), as they are again before the outp.ut of the fi'nal

record ? '-

For a da.ta cut-off frequency of 0.003112' a

obta'lned from the inpr'l1se response of' the i'deal

has beetn found to p'tnoduee satisfactory results'

descrlbed in ChaBter 13. An idea:l integrating

which is constant ovjer the nange +T7, and zero

used. However to produce a minimum distortion

'ratio cannot be incneased by such an extent ag

pass filter.

step-1p'g6aa'ted wei ghti ng functi on

levl-pqss filter with fo=0'005H2

The action of this filter isIow-pas's filter wej,ghting ftlnctio'n'

out'isde th'is rang€n has also been

of the data, t,tr,e signal-to-hoisethat ach'ieve{il bY the idaal lolv-

R]EFERENCES

DIX0N, R.S,, and KRAUs, J.D, (196S): "A High-Sensitivity 1415MHz Study at

Nor.th Declinatio,ns Between l,g0 and 370", Astron0m, J., Zl- pp' 381-407'

KRAUS, J.0., DIX0N, R.S., and FISHERe R.0. (feee1: uA New High-Sensitivity Study

of the M3l Region at 1415 Flc/s". Ap. J., 144 Bp' 559-567'

l,lItLER, I., and F',REUND,.1.E. (1965): 'lPro,bability and StatiFt'ies fo,r EnginQ€fs('

(Prentice-Hal 1 n New JerseY),

SllART, }|.!1, (195S): "Combinatj:on of 0bservations". (C'U'P' , CambridEe) '

Page 283: 2-Whole-digital Data Processing in Radio Astronomy

275.

CHAPTER 13

Some 0bservational Results

In this chapter the effectiveness of the data processing system js evalu-

ated by a study of some results obtained. During February 1971, sixteen

transitsofcentaurusA(areso=!3:22:20'6rruo=-42o46')wererecordedonpaper tape. These recorcts have been examined for spurious noise sp'ikes'

averaged, and fjltered, and the results obtajned are described jn the following

pages.

13.1 The Acquisition and Storage of the Data

Figure 13.L shows the analogue chart records of tlo of the transits used in

the analysis. The antenna arrays were directed at the zenith 16 = -370) and the

post-detection RC filter tjme-constant was tl'tenty seconcls. The recorder sensi-

tivity was 400nrv peak-to-peal<. The time marks above the trace are loca'l sidereal

hour marks supp.l'ied by the clock-pu1se source described in Chapter 7' The tran-

si ts occurred at approx'inrately 4 a .rn. I ocal time '

During all of these observations the occurrence of interference spikes was

high, forming an almost regular pattern. These spikes significantly marr both

of the records shown, and it'is obvious that sorne means of removing them is

requ.ired. The average peak-to-peak no'ise level is approx'imately one quarter of

the peak-to-peak signal deflection. Assum'ing that this noise level is the same

as that during the observation of the Crab l{ebula shown in Figure 4.8, which was

found to be 1200 x 10-26p/nr2ll1z peak-to-peak, then this suggests an observed

flux density of 2400 x t}-2sy1162/Hz for Centaurus A'*

Three hours' data was recorded on paper tape for each tratrsit. The acqui-

s.itjon process was started autonratjcally by the clock-pu'lse source start/stop

program at lzh I ocal sidereal t'inre (^3 a.m. local time) and was terminated at

lsh L.S.T. The s'ixteen transits ana'lysed were recorded on three tape files; #26

containing four transits, and wjth a b'lock length of sjx sanrples, #30 containing

five transits, also with a block length of six samples, and #33 containing seven

trans'its recorded wjth a block length of thirty samoles. The gain of tlte

*The spectrum of Centaurus A published by

densi ty of i200 x 1g-ze p7n'z /Hz at 2001'11-lz,

suggest a higher figure.

Shklovsky (1960) jndicates a fluxbut other results (Kraus' 1966)

Page 284: 2-Whole-digital Data Processing in Radio Astronomy

?76.

i,;, I f-l i. *,' i'r.-.;.1 1; !'

It. t' 'l ';:,',"i.,,,, 'l i '

, ..:r ir. '.1 ii-t ' ',;',f | 1 -

| , tr. 'l 1-i ri I! ti :\- - -r1 Ill-i

Fi:clui"e 13.1: Ana],ogue ,chflFt recol^ds of two trans'i'ts of

Centaurus A (NGC 5128). Antennas we'r€ dirrected

to d = -37o; filter ti'me csnsta'nt was

twenty seconds,

(a) 20th Fcbruary 1,971, (b) 21st February 1971"

During the storage o,f these three files, which took twenty minutes-of com-

puter tim6, no lincorrrect p-at'i:ty chanactens were encolntered. However three

spurious chanacter"s, (inva'lid identif icatisn seQlrsxgs] occulined on #26" and e'leven

words were declared invalid. 0n #30, fou,rteen wot"ds were decilared invalid, but

no data was ]ost from #83, The sixteen three-hout" scanE were storred in forty-

eight pages, of the nine(y-page disk data file RSTAR. The indrex llisti;ng of

the storred data pt'oduced by DUMPX aftef the thlrd tape had been stored is

shown in FiEure 13.2.

13.2 The Analysis of the, Data

anal ogue-to-di gi ta1 converter

the dynamic range t200mV (the

The operation of the two extt"aneous noise

CHAUV and REJEK, is demons'tnated in Figiures

the plot produced by the subroutine CHART at

llas et at twe,nty for all of the transits' making

sahre as that of the chart records)'.

spike reJection subroutinesn

13.3 and tr3.4. Figure 13'3 shows

different stages during the

Page 285: 2-Whole-digital Data Processing in Radio Astronomy

277,

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Page 286: 2-Whole-digital Data Processing in Radio Astronomy

278.

analysis of the data. F'igure 13.3a'is the original data, as read frorr the paper

tape, for the transjt on 21st February. Th'is can be compared directly w'ith

Figure 13.1b, the analogue chart record of the same transit' noting that the

polarity of the analogue chart is reversed (positive belol'J the zero axis)'

Although the time scale-anlpl'itude scale ratios of these tr'ro plots are quite

clifferent, the interference spikes are easily identified and compared'

Figure 13.3b shovls the same data after analysis by the reiection subrout'ine

REJEK. The pronrinent trvo-sidecr no.ise spjke occurring at 13h 57m on the o.iginal

record has been completely removed, atrd others occurring at 13h 16m and 14h 38nt

have been consiclerably reduced. The two retnain'ing obv'ious instances of jnter-

ference on the original record, at 12h 35m and 13h 03m, although still v'isible

on the processed scan, have been significantly reduced in magn'itude'

The record shown jn Figure 13.3c is the origina'l data of Figure 13'3a after

it has been processed wjtlr three similar collateral records by the subroutine

cllAuv. As mentioned in chapter 12, vtith a srnall number of collateral records

on which to operate, CHAUV tends to be too conservative in its reiection' and

most of the noise spikes appearing on the original record (Fjgure 13'3a) are

comp'letely untouched. l'lowever F'igure i3.3d shows the sanre record from 21st'

February after processing with fifteen collateral records by CHAUV' The

similarity betneen the results ob'bajnecl by thjs procedure and those produced by

REJEK when operating on a single record (F'igure 13"3b) is remarkable' 0n these

limited resolution plots the d'ifferences are sniall, except that CHAUV has

been more eff icient than REJEK in rt:moving the spjke at 13h 03m.

A small portion of each of these four records is shown jn more detail in

Figure 13.4. The area examined'is that between 13h 10m and l-3h 20nl' covering

the no.ise spike vrhich occurred on the original record at 13h 16m' Five data

point.s have been rejected by.REJEI( (Figure 13.4b) and replaced by ljnear

interpolation betvreen the acceptable values at 13h 15m 40s and 13h 16nr 40s' In

addition, tvto further points have been reiected from a m'inor spike occurring at

13h l8m 30s. Although this is not such an obvious case of jnterference' closer

examination of the unprocessed data of Figures 13'3a and 13'1b does show an

ut'lusual'ly large negative maximum at this point'

Fi gure

operating on

corresponds

13.4c shows that only one data point was rejected by 0HAUV when

four collateral records. The rejected value, at 13h 16rn 00s

to the maximum of the sPi ke.

Page 287: 2-Whole-digital Data Processing in Radio Astronomy

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Figure 13.3: CHART printout showinrJ the operation of CHAUV and REJEK;--j*r--- (a) unbrocessed data irom 21'February 1971, (b) g afternEirr,'(c) a after CHAUV (4), and (d) a after CHAUV (16).

Page 288: 2-Whole-digital Data Processing in Radio Astronomy

280.

(o! A(tet RE.IEK

Detail of th,e action of CHAUV and REJEK s:how'n

i n ,Fi Eure 13.3.Flgure 13.4:,

Page 289: 2-Whole-digital Data Processing in Radio Astronomy

281.

when operat'ing on sixteen collateral records (Figure 13'4d)' CHAUV

rejected the same five data points as REJEK fronr the nraior spike' Although

the replacement values are not identjcal (CHAUV replaces rejected values lvjth

the average collateral va'lue) the sjnrilarity of the results of the two pro-

ceclures is borne out by th'is p1ot. Hot'tever the nrjnor spike at 13h 1Bm 30s was

left untouched bY CHAUV.

Four records, includjng that of the transit on 21st February' were averaged

by the subroutine AVRG after they had been processed by REJTK' and the

resultant averaged record js shown in F'igure 13'5a' As one would expect' the

noise level has been reducccl by a factor of 2. Figure 13'5b sho;s this aver'rged

scan after f.iltering Lry the subroutine FILTR. The rveighting function used was

the .inrpu'lse response of the ideal low-pass fi'lter lvith a cut-off frequency of

.005 Hz. This 'impulse response was step-truncated to t1000 seconds (i'e" I

to = S/fo producing a transfer function of the form shovln jn Figure 5'6d'

The fjlter has zero attenuation at the signal frequcncy (2.g1 cosd x 10-3llz I

-Z.Z x l0-3Hz). Although the noise level has been significantly reduced by thit I

f.iltering, the effect of unrejected interference spikes is apparent jn the wander

of the fringe pattern about the zero axis'

Figure 13.5c shows the result of averagjng all sixteen of the records after

first processing thenr with REJEK. The noise level has been further reduced

from that in the average of four scans (figure i3.5a). This record was then

filtered by FILTR using the wejghting function previously mentioned' pro-

ducing the record shot'tn in Figure 13.5d. This repr^esents the final processed

output of the system. The orig'ina1 signal-to-noise ratio has been improved

four tjnres by averag'ing sixteen collateral records, and 1.6 tinres by the digital

fi I ter*.

This stage of the processing is sholn'in more detajl for a small section

of each of these records in F'igure 13.6. F'igure 13.6a shows a section of the

orig.inal record for 21st February between 13h 30nr and 13h 40m' The average of

this and three similar records' corresponding to the average of Figure 13'5a'

is shottn in F'igure 13.6b. Here the reduction jn noise level by a factor of tvlo

is obvjous. Figure 13.6c shows the same section of the average of sjxteen

collateraj recorcls, corresp0nging to the record of Figure 13'5c' Again the

f ilter is 1/4RC = 0.0125 llz and the

noise bandwiclth of 0.005 Hz 'is* The noise bandr'ridth of the presampl'ing

'improvement producecl by f iltering w'ith a

f,6flfTffi5 = 1.6.

Page 290: 2-Whole-digital Data Processing in Radio Astronomy

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CHART printout showing operation of AVRG and FILTR;iil tnb aveiioe of foir bollateral records' (b) a

itler rtlTR, (c) the average sf sixteen collateralrecords, and (d) c after FILTR.

Page 291: 2-Whole-digital Data Processing in Radio Astronomy

283,

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Page 292: 2-Whole-digital Data Processing in Radio Astronomy

284.

reductjon jn no'ise level by a factor of two from that in Figure 13'6b is obvious'

The fi'ltered average of all sjxteen records js shown in Figure L3'6d' This

record is smoother than r.tould be indicated by the CHART piot of Figure 13'5d'

The difference is causecl by the ljrnjted resolution of CHART'

A further comparison of the tvro routines CHAUV ancl REJEK is shot'tn 'in

F'igure 13,7. The result of averaging four records after processing by REJEK

js shown jn Figure 13.7a. Figure 13.7b sholvs the corresponding output from

CIIAUV when processing the sanre fclur records. As shown by Figure 13'3c' vlhen

CHAUV operates on only four collatera'l records, tnost of the interference sp'ikes

are left unt0uched. The detrimental efFect on the averagecl record of including

these spikes is obvious from Figure 13.7b, although the average no'ise levels on

the two records (a) and (b) are almost'identical. Figure 13'7c shows the

averaged record of Figure 13.7b after filtering by FILTR' This filtering does

much to reduce the effect of the nojse spikes, but the spikes still cause

abnornial deflections of the record whjclt can be seen by conrparing it w'ith the

filtered average of four records processed by REJEK, sholn in Figure 13'5b'

The average output frorn CHAUV when processing sixteen collateral records is

indistinguishable from that produced by REJEK shown in Figtrre 13'5'

The operat'ion of the systerr vrhen processing a s'ingle record'is demonstrated

in F'igures 13.8, 13.9 and 13.i0. The three records shot^rn in Figure 13'B are

stages of the process'ing of the record of the transit of Centaurus A on 2lst

February Ig71. Figure 13.8a shows the original unprocessed digital record' the

corresponding ana'logue record of which is shovrn'in Figure 13'1b' The same

record after processing by REJEK is sltown in Figure 13'Bb' and in c' the

processed rec'rd has been filtered by FILTR, using the weighting function

prev.iously menti oned. The no j se I evel 'in thi s f i I tered record has been con-

siderably reduced, but the effect of t'he noise spikes at 12h 35m' 13h 03rn' and

13h 57rn can still be seen. The portions of the original and filtered records

between 13h 30m and 13h 40m are sholn'in more detail jn F'igure 13'9' The pro-

cessed record is quite smooth and free from h'igh frequency noise.

Figure 13.10 shows the processing of the record obtained on 20th February

lg7ir. The original analogue chart record is shown in Figure 13'1a' and the

unprqcessed d'igita'l record js sito;tl in Figure 13'10a' Figures 13'10b and c shol

the record after processing by REJEK and then FILTR' Six obvious instances

of extraneous noise spjkes, at 12h 35ni, IZh 4An,13h 23m, 13h 28m,14h 10nr and at

14h 13nr, have been reduced by varying amounts by REJEK' but even after filtering

Page 293: 2-Whole-digital Data Processing in Radio Astronomy

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Page 295: 2-Whole-digital Data Processing in Radio Astronomy

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2t FabrunrYUnpruccssr.d

Detaill o:f the proces5jng of the reco,rd of the transit

A sn 21st February 1971. (a) The sniginal record'

the record after processl'ng by RE.IEK and FILTR'

1971

Oalo

(q)

ilssrelSJ.tof Centauius

and (b)

their effe,et can stlll be seen.

It should be noted that when racords ar€ processed by either R,EJEK or

CHAUV, and unaceeptable data points are replaced by fnterpolati,on o,r averaging'

the yeplacement values take.no part in su sequent avera,ging as theirn flag vlords

are zer'o. gowever to Brovide continuity whenr filtering single uttaveraged

2t tabruory 197:l

oigitoLly Httcr.eo

Page 296: 2-Whole-digital Data Processing in Radio Astronomy

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tt"""""-

iit''

IttrIr

Page 297: 2-Whole-digital Data Processing in Radio Astronomy

records, the replacement values are

Thus the single processed records of

representation of the interferonteter

13.3 Conclusions

289.

recognisecl as val'id data points by FILTR'

Figures 13.8 and 13.10 do not g'ive a true

si-cna1 output near inbcrference spikes'

This thes.is establishes the limitat'ions of a snull radio telescope opera-

ting in a noisy environment ancl descrjbes the design of a digital data pro-

cessjng system developed to improve the sensitiv'ity, and to present the output

data in a form su1table for further analys'is. The resu'lts described in this

chapter, obtained by processing the clata from sixteen observations of Centaurus

A, deinonstrate thc effectjveness of the system'in perfornring this functiott'

The sixteen records, each three hours 1ong, l',tere recorded on paper tape by

the hardware systent. The forty-eight hours' clata occupied approximately 350

feet of paper tape and requ'ired fifteen niinutes of computer time for storage on

a magnetic disk data file. These records were then exatnined for spurious no'ise

spikes, averaged and filtered by the srrbroutjnes of the software systent' The

entire processinq clescribed in this clrapter, including graphical printer output'

used seventy-nine mjnutes of computer time.

The processing system has been sirtlrn to produce a marked'inrproventent in

the signal-to-noise ratio of tlre data, especially when a number of collateral

records are available for averaging. A]though the sigl'ral-to-ltoise ratio of a

single record can be inrproved sign'ificant1y, large interference spikes occufing

with the present telescope cause abnorrrtal deviations which cannot- be sat'isfac-

torily removed.

Two nrethods of reiect'ing these spikes have been developed. The first nrethod'

described in sectjon 12.2, operates on a single record and effectively reduces

the spjkes, but only tvhetl several collateral recorcis are averaged can a sujtable

replacement value be ohtained. The second method, described in section 12'f is

effective only when a large nunber (tio) of collateral records are available for

coml:arison, and as there is very little difference bett'leen the results obta'ined

by the t;o methods under these circumstances, the first method seems preferable'

although when a very large number of collateral recorcls are avajlable for

averaging, the second nrethod vrill theoretically produce the better average'

The overa'll signal-to-no'ise'inrprovement resu'lting from processing the dix-

teen records has been estimated at 6.5, disregarding the effect on the original

Page 298: 2-Whole-digital Data Processing in Radio Astronomy

290.

signal-to-noise ratio of the extraneorrs spikes. This means that the minimunt

detectable flux densjty of the telescope has been reduced to 50!l/m2lHz and with

the imprOvements scheduled for the system, there seenls no reason why useful

observations cannot now be made.

REFI,RENCES

KRAUS, J.D. (1966): "Radio Astronomy". (McGralv-l-ljll, New York) '

SHKLOVSKY, I.S. (t9OO): "Cosmic Rad'io l,javes". (Harvard Un'iversity Press 'Massachusetts )

Page 299: 2-Whole-digital Data Processing in Radio Astronomy

291.

4PPPndir r

Date Aa.qut,sitJ,on System Spesifi catiqn

At.tr The Analorgue-to-Dfdta-l .Cornyerter

Al rll Inpqt

Input range; *4 v,oTts fulT-se'al€,, with an inpu;t amplifien

to ptcovide ga'ins sf 1, 2, 5r 10' Z0 and 50'

trnput i'mBedance: llffi.

l'laximum input voltage: *15 volts.

Res- lution: eight bits pluS sign, two's complement

repres.entationl reduclble to gix b'its plus

si'gn and fsu-r bits Plus sign.

Accuracy: :3:13 $ rull scale.

Aperture time: S0uEeconds fon nine-bit resol.ution; 60 and 40

useconds respectively for seven and five bitressl ution.,

41.12 Outpu!

Mod:e-;

Level s:,

Al .13 Corrtrs]

Nine-bit parallel.

Standal"d t,.t.l ' logic leveli:s; '1r is +2'4 to

+5.0 volts, !0' is 0 ts + .4 volts'

sarnpte comrland: External by 0+1 transition,. Manual by front*

panel Push-button.

Data ready tndication: A 0*1 transition on a 'flag' output'

-41,14 Internal Requirements

PEwer supplie.s: t[5 vo]ts' 200mA regulated- +5 volts, 700mA

regul ated,,

Page 300: 2-Whole-digital Data Processing in Radio Astronomy

2s2.

C:lock: 100KHz, 0+1 logic trans,itt;on.

41.2 The ,SolarlSidere,al D-Jgiral Clock

41.21 OutpUt

Resoluti on:"' 0. I second's ,

['{ode: 84,b,it panallel,

Fornrat: , !.G.d, (8421) of tenths-of.-seconds, seconds,

te,ns-of-seconds, minutes, tens-of-minutes,h,ouns and tens-sf-ftrou'rs.

Levels: Standarnd t,t.l. positive lo,gic levels.

Accuracy:

Solar: t0.1 seeonds/lS weeks.' Sidereal: r0.1 seconds/lS weeks plus a systematic emor

of -0.i seconds in 70 hours.

Standard frequenc,ies: Outputs of lMHz" 100KHz, 10KHz, l.KHzn 100 Hz

and 10He solar, and trOHz sidereal.

Display: Six digit gas-filted tube display of houns

minutes ahd seconds, solar or sidereal.

41,22 Control

Setttngr Slx thumbwheel switches set either clock todeslred time with onc second resolution.

Advance/Retard: Either clock ean be advanced or retarded by

oxe tenth of a second at a time"

$tartlStop: Either clock can be started or -stoppedn elec-tronfcal ly ot^ manual ly.

Synchnonizat'i,on'i Cl,ocks can be sJ:ncht"oniz,ed to tlpsiee of an

external ole-second tick,

42.13 Inte,rnail Reqyifernents

Power Supplies: +4 vo'lts, 2arnps regulated;+Z00 voltsr 100fiNA

unregul,ated.

Page 301: 2-Whole-digital Data Processing in Radio Astronomy

2E:3. I

A'2.14 .Standard FTequ.encJ-0,sqi'! latqr

SMtlzFrequency I

Stability; '1 part i'n L0'sflueek

OutPut voltage: 0'7 volts r'm's '

0ven temPerature: -600C

Oven stabilitY; t0'01oC

A1.3 Paper TiPq Pury-c,h,

A1.3X, InPut

Mode: FortY-bit' Parallel

l-ovels: Standard t't''l' positive logic'

Sources; Ten blts frsm a digital data source

(unbuffered),' analogue-to-digi tal coitverterl

twenty-five bits buffered for use with digital

clocki five bits from switch register'

A1,32 0utput

Mode: Eight' blts even parity'parallel' eight senial

words.

Fsnrnt: Eight groups of five data ibitsr olle: parity bit

and two i dent't-fl cat*ion bi ts '

Spee'd: Twenty charaeters/seco.nd rnaxitRum.

A1.33 Internatr Requlr'euents-

Poruer Supplies; *5 volts, 800mA regulated ' +27 volts regu'lated

10.5A Pea,k, 3.1 amPs average'

Clorck: lKHz' 0+t logic transition'

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294.

Al.4 0ontrg,l

Atr.41 Resof4ing. Interyals

Sample Interval:

Eloclc length:

Firom l to :99 x tenths-of'5€6onids, seconds'

ten s-of -secor,tdS r ffii nutes,i tens-qf -mi nutes I

hours or daYs.

From l'to 90 samP'leso

Acqrlisition p'rocess c'an be started and stopped

at selected hours during the day'' $o'lat" ol^

sidereal .

Seven-b,it switch'rreglsten provided for ma;nual

entry of on€ tape cha'racter - fi've bits of

data, tt^ro of, identi,ficatton'

A1.42 Start/Stsp Pr-oslamming

Ftesol uti on:

A1.5

A1.6, OutpuF faPe Fo,nnq!

Beglnnilrrg of acquisitiotl period mdrked hy a

santple data set of characters fo'|l'oue'd by a

coordinatc set. -Thereafte:F a block-length of

sanrple data sets fo,llowed by a coordinate data

,set.

Page 303: 2-Whole-digital Data Processing in Radio Astronomy

295.

Appendix 2

Theseinstr.,uetionsaredivid.edirrt.othreesections:

AZ.1 Start'ing the Data Acquisition System'

h2.2 Recsrding Data with the Acquisitio-n System'

A2.3ProcessingReclordedDataintheIBMll30Computer.

h2.7 Ertarlting the Data AcqU'isilion S'vstem

Before tnecolding data using the system' the systenr should be set-up in

the foll,owing sequence'.

A2,11 Sq:itching-gn From 0o-1d

Beforetheunitisco.nrtectedtothe2j0vol.t;litains'should be turned off. Mains sw'itches are located

l. oh e.ach of the three pot{er-srupp-lies'

all Botrer swirches

2.onthetapehand'lerun:it(themo'torsvriteh)'

and 3. on the rear panet of the standard frerquenclt sscillator'

See'ondary d.e . switches are located

1. two on the clock power supply (4 volts and 200 vslts)'

2.twgOflthe:gene,ralpgwersupply(5vo1tsandt15vo]ts)'

3. sns :o0 the tape punch power suppl'y (27 volts)'

and 4. one on the tape handler unit (the ,Bunch sw'itch) '

After these switches have been turned off (ur), the unit can be csnnected

to the 230 volt, supply and the mains switches of the three power gtrppl'ies

turned on' The three neon indicato'rs should now glow' Failure to do so may be

c.ause.d by a broun fuse. In addition to the prirnary fuses in the por,"er supptries'

afurthenfuseislo.catedintheinterfere.n.c.efi.ltelrgntheleft-handsideof

Page 304: 2-Whole-digital Data Processing in Radio Astronomy

296.

the unit where the mains supply enters the cabinet'

when the povJer supplies have been turned on, if any of the overload ind'i-

cator lamps are illumjnated, depress the appropr'iate reset buttons' several

times .if necessary , unti I the overl oad condi t'ion 'i s removed ' The regu I ated

outputs of eacrr of the supplies shourd be checked at the nronito.ing tenn'inals

provided on the front Panels.

A2.12 Starting the Stanclard Frequency 0scillator

with the gain switch jn the'set zero'position, the power switch on the

rear panel should be turned on. After several minutes the temperature-error

meter Should read zero jf the'heat'sv1'itch js on the'auto' (down) position'

An adjustment potentionreter" (116) 'is provided iust behind the front panel '

be.Lween the nreter termina'ls. set the gain switch to x.01 arrd the 'heat'switch

to ,full, (up). Theerror meter should now read off-scale on the low side' A

moving iron volttneter connected to the heater vo]tage monjtoring terminals

should read 200v r.m.s. After one hour the error meter should be'indicating

on-scale and the ,heat'switch can be returnecl to 'auto'' l'lhen the error reaches

-l.oC, the gain can be increased to x1 anci the temperature control System should

require no further attentjon. If the unit has not been runn'ing for sonte tjme'

it will take several days for the osc'illator to reach its final stable frequency'

The frequency can be monjtored by the l-1P5245L frequency counter at the front

panel connector. No adjustnrent of the frequency should be made until the final

stable state has been reached. It should never be necessary to make any adjust-

ments other than of the fine frequency control ' l"lhen any adiustnrent has been

made, a stable state may not be reached for several hours'

A mains fuse is located on the rear panel of the unit'

A2.13 Starti nq The Di gi ta] Cl ock

Turn on the 4 volt and 200 volt secondary supply svtitches. If the 4 volt

supp'ly overload indicator is illuminated' press the overload reset button' If

the overload condition persists, turn tlte secottdary si'tjtch off and reset the

supply, and then turn on again. The clock has built-in protectjon to prevent

damage caused by having one supply cotinecied r'.r.ithout the other, but it sht'ruld

not be left in th'is state for any length of tjme'

The visual display register should now

may be nonsensical). Failure may be caused

be i I I umi nated (tne a'ispl ayed time

bv a bloln fuse in the 200 volt

Page 305: 2-Whole-digital Data Processing in Radio Astronomy

297.

supply. This fuse is located on the front pane] of the power supply'

If the standard frequency oscillator js running, relnove the control panel

protective cover, and holding both the solar and sidereal interlock buttons

firmly down, depress the'stop'function button and the'reset'function button.

The displayed t'ime should now be 00h 00rn 00s and no counting should occur'

Check that both clocks are in this:tcrte (tne aisplay-select switches are

located to the right of the visual register together with their indicators)'

Holding both interlock buttons dovrn, press the 'start' function button'

The vjsual reqister should now commence to accumulate one-second counts' check

that both clocks are runn'ing. If one-second counting does not occur, reset the

clock concerned again, and restart. If the clock still does not start, check

the SMHz input from the standard frequency oscillator.

When both clocks are started sintultaneously fronr 00h 00rn 00s, after a few

minutes the deviation of accuntulated siderea'l time should be apparent'

.When it has been ascertained thatthe clock is functioning coffectl;" the

tvro tinre-keeping chains can be set to the desired times using the front-pane1

thumbwheel sw.itches and 'Lhe 'set' function buttotr. The cl0cks can then be

started and fractional-second adjustnrents made using the 'advance' and 'retard'

functi ons .

when the correct times have been estab'lished, replace the protect'ive cover

over the control Panel.

A2.14 Starting the Analogue-to-Digital Convertsr

Turn on the 5 volt power suppiy d.c. sw'itch. If the supply indicates an

overload condition, press the reset button. If the overload persisLs' turn

the d.c. switch off, reset the supp'ly, and turn the switch on again' Repeat ifnecessary. gver'loads occur during turning-on because of the large supply

decoupfing capacitors used 'in the various units'

Turn on the t15 vol t power suppi 'ies d. c ' swi tch ' Reset the over'load

jndicators if necessary, and'if the overload persists, turn the d'c' switch off

to reset.

Connect a sensitive d.c. voltmeter to the output of the input amplifier

Page 306: 2-Whole-digital Data Processing in Radio Astronomy

298.

(vu on the front panel). with the'input shorted, check the offset voltage in

each of the six gain-switch posit'ions. if in any position this offset is more

than 17.BmV, adjust the input offset control. Thjs trinrpot is located iust

behind the front panel; access can be obtained from the side'

llhen the offset voltage has been arliusted to give a satisfactory output

for ai1 gains, tertninate the input jn a 10Kfl resjstance' Check the output

vo]tage for each gajn setting once again. If this exceeds t7'8mV in any posi-

tion, adjust the constant-currettt-source trirnpot, located behind the input offset

control

llhen the input amp'l'ifier has been adiusted for a satisfactory offset level '

check the gain in each sw'itch position using either a low frequency signal

genera.Lor or an adjustable d.c. supply. F'ine gain adjustnrent is provided on the

gain sw.itch; the trirnpot for each sett'ing is clear'ly labelled'

hJith the 'incandescent display 'or'l', check the operation of the converter

using the nnnual sample button for differeirt input vo'ltages' If no conversion

is performed, check the 100t$lz control wa'.'eform from the digital clock'

The over-range

instruction because

the reset button i s

'indi cator shou'ld be 'il I unri nated after

the tape punch is not accepting data'

held dovrn while a sample is taken'

the second sanrPle

It will reset 'if

The reference supply and the control waveforms

front panel of the unit.

can be nioni tored at the

A2.15 Preparing the TaPe Hgndler

(Reter to Plate 7, Pdge 215, which shows a tape correctlY threaded')

Loosen the thumbscrew at the top of the supply drayer and s'lide the drawer

forward. Place the unpunched tape in the dravter as shown in F'igure A2'1'

Fasten the drawer back in p1ace, making sure that the tape passes out through

the slot at the bottom.

Raise the tape guide over the feed sprocket of the punch' The 'end-of-tape'

switch will also be raised by th'is actjon. Twist the tape anti-clockvlise through

90o wlrere it passes out from the suppiy drawer. Pass the tape over the 'tape-

tight, arm and under the punch head. Loler the tape guide over the feed sprocket'

Page 307: 2-Whole-digital Data Processing in Radio Astronomy

299.

forcing the sprocket through the tape. Leave about six jnches of unpunched tape

on the right-hand side of the punch head'

--Tope to

Punch

Fi qure AZ .1": Load'ing a tape into the suPPlY drawer'

Turn thc secondary sw'itch of the punch

'if necessary. Turn the punch switch on the

Check tirat the seven srvitch-reg'ister swjtches (on the

front panel ) are at 0 (up) and that the INT-EXT switch to

is in the INT (up) position. Depress the sr^ritch-register

punch should commence to punch sprocket holes in the tape

por{er supply on. Reset the supp'ly

front Panel of the taPe handler on'

d'i gi ta1 nru I ti P1 exer

the right of these

f'lag sw'itch. The

at a rate of 2O/second.

switch register and the flag sw'itch'

, and w'ill be a 0 or 1 dePending

the punched taPe over

capstan, and on to the

disk on the take-uP

motor swi tch on. lf the .Lape-break' i nd,icator "is .il ]u.

override button until all slack tape is wound in' Check

take-up motor by punching 6" more of blank tape'

Check each data channel punch us'ing the

Remember that channel 6 is the parity channel

on the number of bits Punched.

If the punch'is working satisfactorily, set the sr^titch register to zero and

punch three feet of blank leader tape'

Remove the outer disk fron the take-up spool. Thread

the first capstan' under the tension arm' over the second

ta ke-up spoo't .i n a cl ockvti se di recti on . Repl ace the outer

spool .

Turn the take-uP

minated, dePress the

the operation of the

8" Suppty

Page 308: 2-Whole-digital Data Processing in Radio Astronomy

300.

A2.2 Rec-,O:fdjng Data with- the Acquisition System

The system nUst be,pro,gt"arnmed to give the correct sample and block lengthts

(s,am.ple interval rnust be ten seconds with tlre present systenr; a suit&hle bloClt

length is thirty samp'le-s) and bo start and stop at the desired t'imes drlring the

day. A h,eading must allso be supplied on the tape'

AZ.ZJ, Fro.g,r'a{rtpi ng thE S'y'Ftem

connect the output A from thre cr,ock-pulse, source to thetrsTART" ir'rpttt''

connee,t the output ts to the ,sTop, i,nput. Place the tgtart'pl'ogram card in

s.sc,ke,t A and. the 'stopf prograrn in socket B' Set the selector sw'itch' to pos'i-

t|pn 3 (10 second peniod) 'and the solar-Sidereal st+ritch te the des'ired

c,sordi nate.

Gonneet 16,g 0P oUtpUt, ft"Om th,e clock-Bulse source to the T, terminal of

th,e time interval generato,r, and the RS output from the cloct<-pu'lse rsource to

the V6 terminal of the tine in erval generato'r'

Fatching of the time interval generator is as fsllows:

M,r'inputs

Mr output

Tp

Tc

]

sA

s,B

RA

Rs

Tp

Ys

YoD

sc

'Rc

The ouLPut from Ma shottild

analog,ue-to-digi ta1 converter 'the 'clock flag' inPut of the

M2 inPut

Ma output'

alsobecoRnectedtot.hesarnpleinputoftlreand the output frun l'lz should be connected to

mul ti P1 exer.

For a te.n se,cond samPle intervall and a thilrty s.aftP;le block'' set switch A

Page 309: 2-Whole-digital Data Processing in Radio Astronomy

301.

ts 0, switch E to l and sw'itch C to 3'

Set the analogu,e-to-digital conVerter word length to nine bits' and set

the desired gain., Set the samp'le-mode switch to f ex'ternal "

Setther"esolutions.}liitclnesonthemu]tipleNertoninebitsfortheanalogue-,to-digital co'nrrerter, and seconds for the clock data'

A2,?2 Heading the T?Pe

.Headlng data, described in Chapter 10, is ente'red on to the tape using

the s,witch-register. The desired data is set on the Seven switches' and is

punched by elosing the switch-register flag switclt upwards.

The. heading 'i tformation required by

shown in th,e following table.

ST0PT, the traBe storage pro$rofir i5

Swttch Registen B'its

PTG0 ',Start'

Tape File Number*

Block Length' (30)

SatnF'le l-ength (10)

Gain Settlng, *

Decltnation *

Number of Scansl0ayt

Start Time (f ) 't

432111110000X:rea X,c+ X,sz Xre

Xs [,* Xa )(r

0001111000001,010Xrze Xo+ Xse Xre

Xo X+ Xz Xr

Xtee, Xe* Xsa Xre

Xe X,, Xe Xr

0000000100000010

76010001000t0001000100010001000,100

5

L

Qr

0

0

0

0

0

0

0

0

0

0

0

0

0

0

''.|-* Ffle mlmbenf gilin sett,ing and declination are required in eight-bit natural

blnary EOde with Lvlo's compl-emen't Sign represent'atjo'n as shq'wn'

t \talue"s shoul are for one scan per day, starting at 02h and fini'shing at 05h'

Page 310: 2-Whole-digital Data Processing in Radio Astronomy

302.

Stop T'ime (1)t

PTCC End of Headi ng

A typical set of headjng data' as punched on tape, is shown in Figure AZ'2'

0100060o00o1o1

0

0

1

0

0

0

0

0

1

0

i0

0

0

oQOOO&S6$eoccooooceg G OoO Q o 0 (! e O at a o O O

oaGaaatase0!""re olt""ooen.{of 'o9'c3t'lltt'lrc'lo"!t'c'l''ocoeooolFc@oc(igGoo,o o ee eoo o o a -o QO q',--c o 6

{."nu .'-'..vlr L'-' vv !,i'r't(r!jr !3uii 6 Q (,

e6ooooooeoc'rQOeO@COOOOOOe'e

Fiqure A?.2: A

data and

A?.23 The Event l'larker

For siderea'l hour rnarks on the ana'logue record, connect the sideral hour

output at the clock-pulse source to the input fl. A contact closure, capable

of carrying 500rnA, will then be provided for -50ms at the beginn'ing of each

sidereal hour between termjnals G and F (F is ground). These terminals can be

connected to a battery and resjstance in series lrlith the event-marker solenoid

on the analogue recorder.

A2.24 Ending the TaPe

The tape ntust be terminated with a PTCC'stop' instructiOn and several feet

of blank tape. The PTCC stop'instruct'ion is 01P10000 follor'red by a blank charac-

ter. Before the tape catr be processed it must be rewound, so that the heading

is at the outside.

typ'ica1 paper tape shouring the heading

the beginning of the acquisition'

A2.3 Processing the Recorded Data

A2.31 Storing Data in the Contputer

Before data from paper tape can be stored

subroutines must be stored in the User l\rea ofin the comPuter, the following

one of the sYstem disk cariridges;

STOPT, PARTY, HEAD, TREAD, PAK, DUI4PX ANd TIMEX.

Source listings of these subroutjnes are given in Appendix 7'

Page 311: 2-Whole-digital Data Processing in Radio Astronomy

303.

Two data files are requ'ired by the storage programs; NA[4E1 (RSTAR) con-

sisting of 540 records each of 60 words, and NAf''lEz (INDX) consisting of 90

records, each of 10 wor<ls. These catt be defined by the *STOIIEDATA control

record of the Disk Utifity Program.

Up to 2000 words of common storage area are required by the various sub-

routjnes, and a six word array'is usecl'in the calling sequcnce for STQPT'

A typical source iisting of a program

Figure A2.3, The tape has two scans/day;

and subsequent pages of the dat.a fi 1e, tlte

and subsequent Pages.

to store a Paper taPe is shown in

the first will be stored at Page 22

second vrill be stored at Page 60

// FUII I,J.rII LA CD DSK PR

D I MiNS I irl'l I P.\GE ( 6 )CUi,tilUi\ I Dtri'iY ( 2000 )

DEFif'rE F ILE l0(540r60rUri'i8) r 20l90rl0rUrNA)I PA;tlLl =22I PA.,E ( 21 =60CALL STUPT ( I I'AGE )

CALL iXI T

[-ND

// XEQ OI

*f-tLE5( 10'qSTirRl r l20,lNDX)

Figure A2.3: Progranl to store a paper tape'

A2.32 Analysjng the Stored Data

Before a conrp]ete analysis of the stored data can be carried out, the

following subroutines must be stored in the User Area of one of the system

di sk cartridges;

PAK, UNPAK, DSCAN, Cl-lART, STOCD, DUI4PX, TIMEX, REJEK, Cl-iAUV, AVRG'

FILTR and ERASE.

If any digital filtering is to be carried out by FILTR, then the appro-

pr.iate vrei ghti ng functi on shcr-rl d be si.cl'ed j n the nth record of a di sh dela

fiIe consist'ing of 202-word records. The maximum length rv'iII be 10L weights'

as each floating point vreight occupies ttvo vtords of storage' This file ntust

be included as file 30 in the DEFINE FILE statement at the beginning of the

program and in the *FILES record after the //xEQ statement'

Page 312: 2-Whole-digital Data Processing in Radio Astronomy

304.

Ass,ufie that m scans, eaeh k pages long have been stored in the data file,starting from page j.

The first two sc,ans'will be tabulated on the, line printen by the s.t-atement

\ 0ALL DSCAN(o, 5, 2k),.

If a graphical plot of'the first scan is required, then this will be

prod,uced by

CALL CHART(J! k, e5o),

assuming that the data fully o,ccupies the range t250.

The dqfs bri11 be che,cked fon ocsurrernces of spurious noise spikes by thestatement

CAI-L REIEK(j, k, m, 20),

and these, p;rocessed scans will be avenaged, with the average raritten in k pages

starting from page i by

CALL AVRE(j, k, fi, i ).

Alternatively this rejection and averagirlg c.oh be performed b5r the state-ment

CALL cHAUV(,j, k, ffi, i)

provided that m is greater than 10.

The averaged scan yili then be fi]tened with the specified weighting functionhy

CALL FILTR(i , k, l, n, '1oo)

where the filtened scan vrill be s-tore.d ln k,pages starting from page 1.

Thfs processed scan can then be p:lotted ,using

CALL CI'|ART(I, k, 250) -

If the p'ocessed data is to be stored on cands for future referencc, then

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305.

the statement

CALL DSCA|I(1, I, k)

vrjll produce thjs fornr of output, provided that 3i x k blank cards are

included with the program, after the *'FILES record.

This section has presented only typical examples of call statements to the

progranls of the softrr'are system, but these should provide the user with suffi-cient information to write analysis programs.

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Appendix 3

The Design of a ?9!ttt1z pnase neversl

Germanium Swi tching Diodes

It has been suggested by Aitchison OSAZ) that silicon computer diodes,

with suitable circuitry, can be used to perform r.f. switching at frequencies

of up to 400Mtlz rvith sufficjent efficiency for use in rad'io telescope antenna

srvitches. Measurements on gernlaniunr swjtch'ing diodes have shown that they can

also perform this high frequency srvitching, if the associated circuitry isoptim'ised.

The equivalent snrall s'ignal circuit of a group of inexpensjve germaniunt

switching diodes was rneasured urrder both fonlard and reverse biased condit'ions,

at a frequency of 2001'1H2. These diodes produced very consistent results, the

reverse-biased equivalent circujt being characterized by a small capacitance

(+ t pf) shunted by a resjstance of about 10K0. The forlard-biased equivalentcircuit consrsts of an inductance of about 50 nH in series with a resistance ofabout 160. The overall equivalent cjrcujt is shown in Figure A3.L'

Fjgure A3-_1: The equ'ivalent circujt of a germanjum

switching diode.

where R5 is the 'on' resistance of the diode,

RD and L5 are the lead resistance and inductance,

Cp is the 'off' capacitance,atrd R; is a leakage resistancc, apparent only in the 'off' state.

Smith (1961) has considered both series and stub connected diode switches

and has sholn that ajthough the minimum loss'incurred is the sante for both

cases, practical details usually favour the stub connection.

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307.

Figure A3.2 shows a stub connected diode srv'itch on a 750 transmission

line. At 2001'1Hz-o nonnalized to the characteristic admittance of the ljne, the

'on'admittance of a typical djode is 0.25-j1.0, and the 'off'admittance is0.008-j0.06. It can be seen that the'insertion loss of such a switclr (the ratioof maximum potver transmitted jn 'on' state to actual povrer transmitted*') willbe negligible, but the isolat'ion in the forward-biased case (the ratio of maxi-

mum pouler transnrjtted in '0n' state to actual power transrnitt'ed in 'off ' state*)

wjll be significantly low, jn fact it'is on'ly ZdB. This'is inadequate for radio

astronomy purposes.

F j gure A3 .2: A stub connected d j ode sl'ti tch

The properties of a diocle svritch can be improved by using an impedance

transformation to increase the conductance in the forvlard-biased state

(Aitchison, 1962; Landecker and l,lieleb'inski, 1970). This transformation is

most readily achieved using ),/4 transfornrel^s, so that the diode is effectively

operated on an'inverted'mode; an'off'diode presents a short circu'it' and

an 'on' diode presents an open circu'it.

Snrith (tgOt) has shown that the least loss occurs when the I/4 transformer

has an impedance

0 1'",t=lfrJ

but this does not give the largest switching ratic, and it is preferable to use

a lovrer value of 21 which lvill give better isolatjon, and not seriously affect

the insertion loss. Aitchison (1962) has found that impedance transformat'ions

of 221 are adequate for silicon diodes, and that both the isolation and insertion

* Here the'on'and'off'states refer to the state of the srvitch, and not the

state of the diode.

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308.

suscep tonoe

Igg-13"_1: Admittarree chart illustr^ating the design sf thediode switch,

0N dl'ode, Z^ = 150n;(d) 0.23r from b

tol^=75fi;(f)dwi th".a A.2261t, shortedon e is negligible).

(a) orr diode, zn = 15oo; (b)(c) 0.23r from a"on 1500 line:on 150n 'line; (e) c referred'referred to Z^ = 75fr ; (g) fstub (the effEct of this stub

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309.

loss are improved.

By rep'lacing the inner conductor of a low-loss 50o cable with a very finewire, a cable of Zo = 1530 was obtained. Referring to the admjttance chart of

Figure 43.3, (a) and (b) shol the reverse and forlard biased diodes with res-

pect to this 153fi cable. By nnk'ing the transformer slightly less than tr/4 long'

the reverse-biased djode at (a) trar,sforms to a near short circuit at (c)' stillwith respect to a 15351 cable. With this length of cable, the forward-biased

d'iode at (b) transforms to a poirrt (d) . Seen on a 75n line, the points (c) and

(d) become (e) and (f) respectively. By the addition of an jnductive stub at

the junction, (f) can be moved to the real axis at (q). This srnall inductance

has a neglig'ib'le effect on the posit'ion of (e). Thus the forward-biased diode

has been tra.nsformed to a resistance of 25 x 75CI, producing an insertion loss

of less than 0.25d8, and the reverse biased diode has been transfornred to a

res'istance of 0.05 x 75Q, producitig an isolation of 22dB-

A phase reversing sr.Jitch has been designed using tlo of these diode switches

in a hybrid ring circuit (Smittr,1961). This swjtch is shown in Figure A3-4.

The measured isolatjon of this switch is better than 20d8, and the inser"tion loss

is less than 1dB.

SwitchingSigno t

E

Receiver

Fi gure .A3 .4: The 2001''1Hz phase reversi ng svri tch.

The centre conductors of the coax'ial cab'les are at d.c. earth potential

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3!0.

,because of the inductive tun,ing stubs. This f,act has bee,n taken adVantage ofin supplytng the switching signal ts the diodes. The dlodes are connected inopposite direetions and are fed fnorn a t4 volt square wave via a feed-iliroughcapacjtor at the end of their respective tnansfornlerr sectisns, which prrovides

the signal earth. The diodes are located inside the transformer sectisns.

EETIBEISES.

AITC11156N, R.E, (1962): "The Use of rtligh-Speed Sri,licon Computer Diodes forR,,F. SwJtehl'ng". Trans. I.E. Au:st., E!!4 pp. 7-10.

LANDECKER' T.L., a'nd }.lIELIEBINSKI, R. (1970); lrLow Loss Varactorr Diode Switches

fsl" Radi o Astno.rromy'" . Froc, I -R. E.,E . Au,st. o !l pp . 73-76,

Sl,lITH, F.G. ('1961): 'iR.,F. S-witching 0ircuit:s,and flybnid RinE Circuits Use-d inRadio Astronomylr. Froe. [.E.E. , ].08 pp, 201-204.

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311 .

Appendix 4

The Uackfire Antenna

The antenna requirement for the 200Mt'lz interferoneter was for a basic

antenna, inexpensive and relatively sirnple to constructn readily steered about

one axis, and w'ith a reasonab'ly high gain. Several of these antennas could be

combined in tr.ro amays to form the interferometer. Previously in the 42l4{z

telescope a linear array of non-uniformiy spaced Yagi antennas were used (Lim'

1968). Although this array had a narow beamr.ridth in the plane of the array,

the width in declination could have been improved only by extending the array

to two dimensions. This solution causes beam steering to become very complex.

It was proposed that by using a higher gain antenna as the basic unit inthe 200M1-lz array, the narrower primary beamr,ridth would eljnrinate the irmediate

necessity to extend the array in tvlo d'imensions. The antenna developed has a

beamwidth of less than half that of a five element Yagi, yet requires only a

single feed, and is hence a superior element for a radio telescope.

The antenna, called the "short-backfire antenna" by jts author H.l.|.

Ehrenspeck (1965a), consists of a single half-wave dipole placed between two

reflectors (M and S, Figure A4.1). M js a circular plane reflector of diameter

2.0I; R is a rim of width 0.25I surrounding the edge of M, and S is a circularplane reflector of 0.64I diameter. The distance M to S is 0.5),, and the feed

F is midway between the two reflectors. The radiation patterns in the E- and H-

planes of an X band (gCHz) nrode'l of this antenna are shown in Figure A4.2. These

show half power beamwidths of 25o in the H-p1ane and 30o in the E-plane. The

peak side-lohe level is l1dB belo,;r the maxinrurn, and the back-lobe is more than

20dB down. The calculated gain is 15d8, slight'ly better than a 2.0tr parabolic

antenna.

The backfire antenna origirrated as an endfire array term'inated in a plane

reflector (Ehrenspeck, 1960). Endfire antennas are usually s'low wave structures(e.9., Yagi) in which a surface r{ave is excited at one end and is propagated

a'long the structure with a ve'loc'ity'less than that of 1ight. The surface vrave

is radiated from a virtual aperture at the termination of the structure. The

ga'in of such an antenna is approxirnately proport'iona'l to its length, and ifthe surface \,/ave structure is optirnised, the gain is given by (Zucker, 1.965)

^ tl''"ta =

^-

44.1

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3t2,

20

Figure /{4..1r The short-backfire antenna.

o

dB

10

30*goo

o

rltr

10

go l-g0' 45" Oo 45' 3C

E- and lt- plane patte't'ns for ah X..bandmodel of the short-backfire anterina.

2A

7E.PL.A.NE

J\/

\/\

I !r

I{-PIAI{E

lis,ure-44. ?:

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313.

If a plane reflector is p'laced at the ternrination of an endfire antenna

the surface rvaves, essentially plane in nature, are reflected back along the

structure torvards the feed po'int, and are radiated fronr a virtual aperture

at the opposite end of the antenna to the reflector. This antenna could a'lso

be described as tvlo endfire an'uennas, the original and its image, radiatingin oppos'ite directions (see Figure A4.3)

2+

Figure A4.3: SimpIified ntodel of a backfire antenna

Zucker (1965) has nade the following tr,ro predictions of this antenna:

1. It wi]l behave as a surface rirave antenna of iength 21,, and hence

from equat'ion A4.1, the gairr will be greater tltan that of the or"iginal

endfire antenna by 3dB.

2. The gain will be an additiona'l 3dB greater because the endfire-plus-image radiates into virtual space, i.e., a total increase'in gain of6dB over the original endfire antenna is expected.

Experiments with a large reflector tvl (Figure A4.3) have shown a gain ofonly 4.5d8 over the endfire antenna. This discrepancy can be attrjbuted to the

fact that the reflector S of the original endfire structure obstructs the surface

wave from the image feed F'. Sjnrilarly the image reflector S'obstructs the

surface wave radiating from F. This obstrucEion does not occur with the originalendfire antenna. The two reflectors M ancl S conrbine to form a laser cavity(Zucker,1965; Ehrenspeck,1965b)o and jt has been shown experimentally that

optimum results are obtained when .an extreme'ly high VSIIR exists over the entirelength of the structure, i.e., g should be an integral number of ha'lf-wave'lengths.

It has been found (Ehrenspeck, 1965b) that the gain can be optinised by

adjust'ing the dinrensions of the nrain reflector l',|, and still further increased by

the addition of a rim, as in Figure A4.1. For longer backfire antennas, further

S,IIII--*------{

7tlt!I

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314.

gain has been obtained by the

(figure A4.4). In general, a

optimised reflector will have

1e6e )

addition of a second reflector l4z and rjnt Rz

backfire antenna of length I wjth a suitably

a gain given by (Zucker,1965; Ehrenspeck,

j.e., BdB greater

refl ector wi I I be

same gain.

than an equal

approxirnately

44.2

diarneter of the opt'imised

parabolic antenna of the

$-'

1i-*t4

"h,

q

tenn o

^ 60f,u=-^-

length Yagi, and the

the same as that of a

LI

Figure A4.4: The long-backfire antenna.

For a surface vrave antenna, the wave fronts are essentiaily plane wjthina crjtical anglen and spherical outside thjs ang1e. The reflector shapes shown

in Figures A4.1 and 44.4 have been described as an approximation to a central

plane surface and an outer parabolic surface (Zucker, 1965), which would cause

the reflected wave fronts to be planar. Although this descr^ipt'ion agrees tlel'l

with the experimentally derjved reflectors for long-backfire antennas (Figure

A4.4, t,>21), it does not expla'in the shape of the short-backfire reflector(Figure A4.l) nor does it explain why the optimum t/idth of the rims for both long

and short forms should be 0.25x.

The design of the 200l.iHz antenna is based on a modified version of that shotvn

in Figure A4.1,. In order to make the antenna more simple to construct at longer

wave'lengths, the main reflector l'1 is octagonal in shape. This design was tested

on an X-band model, and optimum results were obiained with the octagon of

inscribed diameter 21,. The half oower beanrwidth of this model was about 260 in

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315.

both E- and'H-planes, and the peak side lobe level r^ras 14dB below the main bearn.

The 200MHz antenna (Figure 44.5 and Plate 1, page 70) consists of a wooden

space frame covered with l" vrire netting. At 200MHz the'losses resulting from

the use of L" stee'l mesh conrpared with a continuous perfectly conducting surfaceare neglig'ib1e (l"loull in, i949).

1Oft

Fi qure A4 .5: The 2001'1Hz Backf i re antenna .

Because the antennas viere to be used on the roof of the School of Engineering,they were constructed in eas'i]y handled sections and bolted together on the site.The ma'in reflector consists of four quadrants, bolted together on a metal sub-

frame. The rim js niade up of eight vljre-netting-covered panels bolted to the

reflector. The 3 foot diameter subreflector is mounted on a half-r,rave length of1!" square aluminiunr which also supports the feedd[po1e, and enc'loses the balun(Bryant, 19i1). The whole structure is mounted on two tripods, and the antenna

can be steerecl in the E-p1ane,600 ejther sjdc of the zenith.

The measured E-p'lane radiation pattern of the 200llHz antenna 'is frown inF'igure A4.6. The half-power beanrlidth is 260, and tne peak side-lobe'level is12dB be'low the main beam. The nrain beam is quite f'lat, with a sharp fall-off on

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315.

both sides.

30" ed goo l,z;ff

for the 200MHz antennaf-i$e 44.9-: E-Ptlane Patte-rn

tsETTBE!CF-

BRYANT, P. (1971): M.E. Thesis, Uiniversity of Auckland. (to be published,)

EIIRENSPECK, H.hl. (1,9,60); "'The Baekfire Antennd' a llew Type of Directisnal Lrine

Sou;l"ce", Proc. I.R.E., 48 pp. 109-110.

EINRENSPEOK, H.lnJ. (fggSa): "The Short-Baokfire An,tenna*n Proc. I.E.E.E., 51pp.1138-X140.

EHRENSPEC,K, H.!il. (1965b): "The Backfire Antennal l{ew Results", Proc. I.E.,E,E.n

Fg, pp. 83,9_641 .

EI{RENSPECK,, H.t'l. (1969)t rtBackfire A,ntenrenrrn Nachrichtentechnische-Ze'itchrift'g pp. 78;6-29? ,

LIM, J.C., (1968): "Non Unif.ormly Spaced An'ay-s of Dir"ectional Elements!'" Ph..D,

Thesis, University of Auckland.

M0ULLIN, E.B. (1949): "Radi'o Ae'riials!'n (0.u-.P., Oxford).

ZUC:KER, F.J. (1965): "Ttle B,ackf ire Antenna; A Qualitative Approaeh to ItsDesignt', Prnoc. I.E.E.E., 53 pp, 746-747 .

0

d,ts

t0

O"

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317.

i{BPendix 5

Tthe Analysis pf So$e Low-Pass Filters

45.1 The trdeal Lotf-P'ass Fjlter

The ideal lss-porss filter is defined as foll ws (graig, L964):

The mOgn'itU,cle of the transfer function iS co'nstant fsr frequen:ctes

-f;f1+fn and zero o,utside this r:ange.

The phase of the transfer funetion varies linearly with f,nequency' eorf€s:-

ponding to a constant time delay tu.

1.

2"

i.e., H(r) = [utt+ro)-u(r-ro]] -iZnrto (A5.1)

low-pass filter.

has been defined in

where Ur(f) is a unit steB functir:on at f = 0,

The magnitude and phase of FJ(f) are plotted'in,Figure 45.1.

Figufe A5-1: Tl,le transfer f-unction of t'he idea'l

A5.1I The Noise Bandvrldth of lhe Ideat Filter

The equivalent noise bandr^ridth sf a low-pass filterEquation 2".3, as

BN= ttil J*e

trt 'ur

= lrr(f) lz}

Whrel'e G(f )

(A5.2)

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318.

i.e. , for the t,deal l,ou-pa,ss filter

lB11 = ;t

A5. L2 0o.ndi t-i onsj0r. Onti[!nr s;i qnaj *t-o-}ioi se improv$ne'Lrt

After Grifffths (19'56), the optimum filter is defined as thatmaximum impnovement in signal-f6-psjs:s ratis for an inpu,t sinusoidfs PIus White noise.

(ns.l1

giving the

at freque'ncy

(As. s)

If the signa"l sinusoid hag en tr.m.s. value Si,, t,he.n the signal power out,soz, is

Soa = 5i' , f, 1f,o iI

trf the nEise has a qpectral pot'ler Nlr thgrr the nsise povJer output will be

llu = l{;.811

= llifo '.

and the output signal-to,.nois€ natio lrti1ll be

(SlN) = Si' +' ' tt'o 'Nl4 ' ts 1 fo

For any Si and Ni, this ratio will be a maximum when fo is a minimum, i.e.,

fo=fs

45.13 The hpulse, RegpqnF€ of j$e. [de?l Fi'l]er

Thc impulse response h(t) is the Fourier transform of the transfen funetionH(f )

i"e., (A5.6)

For compa.rissn r:rith he imp,uls:e rosponses of othe-r filter.s it is (a) thepeak va1:ue and (b) ttre ef-feetirre durration of the imp,ulse response l+hiich ar€ ofinterest. The duration is defined as t-hat time during whfeh the magnitud0 ofthe disturbance has values greater than 0.Otr,.

h(t) = 21u sjn2nfo(t-toLZntn(t-t6)

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319.

(a) From equation 45,6, the iriagnitude is 2f6 (=Zfs for tie optimum filter).

(t)) The disturbance will be les$ than 10.01 when

"TffhEI-- *o'or'

i.G., t-tg = * f

The duration of t'he distunbance fs then += 63.7 seconds when fo>0.005T

and zero when fo<0.005.

A5"t,4 T,he Step Res,p,onse.,.o{ !he.,Ide.al F'iller

The step respon,se S(tI can be obtained by,integratl'ng the irrpulse respotnse

i.e,r, tt

s(t1 = ,r, I

!'n2dg(t-t?l- ut (A5.r)

L

By s:ubstituti,ng x fpr 2rrfo{t-to) this can be redu,ced to

- f2nfs(t-ts)s(r) =#l F-

J-e

The integral

-lzI I srnx dx?f I x

has been plotted in Figure A5.2. The G>99fl{,riise time sf this'ne,sponse ls Eivenby

Znfot" = 1.23n

" _ 0.61tur - -To

_ 0.615= =ff f,orr. tr6s o ,ti mum f i l ter

Page 328: 2-Whole-digital Data Processing in Radio Astronomy

Thirs response has 8.9?5 ovens.h'oot and undershoot,

Flgure A5,2: The step response of the id.eal low-pass fllter

A5,2 lbe_Icleq-l Integ, i

time

i ,,e. 1

The ideal integrating low-pass filter, or 'running mean'

outp:ut which is the average of the input waveform over an

filter, has

inter'va] f

1)

)

320.

(A5.8)

and thus

h (r) = #[, f r4-ro) -utt-['tr{

H(f)=W..-.iZnfto

The nragnitude and phase of lJ(t) are plotted ln Figu,re A5,3,

A5.eI The Noise.$andwidth.of I'hre I{eaJ lnEgrator

Ey definiti,on

plna,(l'It rr .(nfT) 2

EN=

/@

I sinzx a*Jfo

lrlow from Pierce (fOeSl

=T,

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321.

Figuge $5-3: The transfer furrction of, the ideal integrator.

whi ch l'eads to

1Bn=h

45.22 Oqnditlo,ns for 0ptifium Signal -tar:llqi,se improvement

As for the ideai Iow,-pass filter, consider the output signal-to-noiseratio for an input s'inu,soid plus white noise, Si, fs and Nq are as previouslydefi ned.

Signal power o-ut, Sot = Si' lti*ftltL rifrT I

Noise power out, No = N1tsp

,= Ni,

2-l

(As. s1

Page 330: 2-Whole-digital Data Processing in Radio Astronomy

i.E. r

ltou + has

to 0.725. i,€.,

t'''o'l!x2rsTL tfsT

J

a ltt."trt] 1

"Lnr5TJ

x = 1..17 radians

fi I ter

,T = 1.17

r='27rs

The output signal-to-noise ratio is then

Now for eonp.arison with the ideal low-pass

s-i 2 = N1f,

3zr^Ni

fi'ltnr, equati on A5 .5 speci fi es

3,?2,

and this maximum is equal

(As.l,o1

(slrl) =o

a maxfmum when

for the CIptimum

Trf

0l'!

0ompared wlth the optinrum ideal 'lor,,Jpass filter, the output signal-to-noise

ratio of this optlrnum filte,r is

(sln)n = fr* 0.7,25

= 0.461 or -3,.36d8.

A5.e3 The Impulse Be=sF.snse of the Ideai Intggfator

From equation 45.,8i

rl- T T .'1h(t1 = ilu(t+i-to)-u(t-t-to1

This is a r€ctangular pulse of height i and duration T.

(a) The peak magnitude of tlre impulse r:espense ts then rL, or fsn the o'ptimum

filter tt4.r, = 2.7fs.

Page 331: 2-Whole-digital Data Processing in Radio Astronomy

(b) The .0X lievel durration s th,e impul,se response

and zero if 111<,01.

45"24 ThF_ $tep Respgnse Ef th,e ldqq! Intes,ra,tot"

From equation, 45.8 the ste,p re.s,ponse is

323.

ls T (= o'37/1r1 it 1/1>,.0t

fi_s(t) = + | [ut*l-tu)-u(r++r)]at.'),-

i40

('=

This inteEl'al irs shown in;Figune 45.4. The 0+99% nise ttrne i:s .99T*T

.gllf s for the 'optimum fi'lter) and there i,s rlo overshost.

is

Flgqfg $9.1; The step respor,rsle of the ideal integrator.

A5.3 T-he- Simple_(First--0rder) RC Filter

The tnansfer function of a simple (first-oyder) RC filter (see Figure

A5.5) is

tH(f) = I152."Tm-

fo=fu, then

H(f) = t{h

Let

IH(f)| =+(f/ro )

{ (f) = -ten-r1$t,

(A5.11)

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324.

The magnitude and phase of l-l(f) are shovln in Figure A5.6

Vout

Figqre A5.5: The sinrple RC filter

Fjgure A5.6: The trarrsfer function of the sinrple RC filter

45.31 The Noise Bandwjdth of the S'imple RC_ Filter

By defini ti on

f

'-'

I

j

1

1+alro r drBN=

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325.

BN=

= {_o_ (As. 12 )

2

A5.32 Condi t j ons for 0ptinrurn Signal -tq.llgUS-LUpfryement

Assurning the sanre input as for the prpvious filters, tlte signal poi+er out

is

s.i2So' = 1{ (f",- ,|, ''l ro'

and the noi se povler out j s

nf.,l,ls = 11i .t

Thus the output signai-to-no'ise ratjo is

si' z

isl - (r-\? x^,.*€l.NJo

- t-[.fJ 'rr'"o

and 'if Si 2 = lli fs thi s becomes

fLlfs) z [foJ

t.-rrJo=n {H

This functjon js a maxir;unr when fs = fo j.e., the optitnuln filter is

defined by

l1= fo

| 1r"t ox

)o

= tan0, th'is integral becomes

fi,7t-f^1.d0ulJ

o

By maki ng tlre substi tuti on x

Page 334: 2-Whole-digital Data Processing in Radio Astronomy

c - 1 -a'o - Z?R-f, - 's

O'ompared with the opt-imum ideal low-pass filter,ratio sf this filter is

fgl = lx o.EUIJ o Tt

= 0.3tr8 or -4.97d.8.

A5.33 The impqlse RFSpolq.e of the silJile Rc ri.].te,r'

The inverse Fourier transform of t{(f) can be obtained via the Laplace

transfonn to yield

h(t; = zrnfo e-znfot.U(t)

'This func'tion is shown in Figu,re A5 7

2rnto

FigUtr,t,at The irrpulse response of the simp'le R0 filter

The disturbanc-e h'ds I maximum value of 2'nfq and a 0.01 'level duration T

such that

znfne-u*foT = 0,.01 (If znf'o > 0.01)

r l- .'lt = *; ft.ozs + o.l5sln(toU Fo'1.5e x 10-3) (A5'14)

fs < 1,59 x 10-3 then 'the disturbance is' rregiligible.

durnatisn of the im,pulse r€sponSde defined by eq,uat'ion A5.14n is plotted

326.

(45.13,)

the output si gnail -to-h'oi;se

i,€.,

Tf

The

Page 335: 2-Whole-digital Data Processing in Radio Astronomy

327,

in Figure A5.8 as a funct'ion of, eut-o,ff frequency fe.

FJgure A5.qt The ,01 level impulse response duration

of the simple RC filter

A5.,34 lhe Ste.F REfior,rse=qf thg- Sillple RC Filter

The step response is obtained fnom tfre integral of the inpqlse rresponse as

S(t1 = 1-t-2nfot

The 0+99.S rise tirne t, of thjs resjponse is given,by

zlrfotr = ln 100

. _ 0.731u, _ _Fi-

The ste,p resp-onse has no overshoot.

AF.4 .Thu E'*_*ru.l Second_Olidqr F,ilter

The general second-order low-pass filter has a transfet^ funetion

I,l'e)cP30Ia,

c.g'orao

2AItl4a.qE

5tlJ

trOiit

Page 336: 2-Whole-digital Data Processing in Radio Astronomy

H(f) =

328.

(A5. 15 )

Whe,re E is the damping factor. Foth fo and E are determined by eireuit values.

P-anticular exampl6s of ttre second order filter, and their circuit representations'

are discussed in section A4,5.

The magnitude and ,phase of H(f) can expressed asbe

I

and

These

tH(f)t =m

"fu1-[+,]'O(fl = -tari*I

are shown in Figure 45.9

lntr il

tr"ansfer functionorder filter

Fi'gure A5 ' 9: The of the general se,eond

Page 337: 2-Whole-digital Data Processing in Radio Astronomy

The 3dB cut-off f recluency f. i s g'iven by

329.

(ns.to)

(A5.17 )

i s an even '[ttncti on cf x '

f

--aDr'

fc = fo j-ze'*6{+r.+I )

A5 .41

Let

The tloise tlandwitlth of the Second Order Filter

By definition

Let then

r*Bnt=l''l

)o

fF-= Xro

BN=foxa+x2 (+r,'-Z)+t

dxf-II

o

f* dxt = .| ;\+bx41o

Thi s integral can be eval uated as fo'll ot'ts:

f-1l#.,rE)^'o

in equation A5.17,

rO

r_l#*r_,l ',

-"-rt

dxx2

t^lri ti ng1J=-x

l,lott

can

vlrite x for Y, atid

be retrri tten as

noLi rtg l,ii.rt thc i tiicgi'and

rtoldx.lr = | x2+b+I^

lvz

o

thi s

(As. 18 )

Page 338: 2-Whole-digital Data Processing in Radio Astronomy

31310,

Add, together A5.17 and A5,18 to obtain

as,l

I tr*i,ta*2I=lI x2+u+\JX'o

Nowlet u=x_L,th.n

4o=11AJdx, u2=x2-2tL' x4- xz

and the limits become

Nb$r write g_ = tr6ng, tften

t

.lfl=-2dffi

In equatiqn A5.t6n b = 4E''2n BN = fol

i.€,r u*=Tl fis,tg)

F6.4:2 0qnditi -o,ns for .O.p,-timum SigIalJo.'Nqise Inprgve{nent

Assurning the same conditions as in the previous analyses, the signal-to-

ngi,s€ ratio at the output of, a second order filter is

,, = [*---go--" F' l uz+1b+Z)t

4

,@

. Idull= rE-l4r

J u+z

and {f Sit =. Nifs t

[fi].=ffiiffi.#

Page 339: 2-Whole-digital Data Processing in Radio Astronomy

fs

33-1.

(ns.zo1

Ler $i = *, .n*n

[fi-],=+ rqF&FBy equ,atin,g the derivatlve of this function to Z€foi the condition for

maximum improvement in signal-to-noise ratio is found as

*' = lF -ze'*2ffi{)

For a g'iven e the optirnurn'value of fs is given by

(45. ?,l )

The signal-to-noise Ratio for this optimu,m c,orldition can be obtained from

equation A5.20.

A5,.+3 The l.mpulEe Responge q,t s-egqnd-0rdqr Fllters

(a) UnderdarnPed Filterrs (Ect}

For '6<1 the impulse response of a secondL-order filter is

I _ /3'fs _'o f'ze'z*2,Fffi'11

h(t)= ry+*{2rrfot*tn(znfetr'17) (A5,2'2)

ffi

This,response is showrr in Fi.gure A5.I0 for E = 0'59' T'he maximum value

of the response occurs when

1r-.,E1Znf ot = ffi; $-tan-' ffi, ) '

If the exponential term of equation A5.22 is considered as the envelope

of the sine'tenn, then the fluctuations wtll be les's than t0'01 after timQ tgiven by

Page 340: 2-Whole-digital Data Processing in Radio Astronomy

AnI,n. . .-dztfot = o.-olfrry

332.

(A5.23)

(A5.24)

i.e., r = # [i.ots + o.r5ern,#Fl

[h(t)]max = 2.3lfo

The duration of the impul:se Yesponse is plotted in Figure A5'12 as a

function of cut-off frequency fe, for 6 = 0.69 and E = A.825.

(,U1 Critrl:cally Damped Filter (g = 1)

For a crigcally damped second order filter, the impulse response is

rh(t) = tnro (enfotle4ofot

Thts has a maxirmur1 when &rfet = 1r dhd the Beal( value is

f;t

orderFlgure A5.10,

The 0.01 level duration of the ps:epons@ is given b'J

The impulse nesponse of the second

filterwi'thE =0.69

znfot *-Znfot = 26ffi

Page 341: 2-Whole-digital Data Processing in Radio Astronomy

fg.

(cl

333,.

This duratisn is shown in F'igur.,e A5.12 as a function of cut'off fnequency

Overdamped Filterrs (ftf 1

The lmpulse response o,f an orverdarnped Second order fi:lten is

h(t) ,' rh [-"t, -thJ

where- Tr,Tz = ftylfi )/(znfs)

T:his response is a maxt,muni when'

t=- 1 ,ln(e+Ei.)Znf s;tz -l

l (A5.25)

The max{num Value Of the impulse response of a sec,o:nd order filte'r isplotted in Figure A5.11 for values of 6 between 0.5 and 1.5.

For 6,= 1.5,, t'he .01. leve'l duration of the impulse response is plotted in

Figure A5.12 as a function of, cut-off frequency f6.

.5 .:6 ;1

Fi-qure AL11:

.8

The

,of

.g 1.0 1.1 +2 L3

maxlmum value of trhe imPulse

a second-order filterr

1A 1.5

response

Page 342: 2-Whole-digital Data Processing in Radio Astronomy

334.

Figure A5.12: The .01 level duration of the,lmpulse

response of some second-order fi lters

A5.44 [he, $t-ep, Responses of Second-0rder Filters(a) Underdamped Filters (e.1)

For underdamped second-order filters the step Fespo'nse is given by

\ft 825

IItIIIII,|

I

,E :,69

\\r\1i\

\,

,

L

I,l

ti!itiitlitr=l /,.

IItltltl

\\.\\'ry:1.5 -N

\

-e?nfoLS(t) = 1 - .g.'"'o" sin(2nfs'G:7't - 0)

fl-e

g = tan-l E-

80

uEcI.t,t)v,:

4:0t.eE.lrtcfrt.E

iaoE

where

Now the step response hag max'inla and minima at the aerq cfiosgings of the

impulse rcsponsen i.e., 'l'lhe,re

t = -4 (n = 0,1,2 .....)2f oh-e2'

Substitriting this vallue of t fsr n=0 into t,he step nespoil's,Br the maximum

overshoot is obtained as

Page 343: 2-Whole-digital Data Processing in Radio Astronomy

qlr-ffiovershorot = e

The 0+g9% rise tirre tp of the step response is plotted in Figune

(b) Critically Damped Filter (r " 1)

For a critically danrped sqcond-order filte'r th'e st-ep respsnse' is

-?nf^tS(t) =1-. u(l+zTrfot)

T,his has a 0+99% rise tine of

335.

(A5.26)

A5.13.

and

(c)

. 1.06rr = -T6-

1)

,overdamped second-ord,er f ilter is

1 -t/h -T ue't/TzlI * T;iil (T'e

'This respo:nse has no o-vershpotn a:nd the 0*99% ris'e tirne is piot'ted in

Figure A5.13, together with that for underclamp-ed filters.

A5.45 Sorne Examp]es--of Sepgnd:0rder Fi lters

The general.second-orden fflter can be realized by an active eircu'it,using a sinE'le operationLa'l anrpl'ifier, as s,h,own in Figure A5.14 (Coope'rr, 1970).

Anothe,r filFr of interest iE the case of tl'ro eascaded Re filte'rs of.identi cal clranae ue-r"i sti cs (Fi gr,rre A5 .15 ) . The transfer functi on of thi s fi lter

i-s

thene i:s ho overshoot.

Overdarnped Filters (E >

Th,e step resPonrse of an

S(t) =

ll(f) =

fo=

6 :is I -5.

1+3j

t'''''''-tm

luJhere

i,€,, r t:he darnping factor

'{,(A5 .27)

Page 344: 2-Whole-digital Data Processing in Radio Astronomy

336.

V.5 .6 .7 .8 .9 1.0 '1.1 t.L

ti me

1.3 1't, 'l'5

of second orderLi gure A5.13: The step response rl se

fi l'bers.

!jsLte_A5.-l-l-: An operational ampljfier second-order filter

lsl _e_?trf^ R

?, rz = 4FtoER

!r_J-:_q_ta.!s4_!!__F_il_tr11

The transfer function of l,l 'isolated RC filters (see Figure A5.16) isA5.s

Page 345: 2-Whole-digital Data Processing in Radio Astronomy

-T- .I_)_ _

l_fryfe_45_,lq_: A f i1ter fornted

RC netvrorks , i sol ated

by cascadi ng I'l i dent j ca I

from one another.

o--r r-- :ttl_l

_ll_

[ss-re--41-J!-: Two cascaded RC filters

337 .

(ns.zs1

H(f) =

The magnitude and phase of H(f)

-1to = 2tRT-

- r" 't-.t11

1,.,, [.i=.j]

tl-n

fr;

where

and

where

lH(f ) |

are respecti velY

1

=

-[^a(1+X')"

o(f) =

X=

l.-nlnl tnrt

I'lctwork

Isotot rng

Ne.twork

tan-lx

Page 346: 2-Whole-digital Data Processing in Radio Astronomy

I

A5.51 The NoiEe Bqndurid-th of the llth O!lde!' Fi'lt9.r.

339.

(Rs. zg)

o

f1=toJffi'o-o

le,tti,ng X = tan,0'r th:'is integral becomes

lt

B"=r lz otN=ro,lr*-:-r*r--r-t0

TIT

= f^ | ,or2N-Ze.du'Jo

By exp-ressing cos6 as Lr"j,e*"-jg, and by taking thc resultant binornial

.expans.ion for costo, then forr m even'

I[ .r,7-rml,cosmo = i*-r [_o k1hm cos(m-Zk]e

*l*'ffi m5'30)

As f,t is an ihteger in equation A5.29, th'e'n 2tl-2 is evenr srtd equabion

A5.30,cirr bB ussd to evaluate the integral' As (m-?k) is even when m is even'

the-n all terms in t,he sunmatisn of equati'on A5.30 tt'iXl contribute nothing to

thc ,i,nteg,p61 fnom 0 to r/2, and the only term requined is the final one, otttside

the surtrnati on.

,T

i.e., BN = fo l-r ^ - (zn;?ll- ao

J sz'I-z ^ I (n_r) !lu

o

Page 347: 2-Whole-digital Data Processing in Radio Astronomy

339.

= ro X V--t- tftf-h (A5'3r)

A5. 52 Condi ti ons for OptjrirlL ::-tS!e-]-tgl!-q5-e--!fplgiqlel!

Assuming the same corrcl'itions as irr tlre previous analyses, the signal -to-

noi se rati o at thc output of the lltil ordr:r fi I tr:r i s

f:l = #ht* i.lrorr;It{J o \r ., l

where

and x=h

If Si' = l'li f5, then

k = oL x (2N-2)! -zttr-L [(n-r)!]'

(fr].= ir,*4"

This 'is a maxintunt tvhen

i .e., for ntax'inturn s'igna1-to-noi se intprovcnrent

fo = ,fffi' ;,

The signal-to-nojse ratio for this optimunr filter can be calculated

1

X = ,ai'T:T

(A5.s2)

f sl = n:l:l[[joo, ("-#

rrr^tl

_ z'*-' . (ry-r )''-2. [(ru-r ) l] ' (A5.33)

l,lr'r.ri . (2ll-2)!

Page 348: 2-Whole-digital Data Processing in Radio Astronomy

I 340.

I A5.53 lIF-Itnpulse FesnEnse of the f{th Qrdeq" rilterThe imp,ulse nesponse, o,btained frorn the inverse rFourier transfonm of the

i transfer functionr is

h(t1 = (zufo)N . s . .-2rrrgt.u(t) (As.3+)

This i$ ,a maximwr when

. N-1r = ErE-

and this maximurn value is shsw.n Jn Table 45"1.

The ,01 level duration of the irnpulse response fs plotted in Flgure,A5.17

forN=5andN=10,

N 2 3 4 5 5 7 I I 10

2.3[ 1 ,70 1.41 1.23 1.10 I .01 0.94 0.88 0,.83

Table A5,1i The peak value of t;he impulse re,sponse of the Nth

order filter,

45.54 lhe. ltep ttesponsg of -thP.t'lth 0rder Fi I tgr

Tlre step respo.n:se ean be o,,btained by integrating the inpulse response

(equation A5.34)

ft *, *N-1s(t) = | tznro)Nnffi "-2nfot6. (A5.35)

)CI

As th,e impuls"€ respronse is zero only at infinity, the step respons€ willhave ns o,v,ershoo:t.

Fr.om Pierce (tgeg)

[*r.u*a* = edXt# r*m-r . d+I*n-Z..., + (-1,. ft -r]J-Fa2a3arrrJ

Page 349: 2-Whole-digital Data Processing in Radio Astronomy

341.

lA

Easo(,agD

c'q.

g?-?0r,J4Jcie

H

f6 ( l{z)

F--leu're A5J7: The impuls€ l^Bsponse drrnation of two

Nth orcler f,i'lters .

=-e

The 0*99% ri se tirne

vftere m = N-1 ,

._znr6t [#_,The solution to this

in Table A5.2

* mtztnl-l + mft-l1T'1,m-2.... t mffffil

the response of equation A5.35 is given by

"-2-rlfgt6, = 0.gg m!

-

-tlrfrrmL

Thus

fo*"-ttt

sf

I .mIEI

0

*tr-1,;=-E .... + m!,l 4rti I rO ,

equat,ion for m s

(2nfs)m+ o.ol1znfo

1 to m= 9 (N = 2 to 10) is given

Page 350: 2-Whole-digital Data Processing in Radio Astronomy

34e.

Tab]e A5f: The 0'*99/' itep response rise tfme of the

[{th order filter.

REFERE$.JOEs.

C0gPER* E,F.C. (1970)': oPost Detector Filtering in Radiometry", Proc'

I.R,E.E. Aust,, 91. PP. 41-48.

CRAIq, E.J, (lg 4): "Laptlace and Fsurien Transforms for Electnical Engineqrs'r.

(,Flo'lt, Rinehart and lJinston, Nevl vork)'

GRIFFITTIS' J.[,1.R. (1956): "0pttrrum RC Fi lters". llli re]ess Engr. 33 pp' 286'-270.

PIERCE, 8.0. (1,92,9): ,14 Short Tabile of l,ntegnalS". (Ginn,,New Yor'k).

N ? 3 4 5 6 7 I I 10

f'o tr 1 .06 1"34 1.60 1.84 2.08 2.32:: 2.54 2.77 2.98

Page 351: 2-Whole-digital Data Processing in Radio Astronomy

Alpgndjt _A_

The Calcul ati on of Local Sidereal Tintg-

In Chapter 3 it was shown that local

cul ated f rorn the rel at'ionshi P

sidereal time (t-.s.f .) could be cal-

L.S.T, = U.T. + R - west longitude (r .11

where U.T. is universal b,ime and R is the accumulated difference between solar

and sidercal tintes, tabulated jn the Star A'lm,rnac (tt.M.S.0., 1970) as a function

of universal tirne. A computer program SIDER has been developed, which given

starting values of local zone t'ime and R, tabulates local s'idereal time as a

function of local zone time. A typical page of output from SIDER is shovln in

Figure A6.1. The program is illustrated jn the flowchart of Figure A6.2 and a

source pro-cJram l isting is given in Appetidix 7.

All nranipulations of times wjthin the program are performed in 0.01 second

quantities. Before the output of any tinre:, a subroutine TYME rationalizes

these quant'ities into an array fT(B) , wltich represents IT(1)iT(2) hours'

IT(3)IT(4) nrinureso and IT(5)IT(6). IT(7)IT(S) secottcis, and a tl'renty-four ltour

overflow indicator ID. If the input 0.01 second quantity vuLG is greater than

orre day, then ID is set, to I and VULG reduced by twenty-four hours'

Tabulation for up to a month can be producecl by SIDER with two input data

cards. The fjrst of these contains the desired increment (in hours) of local

zone time at vrhich sidereal tinre is to be calculated. The secotrd card, atr example

of which js shown in Figure A6.3 contains the year, month, starting date, R, and

the number of days for vrhich tabulation is required' The value of R is taken

directly frotn tables for U.T. = 00[ on the given date. As]ocal zone tjme'is

12h ahead of unjversal time, the correct starting value of R, Rs, for 00h local

zone time on the given date 'is obtained front

343.

(A6.1 )

of arc or lLh 39rn

be calculated for

Ro=R-12h

where 6R/6t is 3nr 56.556 s/day (see Cirapter 3)'

The east long.itude of the te1escope 'is 1740 46' 11.64"

04.78s of tinre. From equation 3.3, locaj sjdereaj time can

loca'l zone time (1.T. ) as

6Rxu1

Page 352: 2-Whole-digital Data Processing in Radio Astronomy

344.

DATE

\,

T I M'u

li?

() tt

0i)OB

IOt')LL

I4l6IB2022000t

LI]CAL S I DEREAL

L.TtlR l'lhl sEc

00 u0 00. u0()? 00 00.0004 0'J 00.0006 00 00.000B 0u 00.0t)10 00 00.00L2 00 00'0014 00 00.u0l6 00 00.001 B 00 00.0020 00 00.0022 00 00.00

00 00 00.0002 0rl 00. tlO04 00 00'0006, 00 00.0008 00 00.(r0I 0 00 00.00L2 00 00. c0lr+ 00 00.00I 6 00 00.00I B 00 00.0020 00 00.0022 00 00.00

F0i. t)ECtsR t

L.S.TMN SEC

46 23.2046 42.9041 02.62.4.7 22.32t+7 42 . 044U 01.764 tt 2L.464b 4I.lB49 00.9049 20.6049 40,3?sio 00. o0

l9 70.

HR

r rri

050505Lr5

c)505/l r;

ob

0505

rJ,/1 C,

050505050,05c'5050505

07 Lg.L207 38. B301 58.55OB L8.260B 31.91oB 5 ?.6809 I 7.400? 37.1109 56.82I0 I6.53t 0 16.?5I0 ,5 ,96

11 L5,61lI 35.381I 55.I0L2 14.81L? '34.52L2 54.23I3 I3.95I3 Z).6bI 3 53.37L4 I 3.08l4 32.80l4 52.5L

R

t']N 5LL

l0 04 50 I 9.74u6 50 39.460B 50 59.1610 51 IB.BB12 5 1 38.6014 5 I 53.30l6 's'?. I8'Oz]8 52 31 ,722D 52 57.4422 53 I7.160 f.r 53 36 .8/+02 53 56,56

04Ub06l0L2I4l6IB202200o2

tt 00 0002 0004 0006 00oB 0010 00I? O014 0016 ()018 0020 0022 00

00 0c'02 0004 0006 rjo0B 00I0 u0L2 0014 00l a. (rD

lB 0020 0022 00

00,0000.0000.0000.0000.0000.0000.0000.0000.0000.0000. 000c.00

00.0000.0000,0c00. u000.0000. o000. c000.00r'rI. l1!00.0000.0000.00

545ttrt4

5'55555656rt6

575757

04 5ii0$ 5tlOrJ 5cjI0 59I? 5914 59L7 OU

19 002I Otl2) 0l0l 0r03 0t

16.3036.0055.7 2L5.4?35.L454.8 6I4.5634 "ZB54 .00l3 .68)3.4053. L2

L2.8432.5652.26l1 .9831.7051.40lI.l230.825^.94L0,2+29.9649.68

05 1505 1505 1505 16c)5 16a5 1605 17u5 17(r5 17C5 IB05 18t,5 IB

v5 1905 1905 1905 2005 2005 20u5 2L05 2L05 ?-lt,) 2205 2?05 ?Z

L2.223l .9351.6511.3631.0750.7810.503Cl.2Iq9,9?09.6329.3549.06

08.7728.4848.2007.9121.6241 .3-)07.0526.7 646,41Uo. I ti25.9Q45 .6L

L?

Figure A5.1: An exarnple of the printer output produced by SIDER.

Page 353: 2-Whole-digital Data Processing in Radio Astronomy

345.

-slotR

START

Reod D LT

Reod Se-cond

Dqto Cord

Co Icu lcrte

ond

Heod

SIDER florvchart;s i derea I ti rnr: .

LST -- LT+ R --1

+ LoN G __-l

CALL TYME ( LST )

Figure A6.2:

write DATE,

LT,LST ond R

program for tabulating local

Page 354: 2-Whole-digital Data Processing in Radio Astronomy

After each

fnom the firs,t

L.S.T, = R +

=R+

=R+=R*=R+

,ca'lcu:lation, L.T.

data card, and R is

346.

u.T. - west longltude

U.T. - (24h - east longitude)

U.T, + east longitude

[r-.f. - r2h) + erlst longitlrde)

(A6.2)

L.T. - (00h 20rn 55.22s)

is 'increme,nted by' 6(1,T.), the quantity nead

;incremented by

gB6t .6(1.T. )

l+lhen eithen R or L.T" cros's throurgh twerrty-fou,t'hours, th'ey are automati-

ca1ly reduced by twenty-four her,urs when TYME is called prior to printing.

ggEu

ru I o [t g 0 r rr ts B t E0 I lEt t 0 0 ! c ct fl [ [ 0 g lr N t'] | [.g t u n n t .; 0 t | [ i t g $ c 6l I ij:'r I t tr lt 0 D 0 0 ! $ 0 il I i .l 'r 0 0 ti 0

li3{sGlr4lrtii ;i;;iiiirj,iiitIII1itIIIrIIiIr11 rEirrrIr1|rII||IrirrIIitt1tiIIII|trIIII|1IIIII||tr:21t L Z t t tllz ? 2 2 ?2 s 1211 1? 2 2 2,2 I t2 2 2 2 2 22 2 2 2 | tr ? 2 2 2 z tr 1? I ? 2 1 t i I 2I t I L12 2 2 2 2 1L 2 2 2 2 2 7 1,2 2,1

i s s g $l I I El t i 3 t t i s i i t l Et l,r I aE s s c I rEl 5 3 3 t: ' I t g l "'t 0;3 $ 3 ?,1 3 i I 3 3 3 l i 3 i s s I I 3 3 i 3 i 3 3 3 3 s | 3 3

,; i { 4* ttAl { 4i i.qie ifl<, i t! t.+ 4H l t I 4 | (+ { r {,t i ; .t 4 r t i1 + { 4 | t ^, i 44 4 4t' t t: t' | 4l' 4 ( 4 | 4 { ${ r' ,l 6 t' 4 t 4 n

5t555[[Eti$5i$5!5ffi[558$rr{fi3rt55:s53]5,[!f5t$5t$[5i5[5$555$&"i.JS5t5'$5iI5'ESt'5[585[55

00t00[6rg06s5$G$s8s0$886600[0$$0{t0$r66[6!0$EE$[,8$[CE&S009t088$i616S0600t0s!$06fit

I I ! i t ? I I I t x 'l I 7 I t I i: t I I I E I i :l l l I I I t l t :l ? ? ? I I ? 1 1 | | 1' 1 1 | 't I 1 | 't 7 | I 1 ? ? I I I I I t t 1- t I I I ? ? ? t I 1

:s80800$E0g8E0stB0fBIBB0[0stHes00000a0$0ts6BE&r0EcBB8tEEs0't$$'ss3$8808'8ht08';8808088

F ! + $ S i I rj ; - I i I I i ,]' : : i I : I I t ; :, I I [ : ] ! i I t : , i I J :' ^ t i l i I I ; ' '" : : ; : : : i ' t r I ' r 1 fi ' 'r I I I i " : i I rt n

l'**1&tulil]t!|lEt't,lLl!|,l!.|i..i?t?t!ia'-.il!|:}g'iir'rl3it'';!${

Figlre 46. : An example of the second data card

requ,ired by SIDER,

H,M. S.0, (l,{er F'tajestY's

Land Surveyot"s forstationery office), ([970] :

the Year 1970r', (Lo,ndsn) .

!'The Star Almanac for

Page 355: 2-Whole-digital Data Processing in Radio Astronomy

347.

8p;Pgndi x_ 7

Da!.a P.rocerssillg System lompuler Proqrant LigtlngF

The soul'ce prog'rdfi listinEs o:f the oomputer progrdms developed to store,o

analyise and output the fnterferomei,er data are contained on the folll:owing

pages.

STCIPT

I'IEAD

TREAD

PAK

UNPAK

DI'MPX

TIIdE-X

:FARTY

ERASE

D$EA[{

srueD

EHAI{T

,c,l,lAu,v

REJEK

AI/RC

FTLTR

SIDER

TVME

Tape Storage Prog'ram (F0R)

Heading Decoding Routine (nS}{l;;

Data Decsding Routine (ASl\4)

FlagreData Comb;i.ning f{outine (ASM)

FIaffData Separating Routine (ASM)

Etsk FtIe Index Pninter (F0R)

Dekasec,ond Gonversi on Rout:ine (fOnJ

faFity ehecking Routine (mR)

lndeN Entry Erase,r (FOR)

Numerical 0utput (F0R)

Cardl Data Stonage Rorrtin€ (FOR)

,Grap.hieal Output (fOn1

Noi:ge Sptke Rejectr'o:n [fonl

Noi se S it ke Rejecti on (F0R)

Record Ave"nagi n'g (FO,R)

Di qi tal F,i I ter ('F0R)

Loca'l Sider^eal Time (F0R)

T,fme Redu'cti on (FOR)

page 34E

353

355

35j9

359

36u

360

061

361

362

363

364

s67

374

372

- 3it4

37'6

377

Page 356: 2-Whole-digital Data Processing in Radio Astronomy

348.

SUBROUT T NE STOPT ( I PAGE )

C **('t \tt(** *+ *,** * *+** tr $.r.i d( {t* *cf f *{t r{< dr * S* *** *** * * *r t** *;,t{.,{<** ****{t * {<*** ** ****f *c*c*c+c*c*c*c*c+c*c*c*Ct(c*

c*Cttc*

c*c*c*

STOPT IS PAPER TAPE STORAGE PROGRAI'I. IPAGE IS A SIX ELEMENT *ARRAY GIVING THE PAGE AT K;HICH THE CORRESPONDING SCAN IS IO *EJE HRITTEN ON DI SI( FILE IO.CONTROL IS BY PTCC AS DEFINED

STARTEND 0F HDIIGSTOPPAUSECOI'IT I NUE

01Pl rltl 0000 00000lPl 00I0 0000 0L'iiO01Pl 0000 0000 00000IPt 0001 0000 00000rP1 1000 0000 0000

*******

IF PAUSE IS ENCTIUNTERED /iI END oF A TAPE' PROGRAM ST0PS. HHEN *A SECOND TAPE IS PLACED IN TIIE READER AND THE START KEY *PRESSID, PROGii&i1 COi.JTIi.IUIS IF FIRST CI.IARACTER T5 A COi\ITINUE. Itr

REQUIRES SUBROUT INES PAPTB I HEADT TREADT PAK' +

c**'t*s***d( ***,F***** *f **(* *****s ** **t* *+******'1.****+*****+*****+********INTEGER START ( 6,) r PTIplEr TRYr PTNr SHIFTTDISKX i l0l rSCANINTEGER BEGI NT ERRDI MEi,ls tut,.l I BUFR ( t()00 ) r JDATA( 5I0 I r t(HEAD t 20 )DIMENSI ON KDATA( 40OI, IPAGE I 6 I I I REC ( 6)COI,II,lON JDATA, KDATA I I BUFIi

INITIALIZE TAPE READ OPERATION

CALL PAPTB { Or IOOO I I BUFR )

ERR=0I NDEX= II SUH=OI C0f'lT=0I NVAL=0NEH=0I PAR=OCALL PAPTB ( I,SOOTJDATAI I1', IFIN}CALL PARTY ( I PAR }

IF( IFIN)5 t6t5

READ AND PRINT HEADTNG DATA

CALL HEAD(KHEADTJDATA( II }, INDEXIt,lRITE(5,500lKHEAD{1)MAX=KHEAD ( 6 )

DO I0 J=l,t4AX

*:B

{.

sr*

*

***

l0 },|R

l'lRIF

TE(5r 501 ) J'KllEAD( 2*J+5 l TKHEAD(2*J+6 I

TE( 5 t 5O2l ( KHEAD( J I r J=2 r 5 IKHEAD(31-t0llrrl2rll

hRITE(5,503)G0 T0 106

TNITIALIZE RECORD NUI'lBERS

D0 l3 .,1=l,i.,iAXIREC(J)=6*IPAGE(Jl-5START ( J ) =360*KHEAD ( 2*J+5 lPTII{E=START ( I }

IX=-I

c*c*c*

lr

L2

l3

Page 357: 2-Whole-digital Data Processing in Radio Astronomy

349,

I Y=0SCAN= Igg$ tlrlrPT I HE

c*C* READ DATA AN.D DECI.DE IYPEcr

20 CALL TREAD(KINDI tNFOr I5PUR,' II{DEXIJDATA( 1I I II Sl,Jl'l=I $Uf'4+ I S PURIF(KIND-t l90r3or40

cfC* A/g ,DATA ROUTINEC{r

?0 IX=IX+lt y= I y+1.

KDATAIIYI=INFOCAtL PAK(IrKDATA( IYI )

TRVEOG*C* CHECK FOR ARRAY OI/.E.RRUNc

IFtIX-100f32r31t3I3t HRITE(5r504132 [F(lY-400le0tt3t9733 t'lR,I TE | 5 r 505 I

G0 TrO 106c*G* CIOCK DAT,A ROUTINEcr

40 TRY=OPT I HE=PT I}lE+ I XIF ( .I NFO-PT I HE | 4? | 42, 47

c*C,* CORRECT BLOCK !{A.RKc*,

4e EBR=OI X=0IFttY-36012OrEor81

c*C* INCORRE.GT BLOCK I'IARKCtr

t+'t, IT*QDO /r9

"fa[sHAXIF l I l'lFO-START ( J l l+9r48 r49/18 trf:rJ49 CONTINUE

tF([Tl50r50r6o50 IF(ERRl5l,r5Lr52

c*Ct FIR;ST btlRONG MARKc*

51 EP.R= IIXN* tXNTN= I NF0PTN,=PT I|dEPT IIIIE=PT I ME.I X

+*

,!f

rt**

*:frF

*:f|t

+*rt

*+*

rl*rt

Page 358: 2-Whole-digital Data Processing in Radio Astronomy

350.

GO TCI AOc*C* SEEONO t{RCING I{AR,KC*

52 D0 53 J=,lr IXNI ND= I Y-I X+J-l

53 KEATA( INDI=OIX,=[X-trXN5H I FT-NTN-PTNI NVAL= tr NVAL+I xN+SH I FTIFtSHIFTl54r56r56

5.4 DO 55 J=Ir trXIND=IY-IX+JK* IND+SH I FT

.55 KD,ATA ( K I =!(DATA ( [N0 tGO T0 58

56 DO 57 J=lrIXlN.D= IV-J+1.K= il\lD+,5H l FT

57 KDATA(Kl=KDATA{ INDI58 IY=IY+SHIFT

ER,R=0PT I l.lE=NTN60 T0 40

c*C* SET FOR NEH SCANc*

6-0 I Y=I Y-lIF( tY-60189f61r6I

6tr NE,W= lIFI tY-360!80r80r81

C*C+ T.IRITE DATA ON DISKc*

80 MOST=IYGO T0 83

81 MOST=36083 llR,ITEt l0r lREC(S9ANl t IKDATAtJI1Js!,rlilOSTl

c*C* UPDATE INDEXc*

DI SKX ( 1,l=lDISKX(21=KHEAD(tlDl SKX ( 3 l =KHEAD I 2,.SCAN+' IDI SKX l4) =KHEAD l 2*5CAN+6 )Dt SKX ( 5I'=KHEAD ( 5lD I'S,KX ( 6 l =KHEAD'( rr IDISKx(71=BEGII'lDI SKx ( I l= INVALDI SrKX [ 9l =10ISKX(10I=0J=IRECISCAN)/6+1HN I'TE I20!J I DI SKXIREC ( SCAN I = IREC ( SCAN I+6

||**

***

!tt*

tdl

*

rfC,f

Page 359: 2-Whole-digital Data Processing in Radio Astronomy

3:51"

C* }IR.ITE HESSAGE ON PRINTERC* RESET COUNTERSe*

t.|R ITE ( 5 r'506 I J r BEGIN' trNVAL I ISUMtMOSTIltlVAL=0I SUM,*'0lF(NEWll08r85r89

85 rBEG I:N=8ErG IN+3,60lF(XV-360186r8'6r8?

86 IY=0GO TO ?O

8? lY=IY-3600O BB J=lrIY

88 KDA.TAIJ I *K,DATA( J+36O }G0 T0 e0

Cttt

C* TN.ITTATIZE FO]R T$EW SCANc*

89 NEH=OSCAN= I TPTIHE=START ( SCAN lBEGIN=PTII'lEKDAT,A( t I =KDATA( IY+t II Y=1'I X=OERR=0GO T0 Z'O

Gr;C* PTCC. AND DEFICIT ROUTINEc*:

90 IF(KINDlt00r9Ir9l91 INTDEX='INDEX+ t SPU'R-5O0

K= L- I N,EEXI F tK 194t94 t92

92 DO 93 J=lrKL= il I'*J

93 JDATA{ Lf=JDATA{ L+50o194 tF( tFINt96r95r969t CAL[- PAP'TB,( l.'SO0TJDATA( 1lI rIFIN]

CALL PARTY ( I P.AR I60 TO eO

96 WRITE(5,507'IFTNGO T0 106

l0O ['IRITE|5f 5og I INFOIF ( INFO-1 1 102r l01 r l0Z

101 HRITE l5t5I0l IYTBEGIN1011 IF I IF-[N I I0L3s I0L2r I0l310,f2 CALL PA,PTBt lr500rJDATAl Il) rIFIN)

GO T0 l0l,It0t9 cALL P'APTB(l.r500rJE:ATA{ lll r tFiNl

CrtLL PAiRTY t I PAR )

I CoNT= ItN'gEX= LG,O TO 20

XO,2 I F I I,MFO-B l I06r lQ3r 106

*+*

,{t

*:t

t+$

Page 360: 2-Whole-digital Data Processing in Radio Astronomy

352.

t03 IF ( I C,0NT-I I t06' I04' 106104 I COtlT=O

I SUM=0GO TO ?O

[06 IF ( lY-60 I l0Br 107r 107I07 NEt.l=-1

GO TO BO

I08 I,{RITE( 5' 509 } IY' BEGINl.lRITE(SI5IIIIPARCALL DUi\1PX

RETURNc+f,C**,f ,t{.*:St***t***t****t,t +**tf *************+**,t***+***t'*****+******+***tcr*

5OO FORMAT(lHlrr*s***.,',s*t*****+*****+'l*+*****+rr/t'****TAPE IS FILE N

*0. I tl4t/ tr ***'f 't*St'****:rtrr******:('******'lt'**r r/ / |

501 F0RI4ATt IH , t SCANt T I2r I IS FROM" I3, r00 HOURS T0t r I3' r00 HouRsr '/ I

5O2 FORMAT(1H TTBLOCK LENGTH =rrI4rr SAI{PLE5r SAMPLE INTERVAL =r;I4*, I SECONDST GAIN =r r I4tt.- DECLIhIATtUN =r r l4r I DEGREES. I t/ /l

503 FORMAT ( IH r I ****SAMPLE INTERVAL IS NOT TEN SECONDS****I ' / I I

504 F0RtlAT(ItJ0rrs;i:i-,i,frlI BL0CL( ]lAS BEI':hl F0Ul'lD il'',1 THE LAST t00 HORDS****t*t//l

F0RMAT(1H0rr****sT0RAGE ARRAY 0VERRUNT N0 BL0cK IN LAST 40 H0RDS***+*t r//l

FSRMAT(fH rrPAGErrI3rr STr\RIING ATr rl5rr DEKASECSTtTI4T' iNVALID l'l

*0RDSr I r l/rr r spuRt0us cHARACTERS, TOTAL OFr r I4r I W0RDS. t )F0RMAT(1H0, r*{r**Ct{ARACTER DEFICIT 0Fr rI4r I AT LAST READ****r I

FORMAT( lHOr I****PTCCI r I3r' ENCOUNTERED**+*I I

F0RMAT( tH0r TREADING ST0PPED ATr I I/r1 t |,ll0RDS 0N PAGE BEGINNING ATr I*I6rr DEKASECS.tt//l

510 F0RMAT(1t-tor'READINc pAUSED AT'r I4r I t,lORDS 0N PAGE BEGINNING ATr*rl6rr DEKASECS.tt//l

5rl F0RMATtIH+ tt4tt INc0RRECT pARITy Cf.|ARACTERS ENC0UNTERED ON THIS rA*PEttlll

c+*Ct****t:f ******+*t(**n ******,fi***,$+**+**********{*****'t***'i***************c**

END

505

506

507508509

Page 361: 2-Whole-digital Data Processing in Radio Astronomy

(1;1[Q 0ltl4lI00

353.

EFIT HEAIJ>Ftr**+.*rF* 16];:t6tl *vr,f *'t>'!.4(:i(/r*rt***{<tf >F**,lt*)N}t{'.+,:.43******+{til rt*.

'S HEAD DEC.UDF5 TiI: iIEADIIiG INFURI'lATION FRU;1 ** A pi{PLil TAPL hFTEq I'f ilAS EEEN RIAD lNT0 *,h A tsLlfl.['l tj,Y P,\Pf[1.* THI CALL ING SEAU-NCE I S T

CALL HE/ru ( ]1DATA ' JDATA' INDEX ) *

'i. TIDATA IS A 20 ELEI'lENT /iRN.6Y CONTAININGF I L f: r L iJt-K r L S AMP, bA I N ' DFCN t SCANS ' START r Sl'tlP . *JDATA I5 A 5()U iLEMEI.tT ARRAY CL'NTAI[IING THE*RAv,i DA'tA FRti;"1 Illt TAPE.READI i{G I5 TO CUI.lMENCI AT I NDEX '

ANDII!D:X I5 IlI(.iI-ii:: ITEIJ TO THE I'JEXT TLEMENT

* AFTi.R THt !-lEADIirG.ALL VARIABLES AfTT ONE I,IT]RD INTEi;EiiS.

d<:*tic>f{:******J;:>i}$$/6):(*d(*/Ftr****,k\trF****(+*rttt**********:B*

TIEAD

tF

*

*+

**

#**

:lr

0ui.t0 (J

0i0 I ul0.tu3 .r

0rr04 ul0ur(16 il0u07 L,IggiJ().1 0OUOb U

0COC (,,IOti0[ t)0u0F !,0,.t I U ri001 I ,'Jo

0tr u0C4 800t,00Dlttt41 4oL 0u0069?tJ65 8U0000C1ii00.r(t IDO 3DC1t B Lr0 rJi.t0BU3E9u J9DJOI690Q0.-,00 LO AD

rF

ttk

*

UT,

LD IsT014DM

STX ILDX I ILD I Isr0LD IA

S

STOLDX LI

LEADI'{ LD 1

BNZi'lDX II'1DM

B

S f/rR T i4DXI"IDM

LDSTO

READI I]S IMDM

llSLA.\

STOREADz 65I

MDI'1r,

READ BUFFER UNTIL

HDATA ADDRS*2GET IlIJATA(I) ADD'1S*AhIN PUT AT HADRSINC llE/rD TU JDATA ADDRS*2SAVE CONTENTS OF XRIJDATA ADDRS+2 I NTO ,(RIStT l:,\DEX AI'lD ASSICN*A LOCAL STORAGEGET JDATA ADD;TS AND*ADD ONE AND SUBTRACT*INDT.}II LATIR II'JIU XRI

JDATA( INDEX) ADDRS*

F I RST CI{R ENCOUNTERED *+

GET C}1!1 AT JD.\TA( IFIDEX)IF NI]T O GO TO STARTIT O IN3 ADDRS AND*I{ETUP,N TO LEADR

*t(,,

SI(IP UVER T CHR

GET 6 AND STORE*AT CUUi,ITBR TO DCODE SUD|I*SIX TITiES' THEN*CONT I NUETAKE LAST l'lORD READT':.,lrLT ;j, 3 ^.11 l-.! 1,+PUT AT COUNTBR TO DCODE SUBR'fc0ut'tT T It'lES rTlrEt't qETURN*TO CAI.L II"IG PqL-]GRAM

0l-lE liDIIADP.S}JEAD,ISAVE+IIIEATJIINDIXHE /rDONEINDTXLOAD+I0

0u13 U

Oul+ (tl0i l6 t)

01,I7 ,llOUI9 U

cI004C 20U0 I A7 LFF7401C).)491 0F9

0START-1I NDIX, ILEADR

r-2T NDLX,2SIXCI]UNTDCDDEc.outiTr-1READII1'': i'-

c0ui{TDCOD Ec0ut'lTr-Ic,EAD2

** READ HEAD I N.; DAT A*

Ui,rIA u0(,Iti rrIOulJ u0't I L r..r

0\rlF O

0r-,1 1i il IAUVZ u0u23 0\' .a

0u25 (r

cr(t 26 0r).t /7 .r IO;tZ) )

7 LFE7 4020 u49CU2CUv LV40 L574FF0ri4B7 0FCI00 t

ooir4rl0 E

7 qFF 0t.t4D70 FC

Page 362: 2-Whole-digital Data Processing in Radio Astronomy

354.

*a*

REIUIfI TO CAI-LI

r 1 l-lE ADIhIPEX

tl IT2t ReTRr{+t

LIOr-0

X3 PTTIGRAH

JDATA A0DR5{.2 INTO xRl*AND RETURN INDEX TO*CALL ING FROGqAM

SET RETURN ADDRS

RESTI]iIE XRl

*t*

Qu21, JI00ec 0(.lur2D u0ouaF 00 ISLJ L)

Oull U0U 3 3. Lr'0

658Cr00tr0c01cD 580[t,Lr o t7 LUZ6,903650t)0!,00ciCtJ00,CIO0

tDXLDtsT0MDXSTX

SAVE LDXR,ETRN B+**0co:08

OE]CODI NG SUBRUUT i I{E

Otr35 00.u35 O

0037 0003E 00u39 L)

0l;34 0O{r3tl 0O03g t)

0'tu30 Lt

0{.,3E 0;0ru3F C'I00,41 00u,42 UloL,lrli J I0q+6 uI

0u,00cr r}0E[, I61004DOT?C.I FFEtl I290,0Flut,E18 88D'4B00uit+87I FE74O20t149?4FF0ur4BIrC EO'J035-

I4.ASK+4TEMF-l14AS K {t

TEMPIB

IIADRS-2lNDcXr2HADRST-IDCOOE

DCLDAND5LAsT0LDANOASLASRTsT0MOX14D14

MDTI

8SC

'0

10 CET JDATA( II'IDEXITAKE tsI[S L? NO. T5MOVE LEFT 4 PLACESTEHP STCIREGET JDATA ( !NDEX+1 I

IAKE IXI TS \2 TCI .15

ADD PREVtOUS CHR

SET SIGi\ siTS

PtJT AT HDI\TA I N }

I NC C0UtrtTERs

ER TO CALL POINT

HDATA ADDRS LOCN

TEI'{PORARY STOR,AGE

ITASK [J000 0000 0000 XIIt*

*1$

iF

:F

*'*

***HAORS DC

INDEX DC:SIX DC

cou,rdT DC

TEMP ECONE DC

:MASK4 DC

c,oNs irAN rs

O,tJ4E 000dt9 0OU/IA 00048 00tlztC u0'04D 0OO,4E U

0Jo00'o000006o0e00000oct01000F

00600Il00orF

+ i'it++'*'t***** ******'tr{'***#**r}*lt*'t**'# * {. * * dr* * #** * **.tr+ *l|*'}F+ +.*.+:+ {. +.!r:r d(:s+t+;ry+ F.al.F +??? +

*rl.

0u50 END

Page 363: 2-Whole-digital Data Processing in Radio Astronomy

0u00 2J.b4',5C++

355.

E.NI TR EAD* * * * *+ * lt rt,rri.* * * * * * * f,- * + * * *,+ * * *,* * + **:{q * *{. Jfr tf + # t {. * * * * * #* ** TREAD DECODES DATA FRCII"l A PAPER TAPE ' ** OfiIE sET AT A TIMI.T AFTER TAFE HAS BEEN +

*. READ IIT;I(] A dUFFTR BV PAFITB. ** THE 9411-lirlG SESUENCE tS *# CALL TFTEAD(IYPE,INFOTSPUI{T INDEX'JDAIAI +

* TYFE IS 0 Fll'R A |.IUN-READ ACTIONI ti-NDl ** 1 F.UR A1ID, DATA* 2 FOR BLCICK PIARK* -l FoR l'rcc:IT SPU:R I S A SP'UR I UUS CHR COUNT.* TNbEX XS TIIE CUR|TE|{T EI-EHEI.IT OF AN ARRAY +

* STAIITINS AT JDATA AND 5IJO l.lORDS LBNG. *'F ALL VARI Ai]LE S AA.E ONE IJ'OID TNTEGERS. 'ft

*$ d( *+ 1F + *, +* d( + *.s + + + :F tr$ * * * * * * *'} * * * *, {t * # *** *'1. * * * * * rF * * * *+

0100 00u0t 0ouoJ 000ir3 0 t0,c05 ci)OOCIt r)0u0E 0[00oA Oil

O,UOC 0OUOD C

00018 ts

000F i.)0Oirtl U

0LILZ d

0u13 00014 00{r15 00bl6 0ou17 0o0r8 0o0!9 0001,4 J105IC iiOOID UIO[,IF U

O*rZ0 tl I

0r100b94A6Aqti65 80e'U0Oc5 8G0CI03D06Z?/i0r+0u00c48000c0BO5E905CD0il166Q00u00co6 3D05 E

4,03DrC{.1'58

1,8 88I8 d6IOEZEO5690 564 C L B0ir309J534C I800;3990i04C 1 80t.1? D

TREAD DCSTX5TXI-DXLD5TOMDM

LD,̂l

5sT-o

LoAD t-DxLD,sT0

BSTCHECK LCI

SRT5RAst- TANDsgr.

5BE5bz

RE ADAREAa62MAS Kdl

F0ultIrTCCFOURDA.TAFOURCLOCK

ID CODES

IND;EXr L

cO,u'tT, IT ESTA,R,EA

I

IF ID=8

IF lD=12

THEN OATA

IH]EI\l BI-OC:K

0I SAVEl+I2 SAVEE+I

II TREADII 3

lNDEXTREAD, +

I TREAOONEINDEXLEAD+I,

L2 0'Z Ef{UCOUNT

TAKE THO EHRS FROM EUFF'ER.CHECK ID CODES

TYPE ADDRS*z.SAVE CONTENTS OF XRlSAVE CONTgNTS OF XRzTYPE ADDR.S+2 INTO XRlGET I hIDE X AND A5S ! GN*A LO]CAL STORAGEINC TI"TEAD TO JDATA ADDRS*2GEI JDATA ADDRS AhID*ADD ONE AND SUBTRACT*IIXPEX, LATER INTO XRZ

JDATAI INDEX } AODRSSET COUhIT TO ZERO

*+**

**+)ft

***

rF

f**

B,R T0 r{EAEl SUBRPTEK UP T!{O CI{RS*AI'ID SEPARATE ID*coDE5

IF ID=4 THEN PTGC

a,a22 010,-r 2 rt 't l'002{t i)o0e7 a0,J28 .u

7401,t0641 tr'.t L,J'J 7 I40,38coqS1'iQ I

If'IVALID

MOM

iJ.D P

BStLDSLA

***

INC INDEX AND CqUNI

TEST SIAE CIF INDEXMOVE FTRSf C}IR*'OUT AND iSRTNG. IN

Page 364: 2-Whole-digital Data Processing in Radio Astronomy

356.

Dr)43cz 00Eori61804'uDu 3F7Ar F7uE4

STOLDANDA

sr0MDXB

,\REA0MASKEAIR EAAREA-ler{EcK

*A NEH

C,11:ECK ID e:ODES

SET TYPE TCI +I

DEC0TDE SATHPLE DATA*AND PUT INTO INFO

C.IJ:RC-r '?9 L)

O,-i2A 0or.',trAU O

A'uZC ,J

0tt20 u0.'rZE u00zF 0

00 3CI

0'J310t-' 3.3(lu l+CI0350u 360tr38

CL)420 58il(}000C(r 39l.003Etlf9D5 80000 t7004

** ]PAPE.R TAPE Cfi{TR0L CU|IMANID*PTCC LD Mt)'NE SET TYPE T'0 -I

STO II O

LD ^REA

PUT LAST FIJUR BITSSRA I *II'IT0 IIIFOAND MASK4SIIJ II 1

B BACK BR TO RETURN SUBR**{(

DATA

DATA DECOD I fIG ROUT I NE

LD ONE

sTo Il. 0tD AREI\SLA V

SRT ;$

sha '!Slf t+

STTJ I1 I*js RE-TURN T0 C ALL I lllc PROGRAM*B.ACK :I.O IND X RETURN INDEX TO ST'OPT

STO IT 3LD ]COUNT RETURN SPUR TO STOPTsro Il zITIDX 15 $]ET RETURN ADDRS

STX I RETIIN+I5AVE1 LDX LI O RESTORE XRISAVEA LDX L2 O RESTOR.E XR?SETRN ts L O

,h

* TAPE READIf\tjJ ROUTINE*READ DC O

MDF4 INDEX I 2 INC INDEX AND TEST

BSI TEST *FOR SIZELD Z A READ ONE CHR

SLA 8ST'O AREAI.D ?, -1 REACI A ?GND ,CHR

,lrlD y,\SKt}

A AREASTO AREAI,|,DX ? -Z UpDAfE J0I\TA(llil,DEXl AI|DRS

6SC I READ qETURN TO CALL POINT

*'**

U

000t)

otj00 *

**

01.,390,u340D3COtr30o'i 3EOU 3FOu/+O00(t I

0t,:430C4{rOu46a0470u49004A004b004D0u4F

00 510c520u 5/fOu550r,56,cto 570,u,580vi'l0CI5A0u50',tiG005D

eLr3lD5,800000c0301u03l8, E

1{J03r 084E5 80000 t

co2'6,D5 80000.3CIJ2AD5BOO002?l 056e0 56r 001000066f-t0,00004c0000u0

***

0'J00(),

0oo00

000000orjooJo(10

rlOI\,f.

0,\

0oJoo0u1

+*,$

00,00740200644uilAc20010 c8DUt5C.EF.Fci I )

8012D0l t1'TFE4C80005I

Page 365: 2-Whole-digital Data Processing in Radio Astronomy

t**T ES'T

INDEX TiST ITOUTIf{E

DUOLD TNDEXS VCIBNN OFLOUtssc I rEsrLD /ERO5T0 Il 0,B tlAcK +3

CT]N,STANTS

EO0I00z.

/000Fq

0/ CIOFF

-t5010/ c0c0IO06

D,ECODtr NG

coUNT r

firEcKARE/\AR FA. 1

REATIAR,EAIrl A,S K D

NOTZT t{CI

I1 0AREA-I3t41.ENI6TENPAqEA. I531

I'1ASK4

3i57.

IF INDEX GR,EATE.R TH'1.N$5OO BR TfI O\TERFLOW

sET TYPE TO O

BR TO RETURN SU6R

TEI4P STORAGE AREA*

MASK 0000 0000 0000 lt11

I'4ASK 0000 0000 1111 ttrl

[{ASK 1r0,0 0000 1100 0000

TEHP STORAG,E AREA

ROUTTNE '

2

MOVE ATiEA TO AREA-IrANrD READ Tt/0 l.{0RE*cr-,rRs ltcT0 AREACH"ECK I D CO.DE5*OF SECOND SET GO TU*NOTZ IF INVALIDsET TYFE TO +2

SEPARATE IO,TI.I.OURS*C0NVER"T Tr0 HUtTRS*T.,Y PIULT I PLY I NG BY IO*AhIE TE[4P STORE

SEFARATE 1*HOURS*ADD TO IG4HOUil5+ANE MU].LTIPLV BY 6*TO CONVERT TO I,O*HIN]5,*AI'JD TEHP STORE

*

{.

l.**

0u5Foo,bQ0061O;$'6:2

Ov6to0660u6701,r,6'9

U

!f,o

u,l01t)u;0r

0

0000cc0e90 t24C L ClQC,6,6/, c tr000 5Fc00ED5 8OOCr0070Die

0FL0H

***

I [\IDE X

0,N,8

AilE A

Tr**0MA5K4FgURCOUNTHASKsHUN:EVCIZEROMASKT)TENTE MP

sIx*!F

*NOTI

CLOCK

00bAOU6A D

036G u006C 00060 00c6E 0Ori6F O

od70 00,071 ()9u12, 00073 U

0074 aO0 75 {J

0.U76 00u7?,J0078 0'0u7cl (,p,

0000o(!00OriU L

0i)0000000{J0?00{)F9U040t,0oOOFFFF.FF0t F50000cilco0c'04oil000O,06

sssDrC

DC

ocDC

DE0rC

D.C

DCtJc

DCDC

DCDED,C

DC

CLOCK

MDM

sLOSTOtrS ILDANDBNZLDsToLDSLASRAM

SLTSTOLDSRTSRASLTAI.JD

***

0074 0I 74Q,Z0o7I0u7c 0 ?ue'7o07D o C0EFOiI TE U DC ED007F 0 +0o1outs,(J 0 coEcSVSt 0 iLUF40-r82 0l 4C200d7A0ij84..t CJEg0085 u0 058C00000u3? 0 eUE4008'8 0 10J3ou8e il IBOEOU8.A O AUEC0r,3$ 0 I r;90OUEC, O DOEE.0080 0 CODE01,6E U 1&85008;F 0 18030u9,0r 0 liBtOJ91 'J Eri0D

Page 366: 2-Whole-digital Data Processing in Radio Astronomy

I OtlZ "t tli)t-5I l-t,t9 3 (,| Ai,tt 5

Q1i94 t.t l(rcJt)0,. ji ti Dtrt-Z0tr9b J C'.ril5Q1t97 (J E tlf 7

0r-,i8 U I r.1 rJ IO{. cJ9 .,r t},lDEi)'9,\ J Alf)cOU'/L J I J9i)Ot 9C o Dtt930r.,rD tl cricEr)(.i /r- U LJUJOir:)F 0 lri0lOirAO C, I Uil30L,AI 'J tJCl)0,1 itZ ,:J iJ U D 5

00A3 ir AuiS0uA4 0 I'i 90U v ,\:r ,,1 D 'tD2riu.\b rl CJC60L)d7 U 183,5OUAS O IJUBUr-iAy u lrjr-lcO.JAA U LUEI0UAti ',1 BrrCC

358.

A T F I.'IJ

F1 SIXSLT }65I0 r[i,iirL.D Ar{Eir-1. SEPAp./rTE I0'}'l1lNSAi{u l,ASK4 *ADD T0 pREVI[rg5 Sut'',l,

SI1A I .itf,.LlLTlPLY irY i0 TU

A tEllP 'lCt)l'IVERT T0 Fl l NS

l'1 IEhl :k/rr\D TE|']P STO|?E

SLT 165T0 T Eili)LDD AREA-I S[PARA'TE I*I'/INS AND

AND FiASK/t itAtllJ Ttl'lP ST0REA T EI.'Pl'1 sIXsLT 16!T0 rEl'i'LD ACEA SEPARATE IO'I.SLCS ANI)

SLT 3SRA 3

SLT 3

SP.T 5SLA 11sRA t4SLT IA TEMP

,:.irUD PR,EV I Ol.iS 5Ui''l /iiJD*FlIJLTIPLY I,Y 6 TO*CI)NVIRT TU 1O*'SECS

*ADD TO SUI,1

Ou.\C {r0 D5tj0O001 ST0 II I SIDRI: IO*SECS AT INF0O,,rAf J 7u94 U DACI( BR Tl.J RETUR|! SUBR

**{(*(**)k>i(*f.<d<rlr*:>k{t>l:rt*/,{'}'ki.(*',1,**t*t'<*t>3ltri:**'ir1<**1k+****+*iY)t}t*4(*

O.IL}U END

Page 367: 2-Whole-digital Data Processing in Radio Astronomy

C' JCU I /052C00

359.

ENT PAK*/s:r,r/,<1k/,:fr.<{:tr,r******t,+/r*:f*******rk******t(f**t(**********+,1.

rk

+

*PAK

SAVERETRi,l

BITSOTU

DC

5 rxLDXLDSLASTOLDAI\ U

A

sTuMDXSTXLDXDSC

PAK CLIMB I l,lES DATA W I TH 'A FLAGTHF: C,1t-LI\i 5[t1-]LNcE IS

CALL P/rl'. ( hlul'l' DA f A )

eTu150F.

^- h r 7 Ao ur LrAtit

0I SAVI+I

II PAKII O

9TEMP

I1 Ii.lAStieTE MI)

I?RETRI'l+I0U

i.iUM ARE PLACED IN BI

lF

**t

*TS *

**

**+

llrl 1111

0u000ut, I0 u020 Ji)400(16OU U-/00030U u,rOUU B

OuilC000 E

OO JF0010OULZ

'.1(_l

,JIrlo

ir00)or-!O

Ll

0UO

UO

0 t, (,,0

69(rf:6tC,00(t00c5B{)000c1.J09D(r uDct{J0000Ii:.J J .)

B 009D58[,0u017 LU?6e i)3650u0r)0O4C 0uCU00

IIII

L1L

I'IUM ADDRS*2SAV-c CtlNItiilTS UF XRINUM ADDRS INTO XRIGTT NLIt4' LEFT JUSTIFY*AND SIORE AT TEMP

GET DATA' REMOVE BITS*[ TI] 6 AND ADD hIUN

STI]RE COlIBINAT IUN AT DATASET RETURN ADDRS

RESTI]'iE XRI

0u 140'J I t

0{rl6

0v0t,

0uCrJ,J0U01 ,.r

Oo02 iJ I0C04 rr0uu d6 ('l

0007 000009 000UUd r/

000c J0i)0D \()OL,UI: U

0C l0 i1

o,rIl ,)(J

0i; I3 r.r0

u OIFF0'J 00

* CONSTANTSfr

MASKg DC

T Li,iP DC,:(

*< *:rt {<ds* * *d<*'t i( *{< ****+* at v,. * * ++ t{t* **:i;{r* ** **8+ *+* ***:li* ****

END

Ei'lT Ul',lPlrK*,F * :* * * * * * * * + * *4 /r I *. * + * +,i. rr * * * * {< * + * * * * + :B * * * + +'fi * + * * * +'|l *8 [JI.IPAK SI.PARAIES DATA AND FLAG PREVIOUSLY ** COI'ILINED t}Y PAK* THE CALL TNG SE(TUENCE I S

CALL UTiPAK ( I"IUM r DATA }

4** COFIL I |.'IED I,.IORD I S DATA I I] ITS O TO 6 ARE ** SEPARAfID ArriD RI-TURNED AS NUM ** :l .t * *,'F * 4* * * :F i. *'t * d.,t * * * *, *,* * * * * + >i * * ),k S + + + )t *'F * * * * * * * * * *

/ OLFF0

MASK 0000 0001TEI.tP STORAGE

2+551 a5Z

00 i06 /106 5 tlO0tJO0C) uuov.ulItj09Dr800,;00ci 80000 II t07I BB7D:iflt)0Ll0l7 LJ26,)0365 0rr,J,-1004C()00i)00

***

ut'IPAK DC O

SIX I S.iV[+1LDX I I UNPAKLD II I5RA5TOLDSLASRT

NU14 ADD;TS*2S,iVE CCIITi:ITS OF XRlNUi"l ADDRS*2 IrtlT0 XRIGET DATA,\ND SEPA!?,{TE*FLAGI STORE AT NUI49

oIIlI 1 GET DATA AND SET 2TS

7 *CUMPLEMENT SIGN AND

7 +STORE AT DATASTO II If4DX I 2 SET RETURI',I ADDRSSTX 1 RCTRN+I

S,\VE LDX LI 0 RESTORE XRIRET;{,\ BSC L O

* ),t

* * * * * * * :rv * )* \k * * t( * * * + * * * r,. * * * * * * * * * * * * * * * * * * :t * * * + * * * t *

OU I6 EI\D

Page 368: 2-Whole-digital Data Processing in Radio Astronomy

360,

SUIlRCUT I NE DUFPXC*f**{.hr+*+**+**+/,::1.{r***+****f.i(*:F**t*':r*+r}$**\k,B**+*+**++:}rt***:t*St**lr******

C****{**{:t**}t***t<***++***>lr****{.***rl***+****t**Jr***{)**********r}*+******f

c*c*c*

DC 3C N=1r90READ(2OIN)INCEXtF{lNcEX(l))?0r10r20

20 iF(8EGllil22tZLt222L EEGIfr=l

HlltTE(5,ICI)22 LEFT=LEFT-l

CALL TII/EX( If\DEX (7 ) I IT Il,iR I TE ( 5' l"C2 ) l{ r ( INDEX ( J I t J=Zr6 ) r lT r INDEX ( B } r INDEX ( 9 ) r INDEX ( l0 }

30 CUI'lI I NUEN=LEFT*6hRITE(5rio3)LEFTTNRETUR.N

C* 'fC*****rtrr******++*+*)$******rt*+*f {.*+**)ir!f t ***'*******+***S+**4(**S*'}*d(*:l***c**

100 FORMAT(lHlr3CX'r***** RSTAR DATA FILE INDEX *****tt//lt'0I FCRilAT(IH rrPAGErr3XtrTAPE NC.r1lrXrrSCAN FRCMrr?XrtDECN.'t3XrtGAIN

* | t 4 X , ' p i G E B e G I N t I 3 X , ' I N V A L I C h D S , | , ZX t I A V E R A c E 0 F , r 5 X r I F I L T E R t ' / I

I O 2 F C R F A T ( i H r [ 3 r I B r I 9 , | 0 0 T C I r I 3 r ' 0 0 t r I B r I I r 6 X r 2 I I r 1 X t 2 I I r I X I 2 I I r* I 10r I I I r ' SCAN ( S ) | r I8)

lO3 FCRf',lAT(lH0r30XrI3rr UNUSED PAGES (,rl3rr RECORDSI IN RSTARtt//l///*t///////l

c+*C******++*********)8*************:r***:F****:(r+t**+)i*)t***+****************c*

END

SUI]RUUT I I{E T II.1EX ( ITI I'1E, I T )

C,l +*+,ir*+ ++it.$>t t**)i< A+* #)f ii* ++ rF+:1.+ trk+ t\:**,i<.!,i.,F*+:k:ir f:t rir+* ***.*)i(rF*****t*;ic***tt ****

c+c*

c+c{.c*

DUYPx PRINIS INDEX Et\TRIES CF ThCSE pAGES Ili DAIA FILE RSTAR *CIJq?ENTLY IIi USE *lr

INTFCER BECINDIT/ENSICN INDEX( IO )r IT (6)EEGIN=0LEFT=96tiRITE(5,1001

READ AND hR ITE INDEXES CF TI-OSE PAGES OCCTP I ED

IiMEX C0NVIRTS DEKAStCTIi\iDS (lTI\iE] INT0 DEKAT'l0URS' H0URST +

rJ[K,;i'iI;rUIE5, ,'il.tUTE-' De(ASLCLJi'i.,S A.'D SeC!it;S (iT(6)]. {<

USED BY CI-IART Ai.,ID DUMPX

***

I

I

I

I

I

I

I

rl

. .t. ,...k \L ,. r. ., :, ) .1. -wL'r rr f,a + f'a

DIMET,ISIt-li'l IT(61 r IFACT(4)DATA IFACT/ 56UO r 36U t6At6/IhIPUT=ITIMEtJO tJ I'l=Ir4I T t ttt )=l r\PUT/ I FACT ( N )I'lPttt=l IPIJT- I F,1if ( \ll *I f (.ll

l0 Cui't l' l,'lUclT(51=Ii'IPUTIl'(6)=0R'E f U'i''l

La'

C +** ++** ++ +** + *** * ****t*** *+*****i< *+*'* ********** *+* +*+******t***+******r,'. *

E hJD

Page 369: 2-Whole-digital Data Processing in Radio Astronomy

I36,I.

5UTJ"I{UUII NE PARTY ( I PAR }

C*{..,.*,t***+$**+*t***+****-{r* 4.#{t:t*t****f t+*:F******t{***lF****+*****+******iC+ pARTy CgICKS T1E PAi-] tl Y uF A 50ir HU4D ARRAY STARTING AI JOATA *C+ AFT[[l. ITEING READ gY PAPI'ts. .- - -

*Ert lF TAI,E i|'JA.RACTER H,A,D EVrrN PAR,IIYT TI{EN IT 1S LEFT 'AL]{J'NE' *C+ IF TAPE CrIA'r{CIER HTD ODD PAl-TITY T}{[ IT5 [DENTIFTCAT ION CODE *c* t s cl-lAi{,i,ED Irl C,lLJSE A SPUR IilU5 C|IARALTER DUR I NG D€CU'D:tr NG' *c* truMbER uF tJF,O PARITV CHnRACTER$ IS I-ETURNED A5 IPAR. *e r*rl::<rt+*.*dcrr**'+*,lr+*+:f :it'*+*r,ei:** *,N******lk*/r<*:ir++****t*******'***''!'*****lt**'***

COM}.IIUIr JDATA ( 5ICI ID0 zJ K=llr5trOI F,l" J0AI A t K't - 256],20r lu r I 0tF ( JDATA(K'-320 l I1, 12,'lzJDATA(Kl=-lGO T[] l5JC)AlA(Kl=0I PAR= I PAR+lCON;T I NUT,RE TUR.N

C{.cs** ******+-*;#+**lF**+*'+ 'B+**'******c?*'t'f'** + *****+*!F++*f **+*'x*{(**++*****'***'8c#*

E:I{D

STJSROUTINE ERASEIPBEGTFLiEN' o$*r*,,r+*+*,*****,***ct**,F*t1*g{f;*,{z*x*****+*}fi!t ***r*$*.+tF+:**+*r.:t.**,!t*+:R***+*li*C+ ERA,SE DE]I-ETE'5 T'H,E IN0'EX EN'TRtrES (FILE ZOt OF PL'EN PAGES O:F *

C* FIL.E IOT BEGTNNING AT_PA6E PBEG. - "-

T*Cr A M,ODIFIED INDEX IS PRINTED. *{.*r{.**:****,*,**r*,**c* + * * * ** rs.* r. * rr * * * f * ** * * * #* *{t + * * * t * * + tcarr+ * * tt * + + ** t* * * s'** *

INTEGER. PBEG I FLEllr PF lNFF I NqP BE.$+PL EN* IIZ=,O ,

00'lO0' .!=PBEGTPFINI{RITE(2OIJI IZ

lOO CONTINUECALL DUTIPXRETURN *

C * r.i- a.&! r&..& &* *,.rr&,& *il..* *,& *.*** tr.*r egg f,*$nlr***tltt t*'i|*+'l'[ * *,* * * * * t * * **+ * fF''r,* * + * * + * * dr** * * * !r tr* ts * * * * * * *+ *'** {t *'** *'* lGos*

END

L0,tr1

L2t5?u

Page 370: 2-Whole-digital Data Processing in Radio Astronomy

C4'c*C+c+i-+

c*c+c*G*c+c*c*

36?.,

SIJBftOU IlNE DSCAhI (U,N t T' FftEGr l)LEN If, rr * *:* * dt * S rt + * *.* rk * + t * * *'t + * * )k * * * + * t * F a * {t f * * *

'X * * + + + * + +'* * * * +rl :k * t<* * * * * }r * * ,* * *

D5CT.|'I DU]MFS IJAIA FROI'I DIS.K FILE IO ON TU THE LINE P;IINTER OR +

0N T{J CA,RDS. *rF ,t]'f.'IIT tS O OrR -'VEr IIJ.IIN DUMP I5 ON PR.INTER *IF Ur,IIT IS +VEI THEI'I DUT'IP [S UN CARDS *DATA IS D-Ut-il,80 STARrINc F|RO-M pAG,E PCEg, Ahl0 CO,NTI:NU.ES FOR *

*PLE:{ PAGES.DSGi\i{-a PRIri[5 20 AUERAGE0 ;ftDU/S FUR EACI-l RECOnq .+DSOAN-I FR I r'.lf,S EVERY lfl I RD DAIA l{tl.qD *DSEA,I{.O P{INTS }2 DI\TA ItiJtJQDS PLI,S FLAGS IDECUDEDI PFR tIt\E. *DEEAI{I PUNC;HES L2 DATA bJi]RDs PLUS FLA.6S ( CUDED } PER CAfiD. *DSCA'hII. REQUIRES 3T CAROS PE]|T I'AUE. IS

DATA DUI'IPED FRIJO4 .OSCANI CAN T}T RESTORED BY STOCD. *C+*****dr**lit,F**+'F+ri;+{;.***'F***>icd.a!*f,4**++,F*.****rh{<-*dc+z"t**vrrt*****+**++S8+*iF

I NTEGER UNIT, ttllEG r PLEI'l'r PF It{COMIII]N NUM ( 60 } , KDATA ( 6O }

c+c*c*

t0

c:*C'rCtt

15

REOU I RED

D0 1G0 irl=PtsEGr PF trftlft,EADt20 r N l t KBATA{ KD r K=1, r l0 ltd,R ITETNUNI T rZ0[ ]F,tr tK0ATA( K) 1K=2 1 l0 INl-l=N*6tll=i:tH-5DO 100 J =NL r iil'iR:EAD(l0rJlKDAfAlF(Unll f l30r30rZClfrRlIEl2,7OZ)KDArAG0 Iu 100D0 35 K=l r6(tEALL U'N['AK( i{UMTK',KDATA( K ) IlFtt-tNITl50r40r1O0IJRI IE ( 5r e03 ] {'l'{Ul'4(K I r KDAtrA (K,l ; K'tr p60lG0 T0 I00I F | [Jtxt T+.1 | 7u r'60,r I00i{R trTbt5, 203t ( krraTA{ K I rK=2r 5s t3loo To 100,[J]U i,l0 K= 1 r 2OY=KE/TTA( 3*K I +KDATA I3*K-I I +KDATAI3*K*2INUM(K)=Y13.+.5., 1, I I -' I r r -ii l t,.iJ,'l ( K'), r 6=l r,Zv lG.B:IgI INUE]RE TU RT{

EALIE{,,LAIE L/TST PAGE +*

P,fi t f,l=FtlEG+ PL Elil- 1

IFtuNITtSr5r toNUN t T=5:Hfttr[E(5rz00lG0 [0, L5f.lrUt'l I T=2REA0(2,?0,31

READ DATA AND OUTPUT /TS

SELECT TIUTPUI DEVICE*r*

*

**+

20

3035

40

5060

70

80

r00

c*

Page 371: 2-Whole-digital Data Processing in Radio Astronomy

363.

C,e**+*** f***ltr+rF+***+*4r**rlr*$r.* *t*{r*g:ir8*****${.**{.++***,F+******s***t'******C4: tl:

200 F0RMAT(lt-tll20'1 F]0.R,PIAT ( IFI r I PAGE t r I3 r | . T,XPE, i ' 9t7l202 FUft,fiiAI ( [aI6 ]2O3 FCIRMAT( lti r ISrZJISl

+c+c**+ *+ ** **** 4!** #.* #*** **,**t!*+***{<** +**+**+*+ ***+r*#*t*#****tlt* 't*** **** ** * #c*

Eih0D

sUflROUTINE STOCDT PTECrPLENIc*+*r[(*{.*:f{rt:r:tt*r*fr*,*******tF**+'f +_*+t'++****jtrt***it*j}*'f **tr*******#****'f )s**{.:t

Cr STgCD STnRES DATA 0N DISK FILE [0 FR0H C,\RI]S pREVI0USLY *C$ DUMPED EY DSEANT. . *C,, STORAGE BEGINS AT PAC€ PBEGr AND CONTINUES FOR PLEN PAGES. *C* 'RE€ULRE:S 3I DATA CARDS PER PAGE. *c***********,'li***+{c.*:s*,lrs,+rtf *ts*'t**********{rtt( +-rl+rl{r*it+**s*lk**f'**'*+*****'**

INTEOER PBEGIPLENT PFINCO;I4MON KDATA I60 }PF TNt-PBEG+PLEN-1D0 100 N=PBEGTPFINREAD ( 2r200 I t KDATA( K ) rt(=2r 1,0 IK,DATA( I, I =I

. l+RlT.E t 20 | N,l (KDATA(K l r6=1 r l0 l'lllH=N*6NL=NF{-5DU 100 J=NLTNHttEAD(?t201)KDATAl,rlRITE( lOr J !'KDATA

!,OO SOMT INIj|ECALL DUfiPXRETURI'I

r;

3l****nn*,****rr+**r*****trt!*,,t t*,+*-*!t *-+*r.******:ts**'**lt:t*+*+***lt*+,*f-*tr****:***G**

?00 FoRr4AT ( r 3X,9I7 I?'0r F0R!|ATt l,2I6l

G**g**+*+rir**f ***r$*'r***,s*':*****rF****t#rNs*t+'Fl|*'t**$**{t*r*'F+***+ **rt +***{.*+f *****G+

END

Page 372: 2-Whole-digital Data Processing in Radio Astronomy

I

364. I

SUERUUTINE CHfi,RT ( PBEG' PLEi.'t TS IZE I,C* * **,r?***:s*,*#****.+*+*-* * **+*****#+$+*+fi*t*S*+***S* ***,****** **.**+****'**xC* CHARI IS A PLOTTING StJU.ROUTI.\E i,ii|ICh PRODII,CES A DISTOLACEI''IENT *E* T II4E FLDI SII'4ILiIR TD THA I]F A FEN ITECOI?DER. *C/lt PLEl,r PA;ES nnE PL0[[ED U[;l:Ji'iINC AT PEEG. *C+ StlE tS ll'lE M0DULUS UF T:-lE PEA[i DLFLECTITJi't 0F THE lNPUf. +

C* T}{tt I9AGES OF DISK D,'ITA Aq.E PLtITlHD PER pRlNfER P,\GE. +

[****d:***r*+,**r**<]'F+++r*+St*'rr*'!****+rtr?F,***/4u***rlr**++*,s++r/.*s***+**+*****+****INT{-5'Ji{ PSEG, PI-;N 1S I ZE.r SLAi.IK r AS T 5I( r V.AX I5

' HAX I S

cot4MoN i,tAl'{ luo},triAx( [?0) rMl,!{ 12.0| ,lTt26 )

DATA ULAt{KTASTSKTVAXISTHAXI S/ | | t t*r t | . r tt-'INE}{= II PA;E=PdEG

c*E* READ HEAOING DAT/\ AI.ID ,HEAD PAGEc*

2 READ( 20 | I P'AGE) tl4AP (.J I r,J,=l r 101hl:R I T E I 5' 500 I ltiAP ( 2 f r t4AP ( 9 t' HAp ( 3 ] r MAP ( 4 ] r lslA'P ( 5 I r MAP ( 10 IITIME=I'iAP{7}

c*CJT READ DATAT SCALET ANE SET PEN RAISE A,ND LOhIiR ARRAVS.g*

5 EO 5,t) J=lr3t{RC"C=l*( J,-,[ ) +G+l pAGE-5R.,EAD ( trI) ' NII.EC) IlAPD0 l4 K=lrl.2OCALL'UJ{PAK(NIJMrfiAP( K } IlF(l':AP(KllSrlt)r9

I t4AP( K I =MAP(K l+t.2./SIZE-0.5GO T0 l0

9 MAf,, ( Kl =iaAP ( K ) *L2. /S IZE+iO. 5l0 IYIAP{ K }=13-'FIAP( K I

IF(iqAPtK)lI['L]'11l1 MAF(Kl=1

GiO TU lrtL2 IFIrlAP(K)-25 I t4 r 14r l3L3 MAP(Kl=2514 CTIIT T I NU E

DO b0 K=lr40K3=l(*3K?=lt1-LK tr =K3-2IF(K-40)t.6r15,15

X5 K4=K3GO TO L7

I6 K4=t(3+ tr

l7 IX=lJ-t)*40+KI F { liAP(K I l-Frrpr(KZ I } l8' ).8 r 20

l8 tlAXllX),=${AP{KIIHINt IXI;fiAP(KZlGO rO 25

2el MAx(IXl=l4AP(KZlMIN(XXl=MAF{K1l

25 IFtMAPIK3I-MIN( rXl | 35r 45r3030 MIN(lXl=HAF(K3I

tF

rF

rlr

*r

,f*

Page 373: 2-Whole-digital Data Processing in Radio Astronomy

365. I

46 ltllN(tXl'=MAF(K4l60 rti 50

+7 lF( I'lAP(K4l-l'jAX( IXI )48'SCti 5048 MAX(IXl=l{AFlK4l,A CUlJIll.lUL

c#GS SET UP C[}ROth}I\T.E GR.IOcr

L L l{E=.1D0 55 K=lr6IJO 55 J=Ii20I X= ( K-1 I *?0+.Jl,l'AP( IX)=8LAi{KIFIJ-1152t52t55

gZ MAf'l IX,;VAXIS55 C0l$[ li\iUE

c*'c* LotitER PEf,lsc*

60 D0 70 l(o116D0 70 J=lr20lx= lK-Il*20+JIF( LII*IE-MAX( lxl 163 r6l, '6361 l4AP(IXl-ASTSK

c*C+ RAISE PENSC*(

6x IF ( L INE-,plIN ( XXI -1t 70, 65 r 70

6rJ ro 4575 tr F IF:AF'/r0 MAX( IX45 I;F (MA,P

K3 l-Fl/tX t I X I )40 t45 t45=t4AFr (K3IK+) -M,l r.l( IX) l,i7'5Or 46

= B,LAlt{KoBr68r?0-VAX ! Sr

*rfrF

65 IFIATJ{ tXIF{J-T

6,8 t4API lX70 CONT IT{U

c*C * Pt I it{T ,0,rlE RUI'J

c*IF(LINE-13t7Zr73t72

7Z |.{R I:rE ( 5n 50l t t4APLI I'th=L I r.,tE+1IF(LIhtE-25)60,60r9C

c*C* PI{INT ZERO /\XI$c*

73 D0 15 J= [ r 1,20I F ( MAp ( J | _SLA:i\K ) T5 tV4t7 5

74 MAP(Jl=ttAXIS,75 C0i'.1r I,NUE

!',RtIE(5r50t,lMAPgO uC J=l,li3! F ( 14Af,I J I -HAX I 5 I 80' 77 r BO

T7 l'4AP(JI=E,LANK80 coi\l I I .!.t E

a+s

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Page 374: 2-Whole-digital Data Processing in Radio Astronomy

366.

LlNt=LIllE+lGO fil 6u

Ci{ *Ci' Ptlrvl TINE SCt\Li *C:' *

90 D0 9, J=l161 X=4 *J- 3

CALI TI,'1:X( I I III:, IT( IX} }

tTIXt:=I IIl"l[{e,Ot)5 C0;!l I i,tr.JE

lil{lT[( t' 5u3 ] ( I l- ( J ), J=L,24 I

IPA'lF:=li'AGE+lI F ( I Pr\G--Pt-lIG*PLtl-l I 96 r IfJ0 r IU J

g6 i,Jll.l=rtIfl+ 1.

IF(Nt_t'r-z)97,97t.9?97 hRif[(t'502)

G0 t0 5'?B NEW= I

3tr ]'Ll 2IUIi RETUIlN

Cr\ *C ri( ** tr.:< ***,'t * **;* )ff.t* * 'it

>krt )3,F* *:t * it+,k;il* '! **d.:i. + )F tr)i.:F:i<**d<*** * + rk*f+ *** ** * ***f:lf d<*

C+ rk

)J0 FORIIAT(Iil1rr0,\TA FRril"l TAP[:trlSlrrrrI3rr SCAtiS FROMrrl3rr00 T0trl3r,1.|(-)(-),^l DECi.l. I I IlrI |. FILIiRt r I4,/ |

501 FtJRt,iAT( lt1, l20AI )

"s02 FUP.i'14 I ( IFlO' / )

503 FURI\iAT ( lll tbl2l l,' .' t?lLr I5X ) )

C'i. *C'frr*'k+.*>1.{<,'r*;i<*ri**+-",.f*,i:>i,rjr>i..i<;i:*+*v,(,if*,iilt**j('k*:*.{.)i:***)tts)ir**t.>krFtk\tt'i********rk>l'**vrc**

E l.'lD

Page 375: 2-Whole-digital Data Processing in Radio Astronomy

367.

SU.SRJ.UT I NE CHAU / I:PbEG r PL E.N.r t{5 ET r T'A,NS )

Crr*'1.********++*+:tt**+**+*****rtr***'fiti.**+x++*****d(****+********t#****++**{(*csC{,c*c+cf

C'rc*c*

c*c*c*

LS2,A

e*c*:e*

2?

C'ftC't*

c*c*

CrF

G,*G*

I5crc*C*t,

cHiA.UVEt\iTrS CRIilEtRt(Jr{ sutlRrilJTiNr rrt* i*

NSET SCAI,ISI EACH FLEI{ PA6E5 LUi{G' STARTING FROM PAGE PEEG *AiiE thAf.llr\rED Ar.lD THAT DATA rrrt{I,Ci-,t IS Ut{LIKELV Tg e,,EL0NG TO ITS *C[JLLATE],AL SET il 5 It=''EC I [0. TI.IE AVE'R,AGE OF THE ACCEPTABLE D,AIA +

IS I,ilITITTEN IN PLEI! PAGES I}EJII'JNIIIG AT PA|.IS *G *** ** ***+ 'F *f + ++8+**'F+** **** +*++ **+* **+{.** ********** * {r:lr+****,**'**s**f **

INTTGIR PDEGIPLINr Pili5 r UI SKXI 1O IDt I4ENS I ON ERROR ( 3O }

C0f4Mtll[ l DAfA ( 60 r 3Q ] r Ntl( 3'J I r I X t 30 ] r tr l\VAL t 10 I r JDATA ( 60 I r DI SKX

REJECTtr0tr{ TCRITERIoN ARRAY

DATA EfttOt/ I .36 r t .63 r I " ?71 I .87 r I "95 t2.01 r 2. Od r 2. n0 r ?. l4 r 2. [8 r*2. z.tr t2, 24 r 2'.26 r 2. 28 t2. 30 | 2. l? t 2.14 1 2. 36 r 2'. 38 | 2-40 t 2.4I r 2. 43 t*?. t+4 t 2. 46r. 2, 47 t 2. 4B t 2. 49 r 2. 50 r 2, 5 L t 2.52 |

CHECK ThJAT NUI,IBER UF SCANS IS L'ESS THAN 30

IF(f.lSET-30l6t6t5l*RITE(5r?00),G0 T0 tIO

SET PAGE NU;MBER IIII EAC}I SCANS,ET REQUI RED RECORD l0ITHIN EflCH PAGE

D0 100 I=lrPLENDO E K=I'NSET{NVAL{K}=0.INVAL=0D0 S0 J=lr6

READ OI'IE R.ECORD FROM EACI-I SCAN

D0 l5 K=lrNSETTN.REC=6* ( FBEG+ I K-L l*PLErN+I-2 l +JREAD ( 1,0 | Nll,ECl ( IDATAllN,riKN q ll=l, p50 )

tl|ORK THROTJGI{ EACI-I CLILLATEI{AL DATA SET OF hIES6 Pg[AftDS

DU 50 L=1r60DO ?0 K=lrNSETIX{KI=TDATA(L'KIEALL UhIPAKIINDIKI I TX(KI IIF{i{0{K}ltBrZ0r20Ntl(Kl=0CONTIITIUE

CALCTJLATE AVEI{AGE AND STAI{DARD DEVI /rT IOt{

5t-lid=i.SUf4S 8=0 "Ill,JM=000 23 K=lrNSET

*#*

fri:*

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Page 376: 2-Whole-digital Data Processing in Radio Astronomy

368.

24

z'3'

25

SUPl=SUM+NU(Kl*IX(Kl5Ul!45Q*SUMSQ+Nt,( K I *I X ( K ) * I X (K )

NUM:NU[4.}NO ( K Ii FI N:l.rM |'l+ r 2q ,25AViIG=O.J IIIVAL=J NVAL + 1

Gt TO 4bA r, tt'3 = SUfil/NUMSTDV=SeqT t ALS ( AVRGv..,lVtiG-SU,!45(t/ i.jU14 ) I

CALEUTATE M;\XIMUM D]HVI&TION

DMAX=0 rt I'IDEX=0Dtl 30 K= X r il|5 tTIF(N0(Kl 126 r26,2iIX(K)=[\tf,g+r5GO TO 3(JDEV*AB5(TXIK)-AVRG}IF t CEV-DMAX I 30 r 30r 2,8'0l4AX

=D.E V

I NDIX=KC0l'l f ,[NUE

CFIEC,K l,||I TH. /ILIOI4AE.LE DEVIATTON

ADEV=ERROR ( NUM} *ST.DVr F ( Df"tAX-AD:EV 140,40 | 35NOI TNDEXI=OINVl.L ( If{DIX } =I NVALI TNDEXI +IG0 T0 22

WFIFI..I ALL DATA OF T}{I5 COLLATiERAL SET

DO 4e K=trrNSETCALL PAK(NIO(hiI ? I X(KI )

IDAIA(LrKl=tX{KlJOATAI L ! =AVRS+.5CALL PAK{f,J'Ul'ir JEATAT L I IEONT I NUE

HRTTE COLLATERAL RE.CORCI5 ANO AVEITAGEO

DO 6U K=lINSETNREC=6* ( PBE$+ ( K-1 ) *FLEI'l+ I -2 I +J'rtRtr TE tIu tr{REC! ( I DAI'AtNr K I rN=l '601N/\riS: ( PAi!5+ I -2 l *6+JWRI TEI IO.| NAilIS ) JDATACOI'lT t hlUE

E'N.D OF A PAGE ** UPDATE TNDEXES

O0 90 K=1r FlSETNFAGE=PBEG+ ( K-1 ) +P[-EN+ I -1'R,EAD ( 2O I NP,A,GE I O I SKX

c*C.'-to

c*

*{t*

26

?T

e8

30rc+

c*c*

35

c*c*c*

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+**

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DATA BACK ott DI SK

t;rt

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Page 377: 2-Whole-digital Data Processing in Radio Astronomy

369.

DI SKX(B ) =DI Stix( B ) + I iVAL ( K )

90 ll? I IL. ( 2r;ri"j['itGE ) DI SKXDISKX(l)=Ii.llSliX(8)=J|J\.'ALDISKX(9)=l\l5i:TIAi.ls=pA,,,lS+I_it,l1 I TE ( 2u I l/ri\S ) DISKX

t0{i c0i!I I NUEc*C* I'l1lTE MESSAJe ilrtl Pltl,.lT[Rc*

I'J!l I TE ( 5, ziJ I ) ''JSET, PbL C, PLEN, PANSIIO CAtL DUI,lPX

P.ETURl.,l

c*C****dr\kl(:t****'f tF**4 )F**{<*}t,F***{.il**:'ktr',,f ,,1*4:4<*d<*r,:**<tt t *****i./,.**tt+********{.**1kC*r *

200 [:r.rRriAT(IH0rr{.*** 1.10,'E TtlAN 30 SETS r,F DATA T0 Bt AVERAGEDT )

?OL FilP.i'lAT(il10rl3rr SET5 0F DATA STi'TRTIIJG FQOM PAGEr'I3'rrrrl3r:NI PAGES LOi.J- AVERAGiD AT PAGEI,I3}

c*C****drik*,i.+lt**,k**/F{(*v6ttFll+{<d.*,i<*)rk,F*/,if*:t,it)i(.l**+*{.*,i******,i<*****4.***+t4(+nt+**c+ ,6

EI'lD

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Page 378: 2-Whole-digital Data Processing in Radio Astronomy

370.

SUd;R,0UTXNE REJ€K ( PgES r p,l.ENrr,lSET,I Il'll T Ic'! ***,**.** * $# *++**+ +*** ****d.* *$ * ***+* * r.** **sr$it****4 * r**+* **+***+** + ***+*E4 RiJLK REJIECtS T}|OSE DA:TA t,lHFII,E IhE STA^IDA&D DEVIATION OVE]R fC'S TFIE PREVIOUS SIX POINTS EXCEEE LIJ.,ltrT. *c**** ***+rlrl****,*/***s*+*8f ** **++,*'$*,*.**# +* #* ***********'*++**.'F*!t'l.ti*'ls*{t***

II.ITEGER PDTS, PLEN,DiSKX (IOICOt'41{elN IX( f B06l TDISKXc**

C+ REA.D A F4AXIPIUII'I IJF FIVE PAGES OF DATA +

c* i.MAX_ t,pLEN+ +l l5I Cr!,00 I00 tr ='[ T,NSETDO 100

'J,= I r MA,X

NPAGE=5IF(J-,MAXl7r5r5

5 NFAT,E=pLEt{-5* ( l.4AX-l }

7 ND=360*[$I-,AGh+5tr.itREe =6*(pEE5+{ I-L}*pLEN+5t(J*1 l-t }+ttrlEAOI l0' NREC I ( I X (K I r K=6rNE )D0 10 K=1r5

10 IX(Kl=IXtb)IX(,N0+Ll=l,X(tlDI

c*C* CALC ULA.fE STAFiIDARD iDE\rlATtottsC* EXAMNNE DATA FUIR ZIRO F.LAGS AND BEIDGE AMY GAFSc*

JFLA$=0D0 60 K=lrNpACEI NVAL=OD,O 50 L=Ir360IIIDEX= ( K- I l'h360+L+5IXL=lX(INDEXICALL UNPAK(NOT IXL}IFIN0)30r30r2;O

2O SUl4=-0.SUllSO=0.BO Z5 ill= I r'6ttl= I NDEX-6+ta

t+{F

IF

CALL UNPAKINOISUM=SUM+trX(NlsUMSQ=5dMSg+1 X

Z5 CALL FAK tNL, ' I XSTDV=SQRT t AtS (

X(N}I

Fll+1x(NlNl IsuFl/61**2- ( suMsSl6l ) )

I F ( STDrI-L I tr{ I T | 49 t49,29Zq I NVAL= I f{VAL+ L

30 JFLAT3=JFLAG+1L A 5 T =.I l,lDiE X - J, F LAGIXL= IX { LAST I

I XN= [X:{ I f{DEK+ I ICALL UNPAK ( I.I, t XL )CALt UNPAKnn'1t lXrillDI FF= ( [ Xt,r-lXL I / ( JFLnG+1 ]DO 35 14=ITJFLAGM1=LA5T+M

Page 379: 2-Whole-digital Data Processing in Radio Astronomy

371

t+9

c.N

c*Ctr

I i'AJ[=P;EG+ 1 1-I ) *PL!,1+ (.J-I )

R,i-/iD ( 20 | I l)rn ii ) D t SKXi/I 5i(X ( ii ) =D I jr'.;i ( i) ) + I i,!/iiLI,/R I r F (2d' I r,A3[ ) DISKXlC=iC+li',lV/it-cuhtT I f'tuEl,lR.l 1 [ t IU t N|{EC ) ( I X ( K )' l(=6r j,jD )

cui"l't I i,lu t'r'r,l IE MIJSSAGE L) \j PP.l NI ER,

K=NSt'.T*PLEhlHR I I E (5, 20) ) IC, K, Pi_ [GRT 1 URN

c*C****ir{<;F{<,.ic:,tYr*.k:'t,*+rk*'Fr'F***rFtr)Ftr('lr+ri*rtttf*:{:rt*:vr*{<4r*,i*,F*,F,it*:*{<*.rk:k*:t***rt**.***)rt***c* *

2OO FOI{l'1AT(lH0rl4rr SPUIIIOUS DATA PUINTS REJECTED FRUI,'lrrI4*rr PAGES llEGli',li{lNG AT Pr\.lE',I3)

I X ( ii I ) = I XL +l.i'iD I Ft:LirLL f,/rN(,,), I

^( l,1l ) )

UO l-t) 5,JJl-Liil=Ltcui.tl I l'tu:

t-ND 0F PAGE */;* UPDATE I NDi XES

,F t;' + K- I

*

*

*

f

60

100c*Crfcs

c*C * * * * * * 'i( i<:h rir * * {< >F * t( * :F * rt * )t >F * 'l * + + * ,i( ,+ /5 rl f, rf ii

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i. * \t( * ):< * )t )k t(,h rt * * lt,it i! *. + :N + + \k * * * * t, *,i: * d{ t< **

Page 380: 2-Whole-digital Data Processing in Radio Astronomy

372,

5UBRtlruTi NE AvRG ( Pir[ "I PLE.i{, i\lSETI i!AtrlS )

C***rl*.+****&:rt#*'iF****+****,**t*******rl{.*ttt8*+*(**,t('t**********'lr,*t(**'*t****'***,

iC+***.{c*+ ** *,**{4 ******** *,& *** **** + *t${*** *#ilE***t*++*' ++*+***+***t*********INTEGEq PBECr PL.Ei:Ii PAhISI DI SKX t IO}DIMEI{SIUN A.VG(60IeoFtf4,ui'I I DATA ( 60 ) rN,Ulii ( 601 r i-ll $Kx

SET PACE N.UIMDER IN .EACH SCANS,ET RESU I RED REC0RD !'l I TH ltl EACH PAGE

D0 I00 l=lrPLErNI NVAL='0DO 90 J=l16D0 l0 K=I r60AVG ( Kl =0.

IO t\l,tJM(Kl=0

R,EAD ONf, REC0t{D FR,Urlt4 EACt-l SCAN

CrF

c*c*c*c*c*

c*clFc+c+

c+c*c*

c*g*c+

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d,vR; rrvERAGEs l'l5Er 5:ETS LJF DATA sTAt{rING AT PAG'E Pac0r EACFI $

SET BE I ,IG f'LEN PAGES LON3, AND I.JITITES TI.iE AVERA6E IN PLEI'I **PA$ES SEGIt'rNlNe AT PAltlS. -

THE tII:UEX EIITRY FOR THE AVERAGE I5 TT\KEN FRCII'1 TI-1E FIRST SET *OF RAI{ DATA. *I,iIEIGIHTIITIG IS ACCOC.DII\I6 TO TItE FLAG ,TSSOCIATED WtTH EACH }iORD. *

D;g A0 K=Lrf,lSETN&EC=g+ t PBEG+ { K-I ) *t'LEl'l+1-l I +JREAO(lIOINREC } IDATADO 2A L=I160CALL UNPAK( N, IDATA{LI I

IFtiltll5'Ibi16N=OruUiltL)=r{tJM(L)+'NAVG ( L)=4VGt L ) +I0ATA( L 1 *f\l

CALCULATE AVERAGEO SCAN

D-O 30 K=lr60IFII,IUM(K) lZAt22t24IDAfA(Kl=0lN'VAL=I;\ AL+IGO TIJ 30I DAT A ( K I =AV0 ( K I /NUM ( K l +.5CALL PAK(iTUi.iTK} TIDATA(K} }

e oNT I i{uE

I,IRITE AVERAOE ON DI $K

IrlAt{S=6* (. [,rANS+ I -2 | +JhJR l TE ( LtJ'r 1$[fl!$ I I UA,TAC0it-1t tliili/E

EftlD UF PAGE ** tlP DATE I l.lrJEXES

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IPA3E=PBEG+l-1

Page 381: 2-Whole-digital Data Processing in Radio Astronomy

373.

i\iPA;L=i'Ari,lS+l-IR l- A;) ( .j il ' I l-' i'''i ) l) I i:li. X

DlsK,,((l)=1LIISKX(tt1-li\V/rLDI SKX ('/ l ''l'iSiTf{l( I T [- ( L,.t | ;]PA;t ) l,I st'-X

IJ0 Ct);lIIi'rUr:

l"lR I I L l'lt-.'r5i*-'[- U'J P'i. i i'iIEii

i'J?. I Tt: ( 5,200 ) \Sf; I, PiiLG ' Pl--11' 1)ir(S

RI TUiIN

+

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2AO FORli,iT(IilU,ztXri3rr 5i:TS OF DirTA FRU:'I PA(lEtrI3r'rrrI3rr PAGES LONG/,.AVIi],AGf,) AT pAGE,, I .]lc* *

C***{< 1: 'F***:I*+,F{. ",r*,,tr**{: it:;.,i(+ 4, ***'1.'i<dlt{, t *** +:i?*;i ,i.*>k*:t:F*vl {e5l,td:*{..*f*** f*)t******c*

END

c4,

Page 382: 2-Whole-digital Data Processing in Radio Astronomy

374.

SUURCIUf I l'lE F' I LIR ( PbEG I PLi-N t PAI{S t,Nt'lAT E r LENfFI If,lk***+***.r,,r*{c****+Sl..ri*ik+,t*t*rr*rt:i:$,{<f{{cri;rt++**+**'}+**+*rt*+*+S***t***{t*.tc'ttt(t!C{{ DIGITAL FILIERINi SUO1UUTINE *}F t'ItIGHTINC FUNCTIU,N CAN *C'h ExTIN,D FR'o,ll -io0 TO +I00 DEKASECUt'.iDS (LENTH=lo0l ** 201, t,.JEIGHTS{'

C+ ALHAYS CENTRED ON II]I *c * * *+ #** *r,r **rf **.******t't **** +* *'! t**t*i|(r1.*f * *s+,*#s*++ !'r **.+***,$* **.**+***** *s

TNTE$ER PbEG, PLEN I PANStNrESE,R 50ATA(60) TDI5KX( 101Elr.lhNsIuN hArE(aor]COI.T''4OT.I IDATA( 29U} r SDATATDTSKX

CtF *C* .C,fflECK TllAtr hlEIGiiT IING FUfiCT [0N l-ENGTfl D0ES NLII EXCEED 201 *c* *

I F t LE'NTh-tj00 l5 r"5 t2z l.IB,ttE{5,200t

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D0 6 J=Irl0,0NqlLtI-j

6 hAT[(NI=tlATE( J+101 )

lMIll=l0l-LEI.tTliiMAX=101+LEl'lf11NREC=6*P BEG-5AIF I N=6+ { PB EG+ PL Eii.l- I INAhIS =6*lj AN5-5I PAiE=louEGd PAG E =FANStr N,D= I

c* 'F

C* IN T T I A;L TZE IDATA ARRAY fe**

READ( 10| f'tREte,! ( I DArA'( j I r.J=lOI,280 IDO L0 J=I0l'2BO

I,O CAL]t. U'.'lPAKIi\tuMI IDATAIJ ) )ITIRFC=ltREC+3D0 20 J=l r 100

20 IDATA(J)=IDATA( 101 lC:{< *C* EAL.EULATE FILTERECI VA.IUES FOR ONE fTECORD *c**

2.2. E0 30 J=l r 60X=0.DU 25 K=tt4ItrrlF|AXN= K+J- I

25 X= I DATA ( t{) *k'ArE ('K t +XtF t x 128 t21 t21

26 S0ATA(Jl"X-.5GO TO 28

g? SDAfA(J|=,(+.52'8 CALI. PAK{Ir.SDATAIJI Ig0 CONT I [rUE

C+*C}T bIIR TT.E F I LTERED DATA !*

c* t'}JRIIE{IOINANS}SDATA

Page 383: 2-Whole-digital Data Processing in Radio Astronomy

376,,

|,{ANS =NArr,lS+ tr

I illDr= I ND+ tc*C* C,HECK FTJII EN.D OF PASEc*

IF(ti'tD-6135t15,3t3l REIID(20r IPAOE I0ISKX

DI SKX ( IO I =NhATEl'rlR' I T E ( 2;i ! .J Py'.GE I DI 5Kl<IPAr,f=IPAGE+lJPA'.rE=JPAGE+I

c#c*cr

3540

t+2

rc*eo0

e0l

NREC=hilREC+IDU 45 J=22 1

' zgn

4, CALL UI-IPAK(NUI{' ID/\TA( JI IG0 T0 a2

50 'D:ll 52 J=ZZLraBd)5Z IDAIAt J] =r$ATAtZa0 I

GO T,g 22c+C* ['|RITE I'IHSSAGE ON PRINTERc*

80 N=pBEG+pLE;{-ll"JR I TE { 5I AOt ! PBE6I N r FAN S, r{LIAT E

RETU{in{C* 'f:Q,{a,* * *'ltr*rlt***+#$+***'lc**t'r****** dt* **$*+**+-**+**s***+** *r*** **** ******#** ***

trND= II;F ( JpAGE-pANS-r'LEN l 35,r 80,80

READ ANUTI{EI{ RfCORD OF 'I D.tT"f'

D0 4r0 J=Lt2'20ITDATA ( J I =IDATA( J+60 I

I F ( tIREC*NF I N I 4 2 t tt?r 5QREAD ( 1u,i''llEC I ( I DA rA ( J I r J=221r e8D )

'rt

F0RMAT ( ltliqr,4X1| I'JEIGHTnN'd F,tii,rCTIUU LENGT'H f{AS BEEN TRUNCATFD, T0 2ol,br lFoR.MAT(Ih0r4XrfPAGESrrl4,i TCrrl4rr FIL ERED ATf rI4rt WITt{ IdEIG-HTI

#rt{i

+**

*!t*

*NG F]UO{CTILJNII r I4Ic+*C* ****** *#a**+ ***.*+**+**+rF*+*.***,**++*,******'B*+*1**s*f *+rf *-*+*$#+********C,*

EN.D

Page 384: 2-Whole-digital Data Processing in Radio Astronomy

376.

g{r*******$,**tt rr*****+*r*{rt+'tt*,+**,*+*,tr**********'***********t**)***#*'14****{c#*ctrc*csc*c*c*c*g*c*g*c+6,sc#c*

StDtR IS A tlAINL INE pRUGlAjri hrrilCH 'C/.T,LCULAIES L[JCAL SIDEREA,L *TIFiIE AT IN'TIRVALS [JF LOCAL /ONE TTI'41 *I llrtlrUT DATA I 5 A.S F0L l-tl',,S

F I R.ST CAi?.0OLT ** TNCRGME[,tT lN LOCAL TllllE It'i F10.4s'Ec{.}ND CARo Ar,lD SrigSg6gIi,lI CARDSYEAR till \4 COLU?.t,'rS I TO 4H,uNTFt Ihl A5 CoLUl,l 'lS 7 T0 I1-STARTIt'l,; LIIrTL If.l I? CtlLtJ!.l"lS !4r15R Il'l 12 12 F6. a COLUM'\S 18 f 0 3lNr0AYs Ir{ I4 eOLUf4\E 32 T0 !5NCI\ CuNf Il{t,ATlut\t GLrUI{f ER Irr I ! gULrJf.lhl 38

R lS FR0M TADLES FI!]R 00 ltR U.T' ON DATENC'{ IS O OR -VE FOR LAST GARD

II,FAD II.IPUT E.ATA AND ,I.,JEAD FA6E

REAO(2,IOOIDLIDDLT= DLT D+36rr000,,FLT= ,D0 LA K= Il ILf{Kl=0READ I Z ' 101 I Y EAR r f''lt tJ r N 1T; H r DATE r I y. r I Y r Z ti{DAYS r t'lCNNPT=ltl0r.\Y 5+24. / DLTD+, 5tt,= 100.* ( z+60. r ( lY+6u.* I x l lD,gLR =DL [*2 36 55 . 623r'fi 640000,R,=il-DELR*l?. I DLTOFLoirlG=9,+I0,0.*l 4.+60 r* ( 39. *6O,.*23l !WR ITE ( 5 r 2tJ0 ) f'lsLIr N r T rll rYEAltr!,t'RtTF(5r2O!lilR I TE{:5 r 20P }JE,LT=[LC.N'f =4

CAt.CUL,ATE LOCAL 5IDEREAT- TIME

F L.ST=F.LT +R+ F LONGCALL f YFiE t FLS l'r LST i LD ICALL TYHE ( R T JRT J'RD )

lF(JDLT)6Ir6Ir60

Pf{II.IT TIMES AND DATi

tIRITE( 5r 21Ol DAfErLTnLSTTJRNED=0LCITIT=LGNT+ZG,O IO 70

PRINT TIMES

kliLl TE( 5' 2tr1l LT rLSTrJRLCNT=LCiVT+INF T=r\lr T- IIFtl.,lPTI90r90rg0

***rf*

**&

{r

te 't,*.#*+*ir+#+{tl++'t**+****

*it* f **** fi+** **,**,***'}**+*****+}il **'#*rF'it****]*****'F++It'l.TEG[R Hr,U r N r Trl'lINTE6ER YEAR I DATEDIMTNSION t-ST( I I,LT(8) rJR{8 !

c*c*c$

c*c+c*

C{.c*c*

60

c*csc*

***

tr0

LZ

30

lrO

'6I

?0

+*f

**+

rr**

Page 385: 2-Whole-digital Data Processing in Radio Astronomy

sv7,

C,,t

f,* UPOATE VALUHS OF R Ai'iD LOCAL T I ME

G*80 R=il,+DLLR

FLT=F]LT+DLTCALL TYt"iE{ FLT r LT r JD'LT }

DATE=DATE+.JDLT1F(Le,NT*56)40r30r30

90 IF (l{CINt e5,95 | l095 STopc**

c:lc**t(*:F* ***+**** 'r****:t*\r***t*+.** *+*++ **,***'lt +*+*****+***+*'F***+******:t+c*

IOO FI]RI'iATIO1 FCIi1}4AT2OO FORi,]ATEOI FORM,ATzOE FO{MAT21O FORM"ATalI Fr]R,il{Ar

,l**

F10.4.)I4rZX' 5AL r 3 ( 2X' l2 ) ' 2X' F6 .2t14r 2X r I I I1l'fl'7X'fLOCA|. 5tDene*l Ttl'lE F0F( | rSAIrr rrrlSrr .t t/lI t{ r T DAT E t r T X r r L . T ! r l 3X 1 r L . S . I r r l*X r r R r ,]

lfj rlXr3(6Xr'Hlt. I'll.l SECrllIl't0 r I 3 r 3 ( !+X t?l I r 2X' 2 I I r 2X'2 I 1 r | . r t 2 I I I Il..H: rlXr3lt*XtZI ITZXTZL Ir ZX rZI I r r. r r2[ I ] )c**

C+**r$t{i+*+.'t+**+)F:+t *****stlr:*******+F**+tt*t*+***#*++*++*******fi********'tt}c*

bND

SUIJROUTINE TYI.XE ( VULS r IT r I DIc * *** 't * * * * * * * * * * 'F

rr *.* * * *.* * rr * * * * {c + * * * * ** * * ** * * * * #* * * *'* * * * f * + * *+* * * * *** * *C* TYI",!E I5 U'.SED EY 5ID:R FOR RAT]O,\IALIZING A VUI-GAR TII{EI *C+ I U, ,= D,[VS *C* VUL,G = VULGAR TtrillrE trrl(r .Ol SECUN,DS *'C* lT = ARRAY FOR r?.ATIUiNAt-ll'E0 TIFIE *c+*+'t-.r +* ++**+*+s+ + *-*+*{isi#+r/*'t* *****'}++ *****,.$****{.****+********r**f **'l. **

DIMEN,SI,UN IT(BlI D-VULG./t}64fJ000.VULri=VULG-861t00O0, * I DITtal=VUu,j./3600O0!REI4=VULi-36U000. *IT ( ZlXTtll=IT(21/LAIT{A)=trT{e}-10*tT(11t T { 4 ) e,R,,EM/ 6.0:!10.R,EM=REM-:60Ort.+ IT ( 4 IITl3)=II(+l/LaI TI4 | =[T (4,]-r0*IT( 3 IIT(Ol=R:EM/100,REH=REfri_,!.O{.J. * I r ( 6lIT(5)=IT(61/I0IT (6 l=I T ( 6 )-I0*.IT( 5 IIT (81=RElil+O.5IT(71=IT(81/I0I T ( S,) = I I ( t:l-Lfl'f.I Tt 7 )

RETURi{c**c * f *****':r#*s,** *+ *+ #fr*.*f *n(* *t***!f,* ******t****:{c****4r*:*,t(**'*****+**,1.******c*+

ENO

Page 386: 2-Whole-digital Data Processing in Radio Astronomy

Arupnrlj1_a_

Log_i c C i i"c-ui ]lyffl4]g

AB.1 The NAND Gate

n -..

n--] \p J l,--olrYc ----LJ

Q = A'ti'C'

Tlris syrrbol is alse u5rtd for an ittverter; only one'input'is

Q=A

AB.2 The Capaci t j vel y-Coupl cd IIAND Gate

378.

shown, i.e.,

A--Jffia -lH li_-ac __1__-z

dB+C

(jg+c

Q=o[

n - rnq- ur1

(pos'it'i ve I ogi c )

(rregative logic)

AB.3 The Type D Flip-F1op

Data is transferred ftransition. SandCare

rom the D inputinvcr[ed leve'l

to the Q outPut on a

direct. sei and clear

posi ti ve cl ock

i nputs.

Ic

Page 387: 2-Whole-digital Data Processing in Radio Astronomy

379.

AB.4 The Monostable Mul ti vi brator

Arr output pul se oftion at the input.

AB.5 The J-K Flip-F1op

The behaviour of this device

n represen'l"s the state before

specified) and n+1 represents

fixed durat'ion js triggered by a pos'it'ive (O't; transi-

is dictated by the following truth-tab1e,a triqgering transjtion (0+1 unless other-the sLate fol'lolv'irrcr the trans'ition.

I

I

K

when

wi se

0

1

;l\n

Jn lrn I Qn*rl Qn+1

Qn

Qn

Kn

Page 388: 2-Whole-digital Data Processing in Radio Astronomy

380.

AB.6 The Decade Counter

These courrters count

trigger puise they resetoutput tlrc cocffjcjcnt ofoutput the cor-:ff icierrt of

AB.7 The RS F1 i p-F1op

Th'i s conrbi nati on of NAND

i.e.n Q is set to 1 by a

transition at. R.

z4 z8

b'inary cocle up to 9, and on the next

1 output 'is the cor:ff ic'ient of 20, the 72.

otrtput Lhc coeff icjent of 22 and tlre Z6

1n

Lo

Z)

23

z2

na tura I

0. Thc Z

, tlie 2,,

gatcs forms a basic nrenlory

Q = S + Q.R

el ement

0-n1 trarrsit'ion at S, anci'is reset to 0 by a &+1

Page 389: 2-Whole-digital Data Processing in Radio Astronomy

391..

AFpendi*9

I

Ssme Additional Circuit DetailsI

/

I Thi's appendix cont-ains: ctrcuit detai:ls of the tape handler unit,the ge,neral po$re,p sup,ply'n and the cl,ock pov{er supply.

Figune A9.1,: Tape handler mains wlnihg49.2: Tape handlc,r pungh control

' A9.3t 'lA9.4: )Genera,I polt€r supply

I

49.5: J49.6: Clock ptilrer supply

lr, ,,

Page 382;

38:1.

385.

386'

387.

3gg.

Page 390: 2-Whole-digital Data Processing in Radio Astronomy

382,

(@

Figure A9.1: The paper-tape handler mains wiring details.

Key:-

1. Motor on-off switch.2. Motor se'lf-Iocking relay.3. 'Motor start'microswitch; norma'lly open, closed

arm at the bottom of its travel.4. rMotor stop'microswitch; norma'lly closed, opened

arm at the top of its travel.

by the tension

by the tension

be on if the motor switch (1)not present.

frorn starting motor if

5. Motor indicator l*p; this'lamp shou'ldis on and the 'tape-break' condition is

6. 'Tape-break' microswitch; prevents (3)there is no tension on the tension arm.

7. 'Tape-break' indicator 'lamo: wi'l'l be il'luminated if motorswitch (1) is on and 'tape-5reak, switch (6) is open.

8. rTape-break' override button; can be used to start.motorwhen tape-break condition is present.

Page 391: 2-Whole-digital Data Processing in Radio Astronomy

383.

sl€G'ogr!5GL

Eoo.t-v

aftt.tJ,o,

.90!*.r'e,oct

'(tE=ia.L,(u

f=l 19t=l ,Gt:t G'

o'fr'g+|''ILoEL(!

CL

Gll.l

otl<lo,lr.LI=l9{t!l

;\t

.i.tr

i"Y-____-.-Yj

'L-l--.-- . -

Page 392: 2-Whole-digital Data Processing in Radio Astronomy

384.

Key to Figure A9.L-

1. 27 volt input; I = +27 volts, 2 = ground.

2. contro'l switch; allows punch and e'lectronics to operate whendisconnected from the frbnt-panel switch (3).

3. Punch on-off slvitch.4. 'Tape-tightr indicator lamp; wi'll be il'luminated if the

punch switch is on and the 'tape-tight' condition is present.5. rEnd of tape'indicator lamp; wi'l'l be i'lluminated if the

punch switch is on and the ''end of tape'condition is present.

6. 'Tape-tigh!, microswitch; normally open, closed if thetape jams in the supply drawer.

7. 8-way connector to front-panel of hand'ler.8. Punch indicator lamp; wiil be i'iluminated if the punch

switch (3) is on ant-tape tight or end of tape ionbiiionsare not present.

9. I'linchester connector to punch.

10. 'End of tape, microswitch; located in punch.11. Data-input socket; punch wi]l not operate if these two

tennina'ls are not bridged.L2. rPunch inhibit, line to punch gates13. rPunch activate' switch; with data input disconnected^

punch shou'ld operate continuously (a'l'l' eight cnanneti)'when this button is depressed.

Page 393: 2-Whole-digital Data Processing in Radio Astronomy

385.

h- +Ev

RqgutotcdI 4o363

+

-il0II

TtK5

2N6971K5

Lomp Suoply

To Rqutotor

I;cl(b)

FiEure A9.3: 5 volt general logiq po!iler supply; (a) ttre vo'ltageregu'lator circuit, (b) the rectiiier, and (c) tne-ove_rl oad indleator ci rcuit.

Page 394: 2-Whole-digital Data Processing in Radio Astronomy

395.

2x (16-0-fltt rrn6

pA723!

(q)

(l

Figure A9.4l t15 volt power supplies; (a) the overallconfiguration sho-uring the two ldenticalregulatons, and (b) details of one of thereg,ulators.

Page 395: 2-Whole-digital Data Processing in Radio Astronomy

38.,7.

l,t

BA

BtCt78

(sl

+1'5v t5v

(bl

Ftgure 49.:5:, t 15 volt pov{er supplles (csn,tinued);Fl an overload indicator circuit, and(b) lne output eonnector of tlre g6neralsnpply.

Page 396: 2-Whole-digital Data Processing in Radio Astronomy

388.

\-j4v . RcAuloted

uA723 G

2x 1N3255

Reg u lo tor

(b)

Fiqure A9.6: Thb clock power supply; (a) the 4 volt regulator,and (b) thb rect'ifibiiiriuits. Overload-indicator is as for Figure A9.3c.

150-0-150 rms