high speed samplers and digital filters for vlbi
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1
High Speed Samplers and Digital Filters for VLBI
Dick Ferris
AT Electronics Development Group
June 2003
2High Speed Samplers and Digital Filters for VLBI
Topics
Digital Filters can provide the identical, stable and linear-phase channel passbands required for an ideal interferometer....
Current Usage in VLBI
Polyphase Digital Filterbanks
The Geocentric DAS
The slow march of ADC technology
3High Speed Samplers and Digital Filters for VLBI
USB LSB
+
- jsinw.t
j
w. -w.
1
p/2
~ -p/2
64Msps
32MHz
IF
I+jQ
LPF
USB
cosw.t
- jw.t e
32MHz
LSB
-p/2 w.
w.
w.
- + +
16MHz, 8, 4, 2...
500..1000MHz
Eg. 1 K4 System (CRL ~1993)
4High Speed Samplers and Digital Filters for VLBI
w. -w.
¯ M
32Msps
IF
BPF
B=16MHz
w.=8,24,..104
B=8, 4, 2, 1MHz
0..112MHz
w.
w.
w.
w.
16* 1MHz Bands
8* 2MHz Bands
4* 4MHz Bands
3* 8MHz Bands
Eg. 2 X_FILT (ATNF 1994)
5High Speed Samplers and Digital Filters for VLBI
Eg. 3 LBA DAS BandSplitter (ATNF 1997)
-
0..192MHz
Fo=Fs/ 4
¯ M
Fs=128Msps IF
LPF
B=64MHz
Fo=32, 96, 160MHz -Fo Fo
I+jQ
USB
LSB
Q I
~
-p/2
+ + +
HT
¯ M
USB LSB
-
¯ M
+ + +
HT
¯ M
USB LSB
-j
n(+1) -1 n -1
B=16MHz,... 1MHz
6High Speed Samplers and Digital Filters for VLBI
Eg. 3 LBA DAS BandSplitter (ATNF 1997)
0..192MHz
Fs=128Msps IF
LPF
B=64MHz Fo=32, 96, 160MHz
-Fo Fo
I+jQ
Analytic Q I
¯M
HT
¯M
n(+1) -1
n -1 T
-M/2 z
Fo -Fo
B=32, 16..., 1MHz
Fo
Fo
Fo
7High Speed Samplers and Digital Filters for VLBI
Eg. 3 LBA DAS FineTuner (ATNF 1997)
-
¯M
+ + +
¯M
USB LSB
-j
~- jsinw.t
cosw.t
IF
p/2
0..16MHz
0..16MHzFo
- M/2 z
Q I
¯M ¯M
T ~
- jsinw.t
cosw.t
IF
p/2
0..16MHz
0..16MHzFo
B=16MHz,... 62.5kHz
Fo
Fo
Fo
B=16MHz,... 62.5kHz
Fo
Fo
Fo
LBA DAS Summary
Input 'virtual' LO at 32, 96 & 160MHz, 64MHz bandwidth
Fine tuner 1Hz resolution over 16MHz
LO-centred single passbands (64MHz), 32,…62.5kHz
LO-contiguous dual passbands 16MHz,…62.5kHz
Flip all passbands, separate duals
40dB sideband separation, 40dB stopbands
8-bit ADC, 10-28 bits internal
2-bit requantiser servos, 12dB range + 12dB AGC
8High Speed Samplers and Digital Filters for VLBI
w. -w. I F
BPF
w.
w.
w.
w. 16* 32MHz Bands
8* 64MHz Bands
4* 128MHz Bands
2* 256MHz Bands
¯ M
1024Msps
512MHz
B=256,128,..,16MHz
Eg. 4 VERA (NAO 2001)
9High Speed Samplers and Digital Filters for VLBI
1
0 1
The Filterbank Alternative
2
1/M
M-10
wk=2pk/M
-jwkne
n=mM+
= e-j2pk(mM+)/M
= e-j2pk/M
=WM-k
WM= e j2p/M
IF
x(n)
x(n)
x(n)
-jwM-1ne
x(n)
M
M
M
M
X1(m)
Xk(m)
XM-1(m)
X0(m)
-jwkne
-jw1ne
-jw0ne
B
Fs=B
eg. B=1GHz
M=1000
10High Speed Samplers and Digital Filters for VLBI
p0(m)
p(m)
p1(m)
pM-1(m)
x(n) WM-
k
p0(m)
p(m)
p1(m)
pM-1(m)
x0(m)
WM-
WM-k(M-
1)
x1(m)
WM-k
x(m)
WM-k
xM-1(m)
x(n)
p0(m)
p(m)
p1(m)
pM-1(m)
x0(m)
x1(m)
x(m)
xM-1(m)
x(n)
y0(m)
y1(m)
y(m)
yM-1(m)
WM-
WM-k(M-
1)
WM-k
WM-k
Xk(m)= y(m)WM-k
p0(m)
p(m)
p1(m)
pM-1(m)
x1(m)
x(m)
xM-1(m)
x(n)
y1(m)
y(m)
yM-1(m)
x1(m)
xk(m)
xM-1(m)
0
1
M-1
DFTasFFT
x0(m) y0(m) x0(m)
Transforming the Filter
WM-k
=n MOD M
x(n) M
Xk(m)
y(n)= h(i) x'(n-i)
h(n)
x'(n)
11High Speed Samplers and Digital Filters for VLBI
1GHz
4k channels
1GHz
4k channels
Subband Analysis
Standard
Zoom
n*Zoom
n*Zoom^n
12High Speed Samplers and Digital Filters for VLBI
Conventional Channelisation
13High Speed Samplers and Digital Filters for VLBI
Filterbank Channelisation
14High Speed Samplers and Digital Filters for VLBI
DAS<->Correlator Tasking
Schedule+DataBase+Clock
Control Process
Pointing
Tuning
(Digitisation)
Delay Tracking
Channelisation
Phase Tracking
(Re) quantisation
Correlation
Schedule+DataBase+Clock
PCFS
Pointing
Tuning
(Digitisation)
Channelisation
2-bit quantisation
Data Transport >>>>>>>>
Schedule+DataBase+Clock
CorrCon
Data Transport
Delay Tracking
Phase Tracking
Channelisation
Correlation (Complex XMULT and Int)
Schedule+DataBase+Clock
PCFS
Pointing
Tuning
Digitisation
Delay Tracking
Channelisation
2-bit quantisation
Data Transport >>>>>>>>
Schedule+DataBase+Clock
CorrCon
Data Transport
Phase Tracking
Channelisation
Correlation (Complex XMULT and Int)
Schedule+DataBase+Clock
PCFS
Pointing
Tuning
Digitisation
Delay Tracking
Channelisation
Phase Tracking
2-bit quantisation
Data Transport >>>>>>>>
Schedule+DataBase+Clock
CorrCon
Data Transport
Channelisation
Correlation (Complex XMULT and Int)
Schedule+DataBase+Clock
PCFS
Pointing
Tuning
Digitisation
Delay Tracking
Channelisation I
Channelisation II
Phase Tracking
2-bit quantisation
Data Transport >>>>>>>>
Schedule+DataBase+Clock
CorrControl
Data Transport
Correlation (Complex XMULT and Int)
15
2GHz
4k channels
4k channels
Multiple Zoom (>2 possible)Multiple Zoom (>2 possible)
2GHz
4k channels
4k channels
Com pound ZoomCompound Zoom
2GHz
4k channels
Simple ZoomSimple Zoom
2GHz
4k channels
Basic ConfigurationBasic Configuration
FFT
FFT
FIR
FIR
FilterbankFringe
Rotators CorrelatorsDMUX
A 2GHz bandwidth polyphase digital filterbank with 4096 channels ... ... will fit into four XC2V6000 FPGAs
FPGA hardware may be completely reprogrammed to
produce many different filterbank configurations, as
different observations may
require.
RF, IF and Baseband Signal Path
Filterbank Architecture
A Wideband Upgrade for the Australia Telescope Compact Array
Luneburg Lens Phased Array Luneburg Lens Phased Array6 * 22m antenna AT Compact Array
16High Speed Samplers and Digital Filters for VLBI
commercialexperimental/military
0
2
4
6
8
10
12
14
16
18
20
22
1E+4 1E+5 1E+6 1E+7 1E+8 1E+9 1E+10 1E+11
Sample Rate (Samples/s)
Sta
ted
Re
so
luti
on
(B
its
)Analog-to-Digital Converters:
COTS / non-COTS
from Bob Walden HRL 1999
17High Speed Samplers and Digital Filters for VLBI
Wavelength-DivisionDemultiplexer
Detectors and LPFs
A/D
A/D
A/D
MultiwavelengthOptical PulseSource
1 2 N....
BASE STATION
Electro-opticModulator
Receiving Element
Antenna 1
A/D
N
2
1
..
1 x K
To K Antennas
DownconversionFringe RotationCorrelationetc
DSP
Antenna 2
Antenna K
From K Antennas
The short optical pulses sample the RF at the antenna
Succesive wavelength codedsamples are separated by afilter and digitised in parallel
High repititon rate, low jitterpulse source locked tostation reference clock
1 2 N....
A Sub-Array Incorporating Impulse Sampling
and Photonic A/D Conversion
from Paul Roberts ATEDG 2002
18High Speed Samplers and Digital Filters for VLBI
Summary
Digital Filters can provide the identical, stable and linear-phase channel passbands required for an ideal interferometer....
Current Usage in VLBI
Polyphase Digital Filterbanks
The Geocentric DAS
The slow march of ADC technology
19High Speed Samplers and Digital Filters for VLBI
20High Speed Samplers and Digital Filters for VLBI
Digital Filter Basics
Two-point running mean: y(n)=(x(n)+x(n-1))/2 >> LPF
First order differences: y(n)=(x(n)-x(n-1))/2 >> HPF
FIR filter as generalised N-point running mean (convolution)
y(n)= h(i) x(n-i) 0<=i<N
h(n) is impulse response h(n) H(f)
Even part: he(n)=(h(n)+h(N-1-n))/2; a(i)=2he((N-1)/2-i)
Odd part: ho(n)=(h(n)- h(N-1-n))/2; b(i)=2ho((N-1)/2-i)
H(f)=a(0)/2+(a(i) cos2pif + j b(i) sin2pif) Fs=1, N odd
he(n) He(f); zero/linear phase, zero/constant group delay
ho(n) Ho(f); quadrature phase Why
21High Speed Samplers and Digital Filters for VLBI
Why choose Digital?
Completely deterministic; no component selection or tweaking
‘Easy’ design, exact modelling, precise performance
Amplitude & phase characteristics as stable as sampling clock
Wider, flatter passbands, perfectly matched between systems
Nil dispersion/group delay distortion across the passband
Reduced closure errors >> better calibration
One sampler, multiple passbands; avoids ‘platforming’
One hardware platform; many modes, functions
Cost effective for high performance multichannel systems– Ex
22High Speed Samplers and Digital Filters for VLBI
Generic VC/BBC
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