N AS A / TM- 1998-208426

A Comparison of Signal Enhancement

Methods for Extracting Tonal Acoustic

Signals

Michael G. Jones

Langley Research Center, Hampton, Virginia

National Aeronautics and

Space Administration

Langley Research Center

Hampton, Virginia 23681-2199

May 1998

https://ntrs.nasa.gov/search.jsp?R=19980201049 2020-07-26T06:58:38+00:00Z

Available from the following:

NASA Center for AeroSpace Information (CASI)7121 Standard Drive

Hanover, MD 21076-1320

(301) 621-0390

National Technical Information Service (NTIS)

5285 Port Royal Road

Springfield, VA 22161-2171

(703) 487-4650

A Comparison of Signal Enhancement Methods

for Extracting Tonal Acoustic Signals

Michael G. Jones

Fluid Mechanics & Acoustics Division

NASA Langley Research Center

Hampton, Virginia

Introduction

The measurement of pure tone acoustic pressure signals in the presence of masking

noise, often generated by mean flow, is a continual problem in the field of passive liner

duct acoustics research. In support of the Advanced Subsonic Technology Noise Reduction

Program, methods were investigated for conducting measurements of advanced duct liner

concepts in harsh, aeroacoustic environments.

When performing acoustic liner tests in a flow duct facility, the researcher is faced

with the task of optimizing two criteria. The first, and most obvious, criteria is to design

the acoustic liner such that the maximum amount of sound absorption is achieved. The

other criteria is to obtain a signal-to-noise ratio high enough for quality measurements.

Obviously, if the measurements cannot be made with certainty, the development of im-

proved acoustic liners will be inhibited. For grazing incidence impedance tests, the above

two criteria are contradictory. As the liner absorptive capacity is increased, the signal-to-

noise ratio at the downstream end of the duct (opposite side of liner from sound source) is

decreased. For this reason, measurement methods are needed that are capable of extract-

ing the portion of the measured acoustic pressure which is due to the sound source. This

is especially difficult when the desired signal is buried beneath the broadband background

noise generated by the presence of mean flow.

This report presents the results of a comparison study of three signal extraction meth-

ods (SEM) for acquiring quality acoustic pressure measurements in the presence of broad-

band noise (to simulate effectsof meanflow). The performanceof eachmethod wascom-

pared to a baselinemeasurementof a pure tone acoustic pressure 3 dB above a uniform,

broadband noise background.

Discussion

Baseline method

The selected signal extraction methods were compared with a :'hard wired" signal

extracted with an existing FFT analyzer, set to a 12.5 Hz bandwidth centered on a tonal

signal 3 dB above a uniform, broadband noise spectrum. Initially, it was desired that this

test be conducted in the presence of mean flow (in a flow impedance tube). However,

changing the mean flow conditions (increasing tile velocity) is likely to change the loading

conditions on the acoustic drivers. Thus, there is no solid baseline against which to compare

the results of the methods studied in the current research. For this reason, it was decided

that the test would be conducted using additional acoustic drivers to simulate the acoustic

field due to a mean flow.

Figure 1 provides a schematic of the instrumentation that was used to conduct the

baseline test. As shown in figure 1, a pure tone (1 kHz) was fed through a power amplifier

to an acoustic driver connected to the end of the flow impedance tube. A random noise

signal was fed through a second power amplifier to another acoustic driver connected to the

flow impedance tube. The respective magnitudes were set to achieve a 103 dB magnitude

at the frequency of interest (1 kHz), with a broadband noise such that the signal-to-noise

ratio was approximately 3 dB within the 12.5 Hz bandwidth centered on the tone.

Figure 2 provides a demonstration of the variability of measurements using this

method. Five sets of data were obtained at each selected data acquisition duration (labeled

as averaging time on chart) to determine the variability between measurements. The six

choices for averaging time were selected to correspond with the data that will be presented

for the three SEM's in this study.

As can be seen in figure 2, the magnitudes of the five sets of measurement signals

convergeto within -t-0.5 dB after 120 seconds of averaging time. However, the phase

components have a range of 10 ° after averaging. Obviously, the results for less averaging

time are even less acceptable. As will be shown in the following sections, the new SEM's

perform significantly better than the baseline method.

A coherence-based method

The first SEM to be studied was the coherence-based method. This method was found

to be quite successful in the extraction of tonal signals which were at least 9 dB below

the background noise spectrum (S/N = -9dB). This is a significantly more stringent

requirement than shown in the baseline test. However, this method is limited because it

only allows for the extraction of the magnitude component of the acoustic pressure signal

(the phase component is ignored). Regardless, it is important to note that this technique

may indeed be the most efficient method when only the magnitude component is needed.

The underlying equation for this method, taken from reference 1, is

SPLt SPL._ + 10 log= (1)

where SPL_ and SPLm represent the "true" and measured sound pressure levels, and

27m,8 represents the coherence between the measured signal and the pure tone source. A

schematic of the instrumentation used to conduct the study of this SEM is provided in

figure 3.

As indicated in figure 3, a random noise generator was used in these tests to simu-

late the effects of mean flow on acoustic pressure measurements. The random noise was

filtered (low-pass cut-off set at 10 kHz) and amplified to a selected level. This signal was

then passed through a scanner, which allowed it to be engaged or disengaged via computer

control. The resultant signal was then fed to two power amplifiers and their respective

acoustic drivers, which were mounted on the end of the flow impedance tube. Simulta-

neously, a pure tone output from an arbitrary waveform generator was passed through a

potentiometer and a low-pass filter/amplifier to two different power amplifiers and their

respective acoustic drivers (also mounted on end of flow impedance tube). The pure tone

3

signal was also fed to an FFT analyzer, as was the signal measuredby the measurement

microphone.

A computer wasused to control the hardware in the :followingsequence:

(1) Disengagerandom noise generator

(2) Setarbitrary waveformgenerator to desiredfrequency(0.5, 1.0,1.5,2.0, 2.5or 3.0kHz)

(3) Set amplification to achievepure tone signal of 100dB at selectedfrequency

(4) Measuremagnitude of measurementmicrophone signal

(5) Engagerandom noisegenerator

(6) Set random noisegenerator amplification to achieveselectedvalue (9, 3, -3, or -9 dB)

of local (within 12.5Hz bandwidth, centeredon test frequency) signal-to-noise(S/N)

ratio

(7) Measure source and measurementmicrophone power spectral densities and the co-

herencebetweenthem using a selectednumber of averages(25, 50, 100,200, 400 or

S00)

Although the baseline results were for S/N = 3 dB, data for the other S/N's were

acquired to provide a better overall understanding of the capabilities of this method. The

sequencefor the number of averageswasused to determine the rate of convergenceto a

"true" answer,which wasassumedto be that determinedfl'om step4 above. A comparison

of the measureddata is provided in figure 4, in which the error (extracted measurement

microphone magnitude minus "true" magnitude) versusthe number of averagesis given

for eachof the test frequencies.

Considerfirst the results for a S/N of 3 dB. As shownin figure 4, the extracted data

for this condition collapseto within +0.3 dB of the "true" magnitude after 800 averages.

A:fter only 200 averages,the results are within +0.4 dB. It should also be noted :from

figure 4 that whenthe S/N was -3 dB, the results after 400 averageswerewithin +0.5 dB.

These results are clearly an improvementover that achievedin the baselinetests. It must

be noted again, however_that only the magnitude componentis availablevia this method.

It should alsobe noted that the FFT analyzerwasoperated in a new high-speedmode :for

eachof thesenew SEM's. Becauseof this improvement, 800 averagescannow be acquired

in 2 minutes. The prior mode allowedfor only 120 averagesto be acquired in this amount

of time.

A cross-spectrum-based method

The second SEM to be studied was based on a cross-spectrum method. Based upon the

results of this study, this SEM was selected as the "best" method for extracting pure tones

from within a broadband noise background. The underlying equations for this method,

expanded from reference 2, are provided for completeness.

The following definitions will be used in the ensuing equations:

Gab

Gab

Hab

Sa

s:

SPLa

_(t)

cross-spectrum between a and b signals

averaged cross-spectrum between a and b signals

transfer function of signal a to signal b

time history of broadband contaminating noise

auto-spectrum of a signal

complex conjugate of auto-spectrum of a signal

sound pressure level of signal a, dB (re 20 pPa)

time history of "true" acoustic signal (pure tone)

time history of electronic source signal fed to acoustic driver

time history of contaminated signal

(pure tone plus broadband background noise)

The following equations can be used to extract the "true" acoustic signal u(t) from

the contaminated signal y(t). By definition

a_ = (s_ + sn)s; = aux + an_ (2)

_x = auz + an_ (3)

Since Sn is not coherent with S'x, Gn_ approaches zero after a sufficient number of averages.

Thus, equation 3 can be rewritten as

ay. =a_x (4)

It should be noted from this equation that the desired phase component of Gyx can be

acquired simply by taking the phase component of Guz.

The transfer function of the "true" acoustic signal to the source, Hux, can be derived

as either

H_, - S_ - S_S_ - G_. (5)

or

H_- Sx - S_S* - G_u

After a number of averages, we can combine equations 5 and 6 to get

(6)

-- m

G_x Guu

Gxx Gxu(7)

Rewritten, this becomes

m2

Gu_G_ = G_z = G_G_ (s)

Combining equations 4 and 8 gives

m2

ay_ = G_zG_u (9)

By inspection,

Thus,

--2 m2

G_ = G_x (10)

_ = (a_au_) °'5 (11)

If we convert our results to a logarithmic form, which more directly matches our measured

data, we get

SPL_ = 101ogl_u I = 201ogl_l- lOlogG_ (12)

The schematic of the instrumentation used to conduct tile study of this SEM is the

same as used for the study of the coherence-based method (figure 3).

Acquisition software was used to control the hardware in the same sequence as was

given for the coherence-based method, with the following exceptions:

6

(1) At step 4, also record the phasebetween the pure tone source and the measurement

microphone

(2) Replacestep 7 with the following: Measure cross-spectraldensity betweenpure tone

sourceand measurementmicrophone (magnitude and phase)and powerspectral den-

sity of pure tone sourcesignal

Analysis softwarewasusedto apply the aboveequationsto the measureddata to determine

the magnitude and phaseof the extracted signal.

A comparisonof the measureddata is provided in figure 5, in which the error (magni-

tude and phasecomponentsof extracted measurementmicrophonesignalminus the "true"

signal) versusthe number of averagesis given for eachof the test frequencies. As can be

seenfrom this figure, the data for a S/N of 3 dB are better than that measuredfor the

baseline casewhen at least 400 averagesare acquired. While the magnitude accuracy is

observedto be only slightly better than the baseline,the phase accuracy is significantly

improved. The phasedata havea rangeof less than 4° centeredaround the target ("true"

answer determined from modified step 4 above), as compared to a range of 10° for the

baseline. In fact, after 800 averagesthe data for S/N's of -3 and -9 dB aregenerally more

accurate than was the casefor a S/N of 3 dB in the baselinestudy.

It should be noted that the rangesfor eachof the data charts have beenset identical

to allow for more simple comparisons. As a result, someof the outlying data has been

clipped and is not shown. However,noneof the outlying data is neededin the discussions

provided in this report.

It is expectedthat this SEM can be further improved if the measurementsignal is

filtered with a narrow-band tracking filter prior to the computation of the cross-spectra.

Due to time constraints, however,this supposition will have to be substantiated at a later

time.

A time history signal enhancement method

The third signal extraction method studied was based on a signal enhancement method

described in reference 3. The underlying equations are included below.

Let x(t) and y(t) represent the time histories of the portions of the measurement

microphone signal which are due to the pure tone and random noise sources, respectively.

The total time history z(t) is equal to the combination of x(t) and y(t); i.e.

_(t)= x(t) + y(t) (13)

If these time histories are subdivided into N synchronous blocks of 1024 samples (xk(t)

and yk(t)), as was clone in the current study, averaged time histories can be computed as

1 N 1023 At_(t)= _ Z (x_(t)+ y_(t)) (14)k=l t=0

where ^ indicates an averaged quantity. By synchronous blocks, we mean that each block

of data (xk(t) and yk(t)) begins at a time where the pure tone source is at a positive-going

zero-crossing.

If x(t) and y(t) are independent processes, as is the case in this study, equation 14

can be rewritten as

1 N 1 N 1023 At_(t)= _ Z ._(t) + _ _ y_(t) (15)k=l k=l t=0

Since y(t) represents a random noise signal, the second portion of equation 15 approaches

zero as N goes to oo, leaving

1 N 1023 At

_(t)= _ Z _(t) (16)k=l t=0

i.e.; the resultant time history is dependent only on the desired portion of the signal.

An acquisition code was used to implement equation 15 for N = 25, 50, 100, 200,

400 and 800. This was done to determine the number of averages required to achieve a

"clean" time history, from which an estimate of the "true" power spectral density can be

determined by taking the FFT of the resultant time history.

8

A schematicof the instrumentation usedto conduct the study of this SEM is provided

in figure 6. The data acquisition routine used a digital signal processingchip to acquire

two data channelssimultaneously at a user-selectedsample rate up to 100 kHz. For the

current study, the sample rate was set to 10 kHz and two measurementmicrophones

were used. Independent analyses(using the equations given above) were conducted for

each measurementsignal, and the results were compared to data acquired with the FFT

analyzer. The pure tone signal at microphone 1 was set to be 3 dB above the local

backgroundnoise. The pure tone signalat microphone2 wasmeasuredto be 1.5dB below

that at microphone1 when the random noisegeneratorwasdisengaged.The differencein

phasebetween the two microphoneswasmeasuredto be 144.8°.

Figure 7 provides a comparison of the extracted signalsusing a range of 25 to 800

averages,as wasdone with the other SEM studies. After only 25 averages,the local S/N

wassignificantly improved. This improvement increaseswith an increasingnumber of av-

erages. Figure 8 provides another view of the samedata for the test frequency (1 kHz).

For convenience,lines havebeendrawn on the plots to correspondto the results at 800av-

erages. This wasdone to help indicate how fast the data are converging. It is interesting

to note that the data convergedquite well after a minimal nmnber of averages.Note also

that the differencebetween the two results (1.39 dB and 143.82°) is almost the sameas

wasmeasuredwith the FFT analyzerwith the random noisegenerator disengaged.

This method would appear to be very attractive for continued usage. However, it

requires a two step processin which the data is first acquired and stored onto a storage

media, and is then subdivided into a number of synchronousblocks for analysis. This

procedure is time consuming,making it unattractive for regular usage. Nevertheless,this

method may prove to be viable for caseswhere a large number of microphonesare needed,

sinceit can be conducted for a larger number of microphonesat almost the samespeedas

for a few microphones.

9

Summary

The measurementof pure tone acoustic pressuresignals in the presenceof masking

noise, often generatedby mean flow, is a continual problem in the field of passive liner

duct acousticsresearch. In support of the Advanced SubsonicTechnologyNoise Reduc-

tion Program, three signal extraction methods (SEM) were investigated for conducting

measurementsof advancedduct,liner conceptsin harsh, aeroacousticenvironments: (1) a

coherence-basedmethod, (2) a cross-spectrum-basedmethod, and (3) a time-history sig-

nal enhancementmethod. Thesemethods were compared to a baselinedata acquisition

configuration, in which an FFT analyzer was usedto read the spectrum directly.

Each of tile three SEM's wasshown to be at least as accurate as the baseline. The

coherence-basedmethod wasshownto bequite efficient, and is recommendedasthe method

of choicefor caseswhereonly the magnitude component is required. The cross-spectrum-

basedmethod was shown to be quite robust, both in accuracy and efficiency. Although

not quite as efficient as the coherence-basedmethod, the cross-spectrum-basedmethod

provides the phasecomponent. It is thus recommendedas the 'work-horse' method for

regular data acquisition.

Because of instrumentation difficulties, the time-history signal enhancement method

was tested for only a few selected conditions. The results of this testing indicated that this

method is also capable of providing quality data. However, this method is time-consuming.

It is thus recommended that this method be used only when more than three microphones

are to be measured simultaneously.

References

1. Bendat, J.S.: "Statistical Errors in Measurement of Coherence Functions and In-

put/Output Quantities," Journal of Sound and Vibration, Vol. 59(3), 1978.

2. Bendat, J.S. and Piersol, A.G.: "Random Data: Analysis and Measurement Proce-

dures," Wiley-Interscience, 1971.

3. Meirovitch, L.: "Analytical Methods in Vibrations," The Macmillan Company, New

York, 1967.

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[] Sensor 2 .... Target 2

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.39 dB

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, , , , I , , , , I , , , , I , , , , I , , , , I , , , , I , I l l I , , , , I

1O0 200 300 400 500 600 700 800

Number of averages

0

0-o--o o o 0

143.82 deg

[]-£]-- - £]........ 13"................ 0 .................................... [], , , , I , , , , I .... I , , , , I , , , , I , , , , I ' ' ' ' I , , , , I

1O0 200 300 400 500 600 700 800

Number of averages

Figure 8. Comparison of extracted signals for two sensors using time historysignal enhancement method

' . ,' i ,¸

REPORT DOCUMENTATION PAG E FormApprovaaOM B No. 0704-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data

soumos, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other

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Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the OIfice of Management and Budget, Paperwork Reduction Project (0704-0188),

Washington, DC 20503.

1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

May 1998 Technical Memorandum

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

A Comparison of Signal Enhancement Methods for Extracting TonalAcoustic Signals WU 538-03-12-02

6.AUTHOR(S)Michael G. Jones

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research CenterHampton, VA 23681-2199

9. SPONSORING/MONITORINGAGENCYNAME(S)ANDADDRESS(ES)

National Aeronautics and Space AdministrationWashington, DC 20546-0001

8. PERFORMING ORGANIZATION

REPORT NUMBER

L-17736

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA/TM-1998-208426

11. SUPPLEMENTARY NOTES

12a.DISTRIBUTION/AVAILABILITYSTATEMENT

Unclassified-Unlimited

Subject Category 71 Distribution: NonstandardAvailability: NASA CASI (301) 621-0390

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

The measurement of pure tone acoustic pressure signals in the presence of masking noise, often generated by

mean flow, is a continual problem in the field of passive liner duct acoustics research. In support of theAdvanced Subsonic Technology Noise Reduction Program, methods were investigated for conductingmeasurements of advanced duct liner concepts in harsh, aeroacoustic environments. This report presents theresults of a comparison study of three signal extraction methods for acquiring quality acoustic pressuremeasurements in the presence of broadband noise (used to simulate the effects of mean flow). The performanceof each method was compared to a baseline measurement of a pure tone acoustic pressure 3 dB above a uniform,broadband noise background.

14. SUBJECT TERMS

Signal Extraction; Signal-to-Noise Ratio; Coherence; Cross-Spectrum;

Signal Enhancement

17. SECURITY CLASSIFICATION

OF REPORT

Unclassified

18. SECURITY CLASSIFICATION

OF THIS PAGE

Unclassified

19. SECURITY CLASSIFICATION

OF ABSTRACT

Unclassified

15. NUMBER OFPAGES

30

16. PRICE CODE

A03

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OFABSTRACT

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-8 ¢

Prescribed by ANSI Std. Z-39-18298-102

26