aeroacousticsvolume 9 · number 6 · 2010

Comparison of microphone arrayprocessing techniques for aeroacoustic

measurementsby

Tarik Yardibi, Nikolas S Zawodny, Chris Bahr, Fei Liu, Louis NCattafesta III and Jian Li

reprinted from

published by MULTI-SCIENCE PUBLISHING CO. LTD., 5 Wates Way, Brentwood, Essex, CM15 9TB UK

E-MAIL: mscience@globalnet.co.ukWEBSITE: www.multi-science.co.uk

aeroacoustics volume 9 · number 6 · 2010 – pages 733–762 733

Comparison of microphone arrayprocessing techniques for aeroacoustic

measurements

Tarik Yardibi*, Nikolas S Zawodny†, Chris Bahr‡, Fei Liu§

Louis N Cattafesta III¶ and Jian Li ||

*Department of Electrical and Computer Engineering, Email: ytarik@dsp.ufl.edu†Department of Mechanical and Aerospace Engineering, Email: nzawodny@ufl.edu

‡Department of Mechanical and Aerospace Engineering, Email: cbahr@ufl.edu§Department of Mechanical and Aerospace Engineering, Email: lfeicq@ufl.edu

||Department of Electrical and Computer Engineering, Email: li@dsp.ufl.edu University of Florida,

Gainesville, FL, 32603

Received November 18, 2009; Revised March 12, 2010; Accepted April 15, 2010

ABSTRACTThis paper presents a systematic comparison of several prominent beamforming algorithmsdeveloped for aeroacoustic measurements. The most widely used delay-and-sum (DAS) beamformeris known to suffer from high sidelobe level and low resolution problems. Therefore, moreadvanced methods, in particular the deconvolution approach for the mapping of acoustic sources(DAMAS), sparsity constrained DAMAS (SC-DAMAS), covariance matrix fitting (CMF) andCLEAN based on spatial source coherence (CLEAN-SC), have been considered to achieveimproved resolution and more accurate signal power estimates. The performances of theaforementioned algorithms are evaluated via experiments involving a 63-element logarithmicspiral microphone array in the presence of a single source, two incoherent sources with similarstrengths and with different strengths, and two coherent sources. It is observed that DAMAS, SC-DAMAS and CMF provide the most reliable source location estimates, even at relatively lowfrequencies. Furthermore, the integrated levels obtained with the array processing algorithms areshown to agree with what a single reference microphone placed at the center of the arraymeasures when the array is appropriately calibrated. It is also shown that, as expected, theaforementioned algorithms are unsuccessful in distinguishing coherent acoustic sources unlessthe frequency is relatively high. DAS and CLEAN-SC are shown to be around 2 to 90 times fasterthan the other three algorithms.

¶Corresponding Author, Department of Mechanical and Aerospace Engineering, University of Florida,Gainesville, FL, 32603 Email: cattafes@ufl.edu

734 Comparison of microphone array processing techniques

for aeroacoustic measurements

1. INTRODUCTIONVarious microphone array processing algorithms have been developed for noise sourcelocalization and power estimation in aeroacoustic measurements. The pioneer of thesetechniques is the delay-and-sum (DAS) beamforming algorithm [1], [2], [3], [4], which,as its name suggests, sums the delayed and weighted versions of each microphone signalin the time domain (or, equivalently, applies appropriate phase shifts and weights in thefrequency domain) so that the signals from a desired acoustic source are addedconstructively while the signals from other sources are not. This simple idea yieldsreliable beamforming maps when the sources are well separated (the required separationbetween the sources depends on the frequency, array aperture size and relative sourcestrengths). However, in the presence of, for instance, closely placed sources (closer thanthe 3-dB beamwidth of the array), the DAS beamforming maps might be misleading.

An important observation about the DAS beamformer is that the DAS powerestimate of a given source is actually the sum of the true signal power of the source andthe interferences from other sources, due to the convolution of the array’s point spreadfunction with the source field. For a well-designed array with a dominant central peakin the point spread function, the interference term diminishes as the distance betweenthe source of interest and the interfering sources gets larger and/or as the frequencyincreases (or, in a similar manner, as the array aperture size increases). However, theinterference can be as dominant as the signal-of-interest under certain scenarios, inwhich case the DAS performance degrades significantly. In order to mitigate thedrawbacks of DAS, a novel postprocessing technique called the deconvolution approachfor the mapping of acoustic sources (DAMAS) [5], which is the precursor to many otherdeconvolution techniques, was devised. DAMAS attempts to deconvolve the true signalpowers from the DAS results by constructing and iteratively solving a linear system ofequations that relate the DAS estimates to the true signal powers. DAMAS2 andDAMAS3 [6] offer alternatives and extensions to DAMAS by making use of efficientfast Fourier transform (FFT) operations and assuming that the point spread function isshift-invariant. Sparsity contrained DAMAS (SC-DAMAS) [7] and covariance matrixfitting (CMF) [7] make use of convex optimization and sparsity to achieve comparableperformance with DAMAS in a shorter amount of time. CLEAN-SC [8] is anotherwidely used beamforming algorithm. The most important features distinguishingCLEAN-SC from the other algorithms mentioned previously is that CLEAN-SC doesnot assume the true steering vectors are known and attempts to estimate them from themeasurements, and it does not assume incoherent sources.

The purpose of this paper is to provide a systematic comparison of DAS, DAMAS,SC-DAMAS, CMF and CLEAN-SC using primarily experiments but also simulationsto support the experimental observations. After presenting a general picture of thebeamforming process and the aforementioned beamforming algorithms in Section II,experimental results are provided in Section III. The experiments considered include:1) a single source, 2) two incoherent sources with similar powers and with differentpowers, as well as 3) two coherent sources. Analyzing such test cases, where the correctanswer is known, is valuable in terms of evaluating the true performance of the variousbeamforming algorithms. The source localization and absolute level estimationcapabilities of the algorithms are investigated (the absolute levels estimated by the

aeroacoustics volume 9 · number 6 · 2010 735

beamforming algorithms are compared with those measured by a reference microphoneplaced at the center of the microphone array).

In the following, vectors and matrices are denoted by boldface lowercase andboldface uppercase letters, respectively. Other mathematical symbols are defined aftertheir first appearance. All sound pressure levels (SPLs) presented are in dB re. 20 µPa.

2. BEAMFORMING IN AEROACOUSTIC MEASUREMENTS2.1. PreliminariesThe very first step of every beamforming algorithm considered in this paper is thecomputation of the cross spectral matrix (CSM). For this purpose, first, the pressuretime record of each microphone is divided into B blocks (which might be overlapping).Then, the FFT of each block is computed after applying a suitable spectral window [9].Let the resulting frequency domain pressure data at the mth microphone and at the bth

block be denoted as ym(f , b), where m = 1,…, M, b = 1,…, B, f is the frequency andM is the number of array microphones [10], [11]. Each element of the CSM is computedvia sample averaging as follows [12], [13], [14]:

(1)

where Gm,n denotes the element in the mth row and nth column of the M × M CSMG(f ), and (·)* denotes the complex conjugate of the argument. Beamforming is usuallydone independently at each narrow-band frequency of interest and therefore in thefollowing analysis, the dependence of the variables on f will not be explicitly indicated.

Since the locations of the sources are unknown in practice, a scanning grid thatcovers a region of interest with a certain resolution is formed and every point of this gridis considered as a potential source whose corresponding sound pressure level at the arraycenter will be estimated. This results in a beamforming map representing the acousticsource distribution in the region of interest. In the following, the scanning points areindexed from l = 1,…, L, where L is the total number of scanning points (see Figure 1).

2.2. DASThe standard DAS power estimate at the l th scanning point is given by [1], [2] (P̂l denotesthe estimate of Pl )

(2)

where

(3)

rl,0 and rl,m are the distances from the l th scanning point to the array center and the mth

microphone, respectively, k is the wavenumber, and (·)T and (·)H denote the transpose

% Kall

l

jkr

l M

jkr

rr e r el l M=

− −1

0

11

,

,[ , , ] ,, ,

,

T

ˆ , , , ,( )P

Ml Ll l

Hl

DAS = =1

12

% % Ka Ga

Gm,n( ) ( , ) ( , ), , , ,fB

y f b y f b m n Mm nb

B

= =∗

=∑1

11

K ,,

736 Comparison of microphone array processing techniques

for aeroacoustic measurements

and conjugate transpose, respectively. The phase terms in a∼l are used to align themeasurements from each microphone so that the contribution from the scanning pointof interest is summed constructively, while the contributions from other points tend tocancel. Note that in deriving Eqn. (2), the spherical wave propagation model is used andthe sources are assumed to be monopoles. The purpose of normalizing a∼l in Eqn. (3) byrl,0 is to match the estimated signal powers to what a single microphone in the center ofthe array would measure.

Under the incoherence assumption of the sources, it can be shown that [5], [7],

(4)

where

(5)

and Pl is the unknown signal power of the source at the l th scanning point. In otherwords, the DAS signal power estimate at a scanning point is a linear combination of the

al

jkr

l

jkr

l MTe r e rl l M=

− −[ / , , / ] ,

, ,

, ,1

1K

ˆ , , , ,( )P

MP l Ll l

Hl l

l

LDAS = =′ ′

′=∑1

12

2

1

% Ka a

z

1 2

L

y

x

Array

r1, m

Scanning region

Figure 1: A logarithmic spiral planar microphone array extending in the xy -planewith M microphones (shown by the circles). The power at each scanninggrid point (indexed from 1 to L and represented by squares) is estimatedto obtain a beamforming map (or image).

aeroacoustics volume 9 · number 6 · 2010 737

signal powers at every scanning point (where the contributions from all points exceptthe scanning point of interest are actually undesired). The coefficients of this linear

system, which are also called the array point spread function PSF(l), are a

function of frequency and the array layout. Since PSF(l), l = 1,…, L, are known, moreclever methods can be used to deconvolve the true signal powers from the DAS resultsas described below.

2.3. Advanced algorithmsDAMAS attempts to estimate the true signal powers from the contaminated DAS results by constructing a linear system of equations that relate the DASestimates at every scanning point to the signal powers at every scanning point [5].The matrix involved in this linear system is ill-conditioned which makes directmatrix inversion impractical. DAMAS utilizes the iterative Gauss-Seidel method [5]by also enforcing the non-negativity of each power estimate to solve this linearsystem. A potential drawback of the Gauss-Seidel method is computation time; thenumber of iterations required by this method to converge can be on the order ofthousands. Sparsity constrained DAMAS (SC-DAMAS) [7] offers an alternative wayof solving the DAMAS inverse equation by exploiting sparsity and using convexoptimization. SC-DAMAS was shown to provide comparable results with DAMASand converge faster [7]. Another alternative to DAMAS is the covariance matrixfitting approach (CMF) [7], which uses the CSM directly instead of the DAS resultsto estimate the signal powers. Similar to SC-DAMAS, CMF is based on convexoptimization and also leverages sparsity. Aside from the aforementioneddeconvolution algorithms, CLEAN based on spatial source coherence (CLEAN-SC)is another widely-used method which, unlike the above algorithms, does not assumethe true steering vectors, i.e., al , to be known. Instead, CLEAN-SC iteratively buildsup the steering vectors corresponding to the dominant sources using the previouslyestimated signal powers and assuming that the sidelobes are coherent with the peakfor a given source. After estimating the steering vectors and the signal powers,CLEAN-SC constructs a clean image of the scanning region similar to the CLEANalgorithm [15], which was originally proposed for astronomy applications. Thereader is referred to the corresponding papers for the detailed derivations anddiscussions of these algorithms.

After determining the scanning grid (resolution and number of grids), the user mightneed to set some parameters with DAMAS, SC-DAMAS, CMF and CLEAN-SC.DAMAS is based on an iterative algorithm and the number of iterations has to bedetermined by the user. In our examples, it was observed that the DAMAS results didnot change significantly after 5,000 iterations and hence throughout the paper, 5,000DAMAS iterations have been implemented. SC-DAMAS and CMF do not require theuser to determine any additional parameters (unless a fast version of SC-DAMAS isimplemented, in which case, one parameter is introduced with SC-DAMAS asdescribed in Section IV). CLEAN-SC requires the selection of a loop gain parameter, aspatial clean beam width to replace the point estimates, number of iterations to run

| | ,%a alH

l ′2

738 Comparison of microphone array processing techniques

for aeroacoustic measurements

CLEAN-SC and also the number of iterations to run a nested iterative algorithm toestimate the steering vectors. (The parameter settings recommended in the CLEAN-SCpaper [8] have been used in our analysis.)

2.4. Absolute levelsThe absolute signal power of a source is estimated by using an integration method withDAS, DAMAS, SC-DAMAS, and CMF, whereas CLEAN-SC uses the clean spectrumit constructs to estimate the signal power. With DAS, the integrated level is computedby summing the DAS power estimates inside the integration region (which is within thescanning region) and normalizing the result by a scaling factor obtained by summingthe PSF values (obtained for a source at the center of the integration region) over thesame integration region [16], [17]. Stated mathematically, the integrated DAS level isdefined as

(6)

where L {1,…, L} is a set containing the indices of the scanning points within theintegration region [16], [17]. With DAMAS, SC-DAMAS and CMF, there is no needfor the normalization since the array response is already eliminated from the results andonly summing the estimated power levels within the integration region suffices toestimate absolute levels. As a post-processing step, after deriving the source levelestimates, CLEAN-SC uses the average of the diagonal of the clean CSM that it modelsby considering only the contributions from sources within the integration region toestimate integrated levels (see Section 2.5. in [8]). The integration region is chosen suchthat it covers the source region of interest and some portion of the sidelobes dependingon the frequency [16].

2.5. Array calibrationThere are many sources of uncertainty in the beamforming process; for instance,measurement errors in microphone locations and temperature (through its effect on thewavenumber, etc.) can have major effects on the assumed steering vectors, especially atrelatively high frequencies [10], [11]. To mitigate such errors, the widely-used calibrationprocedure introduced by Dougherty [2], which attempts to match the assumed steeringvectors to the experimentally measured ones in a well-controlled setup, is employed inthis paper. The calibration setup consists of a speaker that resembles a point source andis driven with a broadband signal (or a tonal signal where the tone frequency is varied).In this way, a complex correction factor for each microphone is obtained at eachnarrow-band frequency. The calibration procedure also results in an overall arraycorrection factor (again at each frequency), which is used to match the array estimatedsignal power levels to what a single reference microphone placed at the center of thearray measures [2].

⊆

Σ

Σl l

l

P

l∈

∈

L

L

ˆ

( ),

( )DAS

PSF

aeroacoustics volume 9 · number 6 · 2010 739

3. EXPERIMENTAL DATA ANALYSISThis section evaluates the performance of DAS, DAMAS, SC-DAMAS, CMF andCLEAN-SC in estimating the locations and the integrated SPLs of the test sources underdifferent scenarios.

3.1. Microphone arrayThe microphone array used in our experiments is the large aperture microphonedirectional array (LAMDA), which is a zero-redundancy logarithmic spiral aperturearray built on a 1.82 m diameter rigid aluminum plate, that consists of 90 flush-mountedPanasonic WM-61A electret microphones. LAMDA was designed by the proceduresdescribed by Underbrink [18], [19] and was fabricated for use at the University ofFlorida Aeroacoustic Flow Facility (UFAFF) [20]. The original LAMDA contains twonested spiral arrays: 1) a small aperture inner array consisting of 45 microphones and 2) a larger aperture outer array consisting of 63 microphones. Only the outer array,which is shown in Figure 2(a), is considered in this paper due to its higher resolution atrelatively low frequencies (the outer LAMDA array is simply referred to as LAMDA).Figure 2(b) shows the 3-dB beamwidth of the array versus frequency at an arraybroadband distance of 1.48 m. The perimeter of LAMDA was treated with an annularring of foam to mitigate scattering effects off of the edges. A 3.175 mm diameter Brueland Kjaer (B&K) type 4138 pressure-field microphone is placed at the center of thearray and referred to as the reference microphone throughout this paper. This referencemicrophone was calibrated using a B&K type 4228 pistonphone at 250 Hz. The arrayoutput levels will be compared with the levels measured by this reference microphone inthe following.

3.2. Experimental setupThe experimental data analyzed in this paper was acquired at the UFAFF using a 68-channel National Instruments PXI-1045 chassis with 17 NI PXI-4462 data acquisition(DAQ) cards [20]. Each channel has 24-bit resolution with 118 dB dynamic range. Allmeasurements were ac coupled with a -3 dB cut-on at 3.4 Hz, and appropriate anti-aliasing filters were applied.

The two acoustic sources used in the experiments were custom built using JBL type2426H speakers. An aluminium tube of inner diameter 0.03 m, outer diameter 0.04 mand length 0.52 m was attached at the output of each JBL speaker, and acoustic foamwas used to reduce reflections as shown in Figure 3(a). The measurements wereconducted without flow and consisted of two setups: one with a single speaker and onewith two speakers as shown in Figure 3(b) and (c), respectively. In the latter set ofexperiments, the powers of and the coherence between the sources are varied. Figure 4shows a 3D rendering of the test setup. Note that the inlet and diffuser were coveredwith acoustic foam to minimize any reflections (the test stand was also covered withfoam although it appears exposed in Figure 4).

The sampling frequency used in the measurements was 65,536 Hz and the blocklength was set to 4096 samples, resulting in a 16 Hz narrow-band bin width. The dataacquisition time was 15 seconds. A Hanning window with 75% overlap was applied to

each block of data before taking its FFT. The resulting number of blocks was 957 (498effective blocks [9]). The beamforming scanning regions are set from −0.3 m to 0.3 mwith a resolution of 0.03 m in both the x and y directions for the single sourceexperiments, and from −0.4 m to 0.2 m in the x direction and from −0.3 m to 0.3 m inthe y direction with a resolution of 0.025 m in both the x and y directions for the twosource experiments unless otherwise specified.

740 Comparison of microphone array processing techniques

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LAMDA with 63 micsReference B&K microphone80

(a)

(b)

y, c

m

60

40

20

0

−20

−40

−60

−80

−80 −60 −40 −20 0x, cm

20 40 60 80

0.6

0.5

0.4

0.3

0.2

3-dB

bea

mw

idth

(m

)

0.1

01 2 3 4 5 6

Frequency (kHz)

8 10 12 16

Figure 2: (a) The microphone layout of LAMDA. The solid circle shows thealuminum plate of LAMDA. A reference B&K microphone (not anelement of LAMDA) is included in the array center for comparisonpurposes. (b) The 3-dB beamwidth of LAMDA versus frequency.

3.3. Array calibration effectsConsider a calibration setup with a single source placed at (x, y, z) = (0,0,1.48) m,

where the array center is at (x, y, z) = (0,0,0) m and the array plate extends in the xy-plane. The integrated DAS levels are shown in Figure 5(a) alongside thereference microphone levels when array calibration is not applied1. When obtaining

aeroacoustics volume 9 · number 6 · 2010 741

JBLspeaker

Acousticfoam

0.03 m

0.52 m

z

1 1 2

z

x x

y y

1.48 m

0.2 m

1.48 m

LAMDA LAMDA0.91 m 0.91 m

1.82 m 1.82 m

(a)

(b) (c)

Figure 3: (a) Acoustic sources were custom built using JBL type 2426H speakers.(b) Setup 1 consists of a single source placed 1.48 m above the LAMDAplate. (c) Setup 2 consists of two sources placed 0.20 m apart.

113 narrow-band frequencies spaced uniformly in the logarithmic scale between 500 Hz and 12 kHz, i.e.,500 Hz, 652 Hz, 849 Hz, 1107 Hz, 1442 Hz, 1880 Hz, 2449 Hz, 3192 Hz, 4160 Hz, 5422 Hz, 7066 Hz,9208 Hz, and 12000 Hz, have been used in all of the integrated level versus frequency plots. Note that thesefrequencies have been rounded-off to the nearest frequency bin available.

this figure, the nominal sensitivities (30 mV/Pa as used at the UFAFF) of themicrophones were used for beamforming. It is observed that there are differences, aslarge as 5 dB, between the array estimated levels and the reference microphone levels.However, when array calibration is applied, the DAS integrated levels match thereference microphone levels as shown in Figure 5(b). This simple example shows thatarray calibration is essential for matching the array output levels to the referencemicrophone levels. The calibration procedure was also shown to be necessary forreducing the uncertainties in the beamforming levels when errors are expected inmicrophone locations and/or temperature [10]. Therefore, in the results presentedbelow, array calibration is always applied.

3.4. Single sourceConsider the experimental setup shown in Figure 3(b) with a single source generatingbroadband random noise at a distance of 1.48 m from the array. Figure 6 shows thebeamforming maps obtained with DAS, DAMAS, SC-DAMAS, CMF and CLEAN-SCfor this case together with the array PSF at 2 kHz. The integration region is indicatedwith the solid rectangle and the integrated (Int.) and maximum (Max.) levels are notedin the upper right corner of each plot. The true source location is indicated by the “x”mark. It is observed that all the algorithms recover the source location successfully andalso indicate consistent integrated levels with each other. In Figure 7 the integrated SPLsobtained with all the beamforming algorithms over a frequency range of 0.5 kHz to 12 kHzwith both simulated and experimental data is shown. In the simulations, circularly

742 Comparison of microphone array processing techniques

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Figure 4: Experiment configuration.

symmetric independent and identically distributed (i.i.d.) complex Gaussian randomvariables [13], [14] are used to generate the signal and measurement noise waveforms,which are then used to obtain the synthetic microphone measurements using thespherical wave propagation model [10], [21]. The simulated signal power is set to 50 dB,the measurement noise power is set to 30 dB and 498 effective blocks are used similarto the experimental scenario. It is observed that the integrated SPLs of all the algorithmsare in good agreement with the reference microphone SPLs with both simulated andacquired data.

aeroacoustics volume 9 · number 6 · 2010 743

1 2

Frequency (kHz)

Frequency (kHz)

SP

L (d

B r

ef. 2

0 µP

a)S

PL

(dB

ref

. 20

µPa)

3 4 5 6 7 8 910 1230

35

40

45

50

55(a)

(b)

B&KDAS

1 2 3 4 5 6 7 8 910 1230

35

40

45

50

55

B&KDAS

Figure 5: Comparison of DAS integrated levels with the reference B&K microphonelevels (a) without array calibration and (b) with array calibration.

3.5. Incoherent sourcesConsider the experimental setup shown in Figure 3(c) with two sources generatingincoherent broadband noise. Incoherent broadband noise was generated by feeding thetwo speakers with independent white noise signals from two different outputs of asingle function generator. Two scenarios are considered: in the first case, the speakersgenerate signals of similar powers and in the second case, the second speaker generatesa weaker signal than the first one. In Figure 8 the reference microphone levels when 1) only speaker 1 is on, 2) only speaker 2 is on, 3) both speakers are on and 4) thecomputed sum from 1) and 2) are plotted. In Figure 8(a), the powers of the two speakersare very similar; the average signal power over the entire frequency range is 47.7 dB forspeaker 1, 47.6 dB for speaker 2 and 50.8 dB for both speakers (computed sum is50.9 dB). In Figure 8(b), on the other hand, speaker 2 has lower power than speaker 1at most of the frequencies; the average signal power over the entire frequency range is

744 Comparison of microphone array processing techniques

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40

20

0

−20

−40

−40 −20

−1

−2

−3

−4

−5

−6

−7

−8

−9

−10

PSF, f = 2 kHz

0 20 40

0

x, cm

y, c

m

40

20

0

−20

−40

−40 −20

DAS

0 20 40x, cm

y, c

m

49

48

47

46

45

44

43

42

41

40

49

48

47

46

45

44

43

42

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40

y, c

m

40

20

0

−20

−40

−40 −20

DAMAS

0 20 40x, cm

y, c

m

40

20

0

−20

−40

−40 −20

SC-DAMAS

0 20 40x, cm

y, c

m40

20

0

−20

−40

−40 −20

CMF

0 20 40x, cm

y, c

m

40

20

0

−20

−40

−40 −20

CLEAN-SC

0 20 40x, cm

Max. = 49.3 dBInt. = 49.3 dB

Max. = 48.8 dBInt. = 49.4 dB

Max. = 48.8 dBInt. = 49.3 dB

Max. = 48.8 dBInt. = 49.4 dB

Max. = 49.3 dBInt. = 49.1 dB

−15

−15

−8−3

−3

−8−15

49

48

47

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40

49

48

47

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40

Figure 6: The array point spread function (levels in normalized dB) and thebeamforming images (levels in dB) obtained using DAS, DAMAS, SC-DAMAS, CMF and CLEAN-SC for a single source located at a distanceof 1.48 m from the array center (setup 1). The integration region isindicated with the solid rectangle, and the integrated (Int.) and maximum(Max.) levels are shown in the upper right corner of each plot. The truesource location is indicated by the “x” mark. Beamforming frequency is2 kHz and the reference microphone level is 49.4 dB. The results areobtained using experimental data.

49.0 dB for speaker 1, 43.8 dB for speaker 2 and 50.3 dB for both speakers (computedsum is 50.4 dB). From Figure 8, it is observed that the computed sum matches themeasured levels, especially for frequencies above approximately 800 Hz. This showsthat the speakers are indeed incoherent for those frequencies.

In Figures 9 and 10, the beamforming maps obtained with similar signal powers anddifferent signal powers, respectively, are shown at a frequency of 2 kHz (the estimatedpower levels at the true source locations are also noted in the beamforming maps). It isobserved that DAS is unable to resolve the sources in both cases, whereas DAMAS,

aeroacoustics volume 9 · number 6 · 2010 745

1 2

SP

L (d

B r

ef. 2

0 µP

a)

3

Frequency (kHz)

4 5 6 7 8 910 1235

40

45

50

55(a)

(b)

B&KDASDAMASSC-DAMASCMFCLEAN-SC

1 2

SP

L (d

B r

ef. 2

0 µP

a)

3

Frequency (kHz)

4 5 6 7 8 910 1235

40

45

50

55

B&KDASDAMASSC-DAMASCMFCLEAN-SC

Figure 7: Comparison of the beamformer integrated levels with the reference B&Kmicrophone levels for a single source located at a distance of 1.48 m fromthe array center (setup 1). (a) Simulated data and (b) experimental data.

SC-DAMAS and CMF can distinguish the sources successfully. The estimated powerlevels for the two sources are similar in Figure 9 and the estimated power level for thesecond source is lower than that of the first one in Figure 10 with DAMAS, SC-DAMAS and CMF, as desired. CLEAN-SC, on the other hand, identifies the locationsof both of the sources and the location of the weaker source inaccurately in Figure 9and Figure 10, respectively (it was observed in results not shown here that at higher

746 Comparison of microphone array processing techniques

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1 2

SP

L (d

B r

ef. 2

0 µP

a)

3Frequency (kHz)

4 5 6 7 8 910 1230

35

45

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60(a)

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L (d

B r

ef. 2

0 µP

a)

3Frequency (kHz)

4 5 6 7 8 910 1230

35

45

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50

55

60(b)

Spk 1 onlySpk 2 onlyComputed sumBoth spks on

Spk 1 onlySpk 2 onlyComputed sumBoth spks on

Figure 8: The reference microphone levels when the speakers generate signals with(a) similar powers and (b) different powers. The levels when either one ofthe speakers is on and both of the speakers are on are shown together withthe computed sum of the levels obtained when either one of the speakersis on. The results are obtained using experimental data.

frequencies, CLEAN-SC was able to recover the locations of both of the sourcesaccurately). The integrated levels obtained with the beamforming algorithms are shownin Figure 11. It is observed that all the algorithms yield very similar integrated levelswith each other and follow the trend measured by the reference microphone (note thatthe array levels do not match the reference microphone levels as good as in Figure 7(b)since in that case the calibration and test schemes were identical). Although CLEAN-SC is unable to recover the second source location very accurately, its integrated levelestimates agree with those of the other algorithms.

Next, the accuracy of the advanced beamforming algorithms in estimating the signalpowers of the two sources individually is considered. For this purpose, the integrationregion for estimating the signal power of the first source (Reg. 1) and the integrationregion for estimating the signal power of the second source (Reg. 2) are defined asshown in Figure 12. In Figure 13(a) is shown the integrated levels (computed using

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40

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−1

−2

−3

−4

−5

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−8

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PSF, f = 2 kHz

0 20 40

0

x, cm

y, c

m40

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Max. = 49.7 dBInt. = 51.2 dB

Max. = 47.2 dBInt. = 51.9 dB

Max. = 47.4 dBInt. = 51.9 dB

Max. = 47.3 dBInt. = 51.9 dB

Max. = 45.6 dBInt. = 51.7 dB

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Figure 9: The array point spread function (levels in normalized dB) and thebeamforming images (levels in dB) obtained using DAS, DAMAS, SC-DAMAS, CMF and CLEAN-SC for two incoherent sources with similarpowers located 0.20 m apart from each other (setup 2). The integrationregion is indicated with the solid rectangle, and the integrated (Int.) andmaximum (Max.) levels are shown in the upper right corner of each plot.The true source locations are indicated by the “x” marks. Beamformingfrequency is 2 kHz and the reference microphone level is 52.6 dB. Theestimated power levels at the true source locations are also noted in thebeamforming maps. The results are obtained using experimental data.

Reg. 1) obtained with DAS and SC-DAMAS when only speaker 1 is on and when bothspeakers are on. Similarly, in Figure 13(b) is shown the integrated levels (computedusing Reg. 2) when only speaker 2 is on and when both speakers are on. The referencemicrophone levels obtained when either one of the speakers is on are also plotted inthese two figures. From Figures 13(a) and (b), it is observed that SC-DAMAS levelsobtained when only one of the speakers is on are consistent with the levels obtainedwhen both speakers are on and the integration region covers only the source of interest.On the other hand, for DAS, due to low resolution, these levels do not coincide well forfrequencies lower than about 2 kHz. Especially from Figure 13(b), it is observed thatDAS performs poorly when estimating the power of the second (the weaker) sourcesince the sidelobes from the stronger source are causing the DAS estimates to be largerthan the true signal power. It is also observed that the array levels match the reference

748 Comparison of microphone array processing techniques

for aeroacoustic measurements

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Max. = 50.5 dBInt. = 50.9 dB

Max. = 48.1 dBInt. = 51.5 dB

Max. = 48.7 dBInt. = 51.5 dB

Max. = 48.6 dBInt. = 51.5 dB

Max. = 49.7 dBInt. = 51.3 dB

−15

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50.546.9 44.6 48.1

48.743.9 44.6 48.6 37.3 49.7

Figure 10: The array point spread function (levels in normalized dB) and thebeamforming images (levels in dB) obtained using DAS, DAMAS, SC-DAMAS, CMF and CLEAN-SC for two incoherent sources withdifferent powers located 0.20 m apart from each other (setup 2). Theintegration region is indicated with the solid rectangle, and the integrated(Int.) and maximum (Max.) levels are shown in the upper right corner ofeach plot. The true source locations are indicated by the “x” marks.Beamforming frequency is 2 kHz and the reference microphone level is52.3 dB. The estimated power levels at the true source locations are alsonoted in the beamforming maps. The results are obtained usingexperimental data.

aeroacoustics volume 9 · number 6 · 2010 749

microphone levels better in Figure 13(a) (with the stronger source) than in Figure 13(b)(with the weaker source). The results with DAMAS and CMF are similar to thoseobtained with SC-DAMAS, whereas the CLEAN-SC results are slightly worse thanDAMAS, SC-DAMAS and CMF but better than DAS (these results are not shown forthe sake of brevity).

Frequency (kHz)

SP

L (d

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ef. 2

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(a)

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B&KDASDAMASSC-DAMASCMFCLEAN-SC

B&KDASDAMASSC-DAMASCMFCLEAN-SC

Figure 11: Comparison of the beamformer integrated levels with the referencemicrophone levels for two incoherent sources located 0.20 m apartfrom each other (setup 2). (a) The two sources are of similar powers in (a) and the source at (x, y) = (0, 0) m is stronger than the source at(x, y) = (−0.20, 0) m in (b). The results are obtained usingexperimental data.

3.6. Coherent sourcesConsider the experimental setup shown in Figure 3(c) again with two speakers but nowgenerating coherent broadband noise, which is accomplished by feeding the speakerswith a single white noise waveform (this is done by using a T connection at the outputof the function generator). Figures 14(a) and (b) show the SPLs measured by thereference microphone and the LAMDA microphones when the two sources areincoherent with similar powers (the same example considered in Figure 8(a)) and whenthe two sources are coherent, respectively. From these two figures, it is observed that thesound spectra of the LAMDA microphones become very different at frequencies above2 kHz in the latter case. To further elaborate on this, the SPLs over the array face at asingle arbitrary frequency of 6 kHz are plotted in Figure 15. It is observed thatsignificant signal cancellation is encountered over the array face when the sources arecoherent. A discussion on this issue is presented below.

Figure 16 shows the beamforming maps obtained with two coherent sources at 2 kHz, where it is observed that all of the algorithms fail to distinguish the twocoherent sources. DAS and CLEAN-SC indicate a single source approximately in themiddle of the true source locations. Although SC-DAMAS and CMF identify twodominant sources, the locations are inaccurate. Figure 17 shows the beamformingmaps at 4 kHz for the coherent sources case. It is observed that all the beamformingalgorithms except CLEAN-SC can now identify the source locations relatively moreaccurately. Since CLEAN-SC is based on removing the correlated source componentswith the peaks in the beamforming map, it only identifies one of the coherent sourcesregardless of the frequency and treats the sidelobes due to the identified source as othercoherent sources.

750 Comparison of microphone array processing techniques

for aeroacoustic measurements

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Figure 12: Integration region 1 (Reg. 1) and integration region 2 (Reg. 2) are usedwhen estimating the power of the first source and the second source,respectively.

aeroacoustics volume 9 · number 6 · 2010 751

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DAS, only spk 1 onSC-DAMAS, only spk 1 onDAS, both spks onSC-DAMAS, both spks on

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B&K, only spk 2 on

Figure 13: Comparison of the DAS and SC-DAMAS integrated levels with thereference microphone levels for two incoherent sources with differentpowers located 0.20 m apart from each other (setup 2). (a) DAS and SC-DAMAS integrated levels for source 1 (calculated over Reg. 1) are shownwhen only speaker 1 is on and when both speakers are on. The referenceB&K microphone levels are shown when only speaker 1 is on. (b) Sameas (a) but for speaker 2. The results are obtained using experimental data.

In Figure 18 the integrated levels are shown using both simulated and experimentaldata. In the simulations, the signals originating from the two speakers are generated asidentical waveforms and the signal power of each source is set to 50 dB. It is observedthat all the beamforming algorithms still yield consistent results with each other butdifferent from the reference microphone, especially above 5 kHz. In fact, the referencemicrophone level decreases with frequency (with both simulations and experiments),whereas the array estimates do not.

752 Comparison of microphone array processing techniques

for aeroacoustic measurements

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Figure 14: The sound pressure levels measured by the reference B&K microphoneand the LAMDA microphones when the two sources are (a) incoherentwith similar powers and (b) coherent.

To understand this phenomenon more clearly, consider the measurement of the mth

microphone, which, under the spherical wave propagation model, is given by [10], [21]

ym(b) = exp(−jkr1,m)/r1,ms1(b) + exp(−jkr2,m)/r2,ms2(b), b = 1, …, B, (7)

in the presence of only two sources and no contaminating noise, where s1(b) and s2(b)are the signal waveforms corresponding to the first and second sources, respectively, and

aeroacoustics volume 9 · number 6 · 2010 753

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Figure 15: The sound pressure level distribution over the array face at 6 kHz whenthe two sources are (a) incoherent with similar powers and (b) coherent.The microphones are indicated by the black circles.

at block b. When the two speaker waveforms are identical, i.e., when s1(b) = s2(b) forb = 1, …, B (the two waveforms might differ in practice due to disparities in wiring,speakers and so on), then

(8)

In Figure 19(a), the autospectra of all the microphones and the reference microphone,

i.e., for m = 0, …, M, where m = 0 corresponds to the reference

microphone, is plotted. In this figure, s1(b), b = 1, …, B, (which is equal to s2(b)) aresimulated as circularly symmetric i.i.d. complex Gaussian random variables with zero

1 2

1B y bmb

B| ( )|

=∑

y b jkr r jkr rm m m m m( ) (exp( )/ exp( )/ ), , , ,

= − + −1 1 2 2

ss b

jkr r jkr rm m m m

1

1 1 2 2

( )

(exp( )/ exp( )/, , , ,

= − + − )) ( ).s b2

754 Comparison of microphone array processing techniques

for aeroacoustic measurements

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Max. = 55.7 dBInt. = 55.9 dB

Max. = 48.4 dBInt. = 56.3 dB

Max. = 52.7 dBInt. = 56.1 dB

Max. = 51.6 dBInt. = 56.1 dB

Max. = 55.7 dB Int. = 55.8 dB

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Figure 16: The array point spread function (levels in normalized dB) and thebeamforming images (levels in dB) obtained using DAS, DAMAS, SC-DAMAS, CMF and CLEAN-SC for two coherent sources located 0.20 mapart from each other (setup 2). The integration region is indicated withthe solid rectangle, and the integrated (Int.) and maximum (Max.) levelsare shown in the upper right corner of each plot. The true source locationsare indicated by the “x” marks. Beamforming frequency is 2 kHz and thereference microphone level is 58.2 dB. The results are obtained usingexperimental data.

mean and unit variance for B = 498. Note that is

normalized so that the signal power is 50 dB. It is observed that the coherence of thesources induces an interference pattern on the array surface and each microphoneencounters significant signal cancellation at different frequencies. The reason why the array levels do not decrease as fast as the reference microphone level in Figure 18 isbecause there is always a set of microphones in the array which do not encounter severecancellation and these microphones help keep the array output estimate larger than thereference microphone level.

In Figure 19(b), the simulated and measured autospectrum of a single LAMDAmicrophone located at (x, y, z) = (−0.56, 0.02, 0) m is shown. It is observed that theexperimental data approximately matches the simulated pattern, especially forfrequencies above approximately 2.5 kHz. This serves as a justification that theinterference pattern observed at the array microphones is in fact due to the coherence of

and | ( )|12

2

1B s bb

B

=∑( )11

2

1B s bb

B| ( )|

=∑

aeroacoustics volume 9 · number 6 · 2010 755

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Max. = 53.7 dBInt. = 56.7 dB

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Max. = 49.9 dBInt. = 56.7 dB

Max. = 53.7 dBInt. = 56.4 dB

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Figure 17: The array point spread function (levels in normalized dB) and thebeamforming images (levels in dB) obtained using DAS, DAMAS, SC-DAMAS, CMF and CLEAN-SC for two coherent sources located 0.20 mapart from each other (setup 2). The integration region is indicated withthe solid rectangle, and the integrated (Int.) and maximum (Max.) levelsare shown in the upper right corner of each plot. The true source locationsare indicated by the “x” marks. Beamforming frequency is 4 kHz and thereference microphone level is 58.3 dB. The results are obtained usingexperimental data.

the sources. When the two sources are incoherent, the autospectrum of ym(b) (see Eqn. (7))does not contain the cross term between the two sources and hence the exponentialterms do not have an effect on the outcome (since they will be cancelled out after beingmagnitude squared), whereas when the sources are highly correlated, the exponentialterms come into play. In fact, all the curves in Figure 19(a) become straight lines at thesame level when the sources are incoherent (results not shown for brevity).

756 Comparison of microphone array processing techniques

for aeroacoustic measurements

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Figure 18: Comparison of the beamformer integrated levels with the referencemicrophone levels for two coherent sources located 0.20 m apart fromeach other (setup 2). (a) Simulated data and (b) experimental data.

The performance of all of the beamforming algorithms degrade significantly in thepresence of coherent sources and alternative approaches such as DAMAS for correlatedsources (DAMAS-C), CMF for correlated sources (CMF-C), or mapping of acousticcorrelated sources (MACS) should be used in the presence of coherent sources [7], [22],[23]. (Note that MACS was shown to effectively resolve the coherent sources analyzedin Section III-F.)

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Figure 19: (a) The directivity induced by two coherent sources at all arraymicrophones (using simulated data). (b) The comparison of the simulateddirectivity with the measured directivity of a single LAMDA microphone.

4. COMPUTATIONThis section elaborates on the computational complexities of the beamformingalgorithms. Table I shows the computation times required by each algorithm for the twodifferent scanning region settings used when analyzing the test cases (see SectionIII-B). It is observed that DAS and CLEAN-SC are the fastest algorithms followed bySC-DAMAS, CMF and DAMAS.

One advantage of SC-DAMAS over DAMAS and CMF is that when deconvolvingthe signal powers, the DAS data reduction equation can be evaluated at fewer points,say L0, than L (L0 < L) while still being able to estimate the powers at all the L gridpoints [7]. Note that in all the above examples, SC-DAMAS has been implemented withL0 = L and another selection for L0 < L would add a user parameter to the algorithmas mentioned in Section II-C. A rule of thumb is to select the scanning grid resolutionto be at most half the 3-dB beamwidth of the array at a given frequency. The resultsobtained using the fast version of SC-DAMAS for the single source (L0 /L = 0.38) andtwo incoherent sources (L0 /L = 0.27) with similar powers case are shown in Figure 20

758 Comparison of microphone array processing techniques

for aeroacoustic measurements

Table I: Computation times (in seconds) on a personal computer (2.53 GHzprocessor and 3 Gbytes of RAM). SC-DAMAS

(Fast) is the sped up version of SC-DAMAS with L0 = 169.

SC-DAMAS No. of grids DAS DAMAS SC-DAMAS CMF CLEAN-SC (Fast) 441 0.3 78.0 12.3 69.2 1.2 4.2625 0.6 138.0 31.8 123.5 1.6 11.6

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Figure 20: The beamforming maps obtained using the fast SC-DAMAS. (a) For asingle source located at a distance of 1.48 m from the array center (setup 1)with L0 /L = 0.38. Compare to Figure 6. (b) For two incoherent sourceswith similar powers located 0.20 m apart from each other (setup 2) withL0 /L = 0.27. Compare to Figure 9.

(compare with the SC-DAMAS images in Figures 6 and 9, respectively). Note that theperformance of SC-DAMAS did not degrade significantly compared to using all the Lgrid points when evaluating DAS. The computation time required by SC-DAMAS bysetting the resolution to 0.05 m (which is approximately l/5th the 3-dB beamwidth of thearray at 2 kHz) is also given in Table I.

5. CONCLUSIONSIn this paper the performances of DAS, DAMAS, SC-DAMAS, CMF and CLEAN-SChave been compared using simulations and experiments consisting of a single source,two incoherent sources of similar and of different powers, as well as two coherentsources. It has been observed that DAMAS, SC-DAMAS and CMF yield the mostreliable source location estimates. When the integration region encompasses both of thesources, the integrated levels obtained by all the algorithms have been shown to collapsewith the reference microphone levels over a frequency range from 0.5 kHz to 12 kHz.On the other hand, when individual source levels are being estimated, it was shown thatthe advanced beamforming algorithms outperform DAS. It has been shown that withcoherent sources, none of the algorithms can distinguish the sources unless thefrequency is high (in which case all algorithms except CLEAN-SC were shown tolocalize the sources reasonably well). It has also been shown that the coherence of thesources results in severe signal cancellation over the array face. Finally, DAS andCLEAN-SC have been shown to be fastest in terms of computation followed by SC-DAMAS, CMF and DAMAS.

ACKNOWLEDGEMENTSThis work was supported by NASA under Grant No. NNX07AO15A. The authorswould like to thank Alberto Gordon, Tom Kennedy and Adam Edstrand of theUniversity of Florida for their assistance on wind tunnel testing.

REFERENCES[1] Humphreys, W. M., Brooks, T. F., Hunter, W. W., and Meadows, K. R., “Design

and use of microphone directional arrays for aeroacoustic measurements,” 4thAIAA/CEAS Aeroacoustics Conference, AIAA-98-0471, Reno, NV, Jan 1998.

[2] Dougherty, R. P., “Beamforming in Acoustic Testing”, Aeroacousticmeasurements, Edited by T. J. Mueller, Springer, 2002, pp. 63–97.

[3] Meadows, K. R., Brooks, T. F, Humphreys, Jr., W. M., Hunter, W. W., andGerhold, C. H., “Aeroacoustic measurements of a wing-flap configuration,” 3rdAIAA/CEAS Aeroacoustics Conference, AIAA-97-1595, Atlanta, GA, May 1997.

[4] Dougherty, R. P., “Advanced Time-domain Beamforming Techniques,” 10thAIAA/CEAS Aeroacoustics Conference, AIAA-2004-2955, Manchester, UK, May2004.

[5] Brooks, T. F. and Humphreys, W. M., “A Deconvolution Approach for theMapping of Acoustic Sources (DAMAS) Determined from Phased MicrophoneArrays,” Journal of Sound and Vibration, Vol. 294, July 2006, pp. 856–879.

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[6] Dougherty, R. P., “Extensions of DAMAS and Benefits and Limitations ofDeconvolution in Beamforming,” 11th AIAA/CEAS Aeroacoustics Conference,AIAA-2005-2961, Monterey, California, May 2005.

[7] Yardibi, T., Li, J., Stoica, P., and Cattafesta, L. N., “Sparsity constraineddeconvolution approaches for acoustic source mapping,” The Journal of theAcoustical Society of America, Vol. 123, No. 5, May 2008, pp. 2631–2642.

[8] Sijtsma, P., “CLEAN based on spatial source coherence,” International Journal ofAeroacoustics, Vol. 6, No. 4, December 2007, pp. 357–374.

[9] Bendat, J. S. and Piersol, A. G., Random data: analysis and measurementprocedures, Wiley, NY, 2000.

[10] Yardibi, T., Bahr, C., Zawodny, N., Liu, F., Cattafesta, L. N., and Li, J.,“Uncertainty Analysis of the Standard Delay-and-Sum Beamformer and ArrayCalibration,” 15th AIAA/CEAS Aeroacoustics Conference, AIAA-2009-3120,Miami, FL, May 2009.

[11] Yardibi, T., Bahr, C., Zawodny, N., Liu, F., Cattafesta, L. N., and Li, J.,“Uncertainty Analysis of the Standard Delay-and-Sum Beamformer and ArrayCalibration,” Journal of Sound and Vibration, Vol. 329, No. 13, June 2010, pp. 2654–2682.

[12] Johnson, D. H. and Dudgeon, D. E., Array Signal Processing: Concepts andTechniques, Prentice Hall, NJ, 1993.

[13] Stoica, P. and Moses, R. L., Spectral Analysis of Signals, Prentice-Hall, UpperSaddle River, NJ, 2005.

[14] Van Trees, H. L., Optimum Array Processing: part IV of Detection, Estimation,and Modulation Theory, John Wiley & Sons, New York, NY, 2002.

[15] Högbom, J. A., “Aperture synthesis with a non-regular distribution ofinterferometer baselines,” Astronomy and Astrophysics Supplements, Vol. 15,1974., pp. 417–426.

[16] Brooks, T. F. and Humphreys, Jr., W. M., “Effect of Directional Array Size on theMeasurement of Airframe Noise Components,” 5th AIAA/CEAS AeroacousticsConference, AIAA-99-1958, Bellevue, WA, May 1999.

[17] Oerlemans, S., Broersma, L., and Sijtsma, P., “Quantification of airframe noiseusing microphone arrays in open and closed wind tunnels,” International Journalof Aeroacoustics, Vol. 6, No. 4, December 2007, pp. 309–333.

[18] Underbrink, J. R., Practical Considerations in Array Design for Passive Broad-Band Source Mapping Applications, The Pennsylvania State University, StateCollege, PA, 1995.

[19] Underbrink, J. R., “Aeroacoustic Phased Array Testing in Low Speed WindTunnels”, Aeroacoustic Measurements, Edited by T. J. Mueller, Springer, 2002,pp. 99–217.

[20] Bahr, C., Yardibi, T., Liu, F., and Cattafesta, L. N., “An analysis of differentmeasurement techniques for airfoil trailing edge noise,” 14th AIAA/CEASAeroacoustics Conference, AIAA-2008-2957, British Columbia, Canada, May 2008.

760 Comparison of microphone array processing techniques

for aeroacoustic measurements

[21] Blackstock, D. T., Fundamentals of Physical Acoustics, John Wiley and Sons,New York, NY, 2000.

[22] Brooks, T. F. and Humphreys, W. M., “Extension of DAMAS phased arrayprocessing for spatial coherence determination (DAMAS-C),” 12th AIAA/CEASAeroacoustics Conference, AIAA-2006-2654, Cambridge, Massachusetts, May 2006.

[23] T. Yardibi, J. Li, P. Stoica, N. Zawodny, and L. Cattafesta, “A covariance fittingapproach for correlated acoustic source mapping,” The Journal of the AcousticalSociety of America, Vol. 127, No. 5, pp. 2920–2931, May, 2010.

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