Using Intermicrophone Correlation to Detect Speech in Spatially Separated Noise

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1 Using Intemicophone Coelation to Detect Speech in Spatially Sepaated Noise The MIT Faculty has made this aticle openly available. Please shae how this access benefits you. You stoy mattes. Citation As Published Publishe Koul, Ashish, and Julie E. Geenbeg. Using Intemicophone Coelation to Detect Speech in Spatially Sepaated Noise. EURASIP Jounal on Advances in Signal Pocessing 6 (6):. Web. Spinge Vesion Autho's final manuscipt Accessed Mon Nov ::39 EST 8 Citable Link Tems of Use Detailed Tems

2 Hindawi Publishing Copoation EURASIP Jounal on Applied Signal Pocessing Volume 6, Aticle ID 939, Pages DOI./ASP/6/939 Using Intemicophone Coelation to Detect Speech in Spatially Sepaated Noise Ashish Koul and Julie E. Geenbeg Boadband Video Compession Goup, Boadcom Copoation, Andove, MA 8, USA Massachusetts Institute of Technology, 77 Massachusetts Avenue, Room E-8, Cambidge, MA 39-37, USA Received 9 Apil ; Revised Apil ; Accepted Apil This pape descibes a system fo detemining intevals of high and low signal-to-noise atios when the desied signal and intefeing noise aise fom distinct spatial egions. The coelation coefficient between two micophone signals seves as the decision vaiable in a hypothesis test. The system has thee paametes: cente fequency and bandwidth of the bandpass filte that pefiltes the micophone signals, and theshold fo the decision vaiable. Conditional pobability density functions of the intemicophone coelation coefficient ae deived fo a simple signal scenaio. This theoetical analysis povides insight into optimal selection of system paametes. Results of simulations using white Gaussian noise souces ae in close ageement with the theoetical esults. Results of moe ealistic simulations using speech souces follow the same geneal tends and illustate the pefomance achievable in pactical situations. The system is suitable fo use with two micophones in mild-to-modeate evebeation as a component of noise-eduction algoithms that equie detecting intevals when a desied signal is weak o absent. Copyight 6 A. Koul and J. E. Geenbeg. This is an open access aticle distibuted unde the Ceative Commons Attibution License, which pemits unesticted use, distibution, and epoduction in any medium, povided the oiginal wok is popely cited.. INTRODUCTION Conventional heaing aids do not selectively attenuate backgound noise, and thei inability to do so is a common complaint of heaing-aid uses [ ]. Reseacheshave poposed a vaiety of speech-enhancement and noise-eduction algoithms to addess this poblem. Many of these algoithms equie identification of intevals when the desied speech signal is weak o absent, so that paticula noise chaacteistics can be estimated accuately [ 7]. Systems that pefom this function ae efeed to by a numbe of tems, including voice activity detectos, speech detectos, pause detectos, and double-talk detectos. Speech pause detectos ae not limited to use in heaing-aid algoithms. They ae used in a numbe of applications including speech ecognition [8, 9], mobile telecommunications [, ], echocancellation [], and speech coding [3]. In some cases, noise-eduction algoithms ae initially developed and evaluated using infomation about the timing of speech pauses deived fom the clean signal, which is possible in compute simulations but not in a pactical device. Mazinzik and Kollmeie [] point out that speech pause detectos ae a vey sensitive and often limiting pat of systems fo the eduction of additive noise in speech. Many of the peviously poposed methods fo speech pause detection ae intended fo use with single-micophone noise-eduction algoithms, whee it is assumed that the desied signal is speech and the noise is not speech. In these applications, the distinction between signal and noise depends on the pesence o absence of signal chaacteistics paticula to speech, such as pitch [, ] o fomant fequencies [6]. Othe appoaches ely on assumptions about the elative enegy in fames of speech and noise [8, 7]. A summay of single-micophone pause detectos is found in []. Othe methods of speech pause detection ae possible when moe than one micophone signal ae available. Using signals fom multiple micophones, infomation about the signal-to-noise atio (SNR) can be discened by compaing the signals eceived at diffeent micophones. The distinction between desied signal and unwanted noise is based on the diection of aival of the sound souces, so these appoaches also opeate coectly when the noise is a competing talke with chaacteistics simila to those of the desied speech signal. Reseaches woking on a vaiety of applications have poposed speech pause detectos using two o moe micophone signals. Examples include a thee-micophone system to impove the noise estimates fo a spectal subtaction

3 EURASIP Jounal on Applied Signal Pocessing algoithm used as a font end fo a speech ecognition system [8]; a joint system fo noise-eduction and speech coding [9]; a voice activity detecto based on the coheence between two micophones to impove the pefomance of noise eduction algoithms fo mobile telecommunications []. This thid system equies a substantial distance between micophones, as it is only effective when the noise signal is elatively incoheent between the two micophones. A elated body of wok is the use of single- and double-talk detectos to contol the update of adaptive filtes in echo cancelles. Although thee is only one micophone in this application, a second signal is obtained fom the loudspeake. A compehensive summay of these appoaches is found in []. In developing adaptive algoithms fo micophone-aay heaing aids and cochlea implants, eseaches have found that it is necessay to limit the update of the adaptive filte weights to intevals when the desied signal is weak o absent. Seveal methods have been poposed to detect such intevals based on the coelation between micophones and the atio of intemediate signal powes [7,, ]. Geenbeg and Zuek [7] popose a simple method using the intemicophone coelation coefficient to detect intevals of low SNR that substantially impoves noise-eduction pefomance of an adaptive micophone-aay heaing aid. This method is applicable wheneve two micophone signals ae available and the signal and noise ae distinguished by spatial, not tempoal o spectal, chaacteistics. Despite its demonstated effectiveness, this method was developed in an ad hoc manne. The pupose of this wok is to pefom a igoous analysis of the intemicophone coelation coefficient of multiple sound souces in anechoic and evebeant envionments, to fomalize the selection of paamete settings when using the intemicophone coelation coefficient to estimate the ange of SNR, and to evaluate the pefomance that can be obtained when optimal settings ae used.. PROPOSED SYSTEM Figue shows the signal scenaio used in this wok. All souces and micophones ae assumed to lie in the same plane, with the micophones in fee space. Souces with angles of incidence between θ and θ ae consideed to be desied signals, while souces aiving fom θ to 9 and θ to 9 ae intefeing noise. Sound can aive fom any angle in a 36 ange, but due to the symmety inheent in a two-micophone boadside aay, souces aiving at incident angles in the ange 8 ± θ will also be teated as desied signals. Moeove, due to the symmety in the definition of desied signal and noise, we estict the following analysis to the ange 9 without loss of geneality. Figue shows the peviously poposed system that uses the coelation coefficient between the two micophone signals to distinguish between intevals of high and low SNRs [7]. The micophone signals ae digitized and then passed though bandpass filtes with cente fequency f and bandwidth B. The bandpass filteed signals x [n] andx [n] ae Intefeing noise Desied signal θ Micophone Micophone Intefeing noise Figue : Signal scenaio indicating the anges of incident angles fo the desied signal and intefeing noise souces. divided into N-point long segments. Fo each pai of segments, the coesponding intemicophone coelation coefficient is computed as 9 Nn= x [n]x [n] = Nn= x[n]. () N n= x[n] Finally, is compaed to a fixed theshold to detemine the pedicted SNR ange fo each segment. Because the desied signal aives at aay boadside fom angles nea staight-ahead, it will be highly coelated in the two micophone signals and will contibute positive values to, povided that the souce is located inside the citical distance in a evebeant envionment. The intefeing noise aives fom off-axis diections and should contibute negative values to. Thiseffect is enhanced by the bandpass filte which limits the fequency ange so that signals aiving fom the ange of noise angles will be out of phase and poduce minimum coelation values. Thus, the pupose of the bandpass filte is to enhance the ability of the intemicophone coelation measue to distinguish between desied signal and intefeing noise. This appoach is attactive fo applications such as digital heaing aids, whee computing esouces ae limited. If necessay, the coelation coefficient can be estimated efficiently using the sign of the bandpass filteed signals [7]. The poposed system has thee independent paametes: the cente fequency ( f ) of the bandpass filte, the bandwidth (B) of the bandpass filte, and the theshold ( ). Anothe impotant paamete of the poposed system is the intemicophone spacing (d). The intemicophone spacing is not teated as a fee paamete, athe it is incopoated into the analysis by nomalizing two of the independent paametes (cente fequency and bandwidth) as discussed in detail in Section.. In this wok, the poposed system is analyzed to detemine optimal settings of the thee independent paametes. Fist, Section 3 descibes a simple signal model and deives the associated pobability density functions and hypothesis

4 A. Koul and J. E. Geenbeg 3 Micophone A/D Micophone A/D y [n] Bandpass filte f,b y [n] Bandpass filte f,b x [n] Finite-time cosscoelation x [n] Yes High SNR >? Low SNR No Figue : Block diagam of the system to estimate the intemicophone coelation coefficient fo detemining ange of SNR. tests fo the intemicophone coelation. In Section, the analysis of Section 3 is used to examine the effectsof the thee paametes. In Section., theoetical esults fom the anechoic scenaio ae used to identify candidates fo the optimal value of the cente fequency f.insection., theoetical esults fom the evebeant scenaio ae used to optimize the theshold. Fo pactical easons descibed in Section., the bandwidth paamete B cannot be optimized based on the theoetical analysis; instead, it is detemined fom the simulations pefomed in Section. 3. ANALYSIS 3.. Peliminaies 3... Assumptions The following assumptions ae made to allow a tactable analysis. (i) Thee is one desied signal souce and one intefeing noise souce in the envionment. (ii) The desied signal aives at the micophone aay fom an incident angle in the ange to θ, and the intefeing noise aives fom an incident angle in the ange θ to 9. Fo both the desied signal and the intefeing noise, the pobability of the souce aiving at any incident angle is unifomly distibuted ove the coesponding ange of angles. (iii) Sound souces ae continuous, zeo-mean, white Gaussian noise pocesses. Desied signal and intefeing noise souces have vaiances σs and σi,espectively. The signal-to-noise atio is defined as SNR = log (W), whee W =σs /σi. (iv) Revebeation can be modelled as a spheically diffuse sound field. This is an admittedly simplified model of evebeation which is only applicable fo elatively small ooms [3]. Revebeant enegy is chaacteized by the diect-to-evebeant atio DRR = log (β), whee β is the atio of enegy in the diect wave to enegy in the evebeant sound. The value of β is equal fo both signal and noise souces, implying that both souces ae oughly the same distance fom the micophones. (v) The filtes applied to the incoming signals ae ideal bandpass filtes with cente fequency f and bandwidth B Signal model While the system shown in Figue pocesses the digitized signals, fo the analysis, we conside the signals x (t) and x (t), continuous-time econstuctions of the bandpass filteed signals x [n]andx [n]. Fo a two-micophone aay in fee space, these two signals can be modelled as x (t) = s(t)+i(t), x (t) = s ( ) ( ) () t τ s + i t τi, whee s(t) is the desied signal afte bandpass filteing, i(t) is the intefeing noise afte bandpass filteing, and τ s and τ i epesent the time delays between micophones fo the desied signal and intefeing noise, espectively. Assuming plane wave popagation, τ s and τ i can be expessed as τ s = d c sin ( θ s ), τi = d c sin ( θ i ), (3) whee d is the distance sepaating the micophones, c is the speed of sound, and θ s and θ i ae the incident angles of the espective souces. The theoetical coelation coefficient ρ of the two signals is E { x (t)x (t) } ρ = E { x(t) } E { x(t) }, () whee E{ } denotes expected value. Unde ideal conditions of stationay signals and infinite data, ρ would be the decision vaiable used in the system of Figue.Howeve,inthis application, we use the intemicophone coelation coefficient, definedin() to estimate ρ fom discete samples of the two signals ove a finite time peiod Fishe Z-tansfomation Conside the case of two andom vaiables a and b dawn fom a bivaiate Gaussian distibution. We wish to obtain an estimate of the theoetical coelation coefficient ρ using N sample pais dawn fom the joint distibution of a and b. In geneal, the pobability distibution of the estimato is difficult to wok with diectly, because its shape depends on the value of ρ. The Fishe Z-tansfomation is defined as z = tanh () = ln ( + ). ()

5 EURASIP Jounal on Applied Signal Pocessing This yields the new andom vaiable z which has an appoximately Gaussian distibution with mean z = (/) ln(( + ρ)/( ρ)) and vaiance σz = /(N 3) []. This deived vaiable z has a simple distibution whose shape does not depend on the unknown value of ρ. Due to the assumption that the signal and noise souces ae Gaussian andom pocesses, the micophone signals ae jointly Gaussian andom pocesses. Even afte bandpass filteing, the input vaiables x (t) andx (t) definedin() ae jointly Gaussian, and the Fishe Z-tansfomation may be applied. 3.. Intemicophone coelation fo one souce in an anechoic envionment We begin by deiving the pobability density function (pdf) of fo a single souce with incident angle θ. Afte A/D convesion and bandpass filteing, the signals x [n]andx [n]ae ectangula bands of noise. The tue intemicophone coelation is [] ρ θ = cos (kd sin θ)sin( (πbd/c)sinθ ) ( ), (6) (πbd/c)sinθ wheek is the wavenumbe, k = πf. (7) c Using the Fishe Z-tansfomation, the conditional pdf of z, given a souce at incident angle θ,is with f z θ (z θ) = ( exp σ z π [ ] ) z z(θ) σ z (8) z(θ) = ( ) ln +ρθ, ρ θ σz = (9) N 3. Using the assumption that θ is unifomly distibuted ove a specific ange of angles, the joint pdf fo z and θ is f z,θ (z, θ) = f z θ (z θ), () θ θ whee θ = θ and θ = fo a signal souce and θ = 9 and θ = θ fo a noise souce. To obtain the maginal density of z, the joint density in () is integated ove the appopiate ange of θ, that is, ( θ [ ] ) z z(θ) f z (z) = ( ) exp dθ. θ θ σz π θ σ z () With this expession fo the pdf of z, wecanusethedefinition of the Fishe Z-tansfomation to deive the pdf of the intemicophone coelation coefficient. Since = tanh(z) is a monotonic tansfomation of the andom vaiable z, the pdf of can be obtained using [6] f () = f z (z) dz d. () Substituting dz/d = /( ) and the definition of z poduces the pdf of fo a single souce: f () = ( )( ) θ θ σz π ( θ [ tanh () z(θ) ] ) exp θ σz dθ. (3) 3.3. Intemicophone coelation fo two independent souces in an anechoic envionment Next, we conside the intemicophone coelation coefficient fo one signal souce and one noise souce in an anechoic envionment, denoted by a. Substituting discete-time vesions of () into () yields ( )( [ ] [ ]) n s[n]+i[n] s n τs + i n τi a = ( ) ( [ ] [ ]). n s[n]+i[n] n s n τs + i n τi () The coesponding expession fo the desied signal component alone is { [ ]} n s[n]s n τs s = n s [n] n s [ ], () n τ s and fo the noise component alone is { [ ]} n i[n]i n τi i = n i [n] n i [ ]. (6) n τ i We now make the following assumptions. () The s i coss tems in () ae negligible when compaed with the s s and i i tems to which they add. () The effect of time delay on the enegy can be ignoed such that s [n] s [ ] n τ s, n n i [n] i [ ] (7) n τ i. n n (3) The SNR defined in Section 3.. can be estimated fom the sample data as W = n s [n] n i [n]. (8) Using the fist two assumptions, () becomes n s[n]s [ ] n τ s + n i[n]i [ ] n τ i a = n s [n]+ n i. (9) [n]

6 A. Koul and J. E. Geenbeg Substituting () and(6), dividing all tems by n i [n], and then substituting (8), we obtain a = W s + i W + = W W + s + W + i. () Equation () expesses the intemicophone coelation as a linea combination of the coelations fo signal and noise sepaately. The pdfs of both s and i can be obtained fom (3). Fo a known SNR, the pdf fo a, a linea combination of s and i, is obtained by [ ( )] W + W + f a W( a W) = W f s W s [ () ( )] (W +)f i (W +)i, whee denotes convolution [6]. Equation () is the pdf of the intemicophone coelation estimate fo anechoic envionments a conditioned on a paticula value of SNR. 3.. Revebeation Until now, we have only consideed the diect wave of the sound souces. We now conside the addition of evebeation. As descibed in Section 3.., the evebeant sound component is modelled as a spheically diffuse sound field that is statistically independent of the diect signal and noise components. In addition, it has enegy that is chaacteized by the diect-to-evebeant atio β. Analogous to () and(6), we define the intemicophone coelation fo the diect components a given by () and fo the evebeation. Applying aguments simila to those used in the pevious section poduces an expession fo the intemicophone coelation in the case of evebeation: = β a + β + = β β + a + β +. () Once again, the total coelation is a linea combination of its components, and fo a known diect-to-evebeant atio, the pdf fo, a linea combination of a and, is obtained by convolution [6]: [ ( )] β + β + f β,w ( β, W) = f a W β β a W [ (3) ( )] (β +)f (β +). Equation (3) is the pdf of the intemicophone coelation estimate conditioned on paticula values of DRR and SNR. It equies convolution of the diect component pdf, given by (), and the evebeant component pdf, deived below. Unde the existing assumptions, the pdf fo the evebeant component is based on the intemicophone coelation coefficient fo bandlimited Gaussian white noise pocesses, appoximated by [7] ρ = sin(πbd/c) πbd/c sin(kd). () kd In the following, () is used as the tue intemicophone coelation fo evebeant sound ρ. The intemicophone coelation fo evebeant sound basedonsampledata is an estimate of ρ. Applying the Fishe Z-tansfomation, z = tanh ( ) = ln ( + ). () The andom vaiable z has an appoximately Gaussian distibution, ( [z z] ) f z (z) = exp σ z π σz (6) with z = ( ) ln +ρ, ρ σz = (7) N 3. Applying () to(6) poduces the pdf of intemicophone coelation fo the evebeant component, f () = ( ) σ z π ( [ tanh ( ) ] ) z exp σz. (8) This pdf fo the evebeant sound field is combined with the pdf fo the diect sounds given by () accoding to (3) to obtain the pdf fo the total intemicophone coelation fo signal and noise with evebeation. 3.. Hypothesis testing The goal of the system shown in Figue is to distinguish between two situations: low SNR and high SNR, denoted by H and H, espectively. Although the peceding analysis was pefomed unde the assumption that the souces wee white Gaussian noise pocesses, the system is intended to wok with speech souces, detecting intevals of high and low SNRs which occu due to the natual fluctuations in speech. We define H to be log(w) < db and H to be log(w) > db. The choice of db as the cutoff point is motivated by the application of designing obust adaptive algoithms fo micophone-aay heaing aids, an application whee the degading effects of stong taget signals typically occu when the SNR exceeds db [7]. The peceding analysis teated the SNR, W, as a known constant, but fo the pupose of fomulating a hypothesis test, it is now egaded as a andom vaiable. Thus, it becomes necessay to know an appoximate pobability distibution fo W. We assume that the SNR is unifomly distibuted between db and + db, so the vaiable U = log(w) is unifomly distibuted between and. Unde this assumption, the two hypotheses H and H both have equal pio pobability. In this case, the decision ule that minimizes the pobability of eo [8] is to select the hypothesis coesponding to the lage value of the conditional

7 6 EURASIP Jounal on Applied Signal Pocessing pdf fo each value of, that is, we conclude that H is tue when f H,β( H, β) > f H,β( H, β) and we conclude that H is tue when f H,β( H, β) >f H,β( H, β). To deive the conditional pdf of unde eithe hypotheses, the pdf given by substituting () and(8) into (3) is integated ove the appopiate ange: f H,β( H, β ) = f W,β ( W, β) du, f H,β( H, β ) (9) = f W,β ( W, β) du. Evaluating these expessions equies substituting W= U/. Pefomance is measued by computing the pobability of coect detections, that is, saying H when H is tue, ( P D = f H,β H, β ) d, (3) and false alams, that is, saying H when H is tue, ( P F = f H,β H, β ) d, (3) whee is the theshold defined in Section. We also define the pobability of missed detections and the oveall pobability of eo P M = P D, (3) P E = P F + P M, (33) again assuming that H and H have equal pio pobabilities.. ANALYTIC RESULTS All calculations wee pefomed in Matlab (R) on a PC with a Pentium III pocesso. Pobability density functions wee computed fom (), (3), and (8) using the Matlab (R) function quad. Thoughout this analysis, the bounday between desied signals and intefeing noise is set to θ =... Effects of fequency and bandwidth As descibed in Section, the thee paametes to be selected ae the cente fequency ( f ) of the bandpass filte, the bandwidth (B) of the bandpass filte, and the theshold ( ). Without loss of geneality, we use two altenate vaiables in place of the cente fequency and bandwidth, specifically kd in place of cente fequency and factional bandwidth in place of absolute bandwidth. Using (7), the quantity kd is elated to cente fequency accoding to kd = πf d. (3) c This altenate vaiable kd pemits quantifying the cente fequency paamete in a way that simultaneously incopoates both cente fequency and intemicophone distance, and we will efe to it as elative cente fequency. Thefactional bandwidth is defined as = B f. (3) Using (3) and(3)with(6) eveals that fo a souce aiving fom angle θ, the tue intemicophone coelation can be expessed exclusively in tems of these two paametes, that is, ρ θ = cos (kd sin θ)sin( (kd /) sin θ ) ( (kdb /) sin θ ). (36) We begin to detemine the optimal value of the elative cente fequency kd by examining the pdfs of the intemicophone coelation in an anechoic envionment. Figue 3 shows pdfs of a, computed by evaluating () fo thee valuesofsnrandtheevaluesofkd with factional bandwidth =.. As expected, when the micophone inputs consist of signal alone (ight column of Figue 3), a is concentated nea +; when the inputs consist of noise alone (left column of Figue 3), a takes on substantially lowe values. When the micophone inputs consist of signal and noise with SNR=dB(centecolumnofFigue 3), a takes on intemediate values distibuted accoding to the convolution of the two exteme cases of signal alone and noise alone. Othe values of SNR poduce pdfs that vay along a continuum betweenthecasesshownin eachowoffigue 3. Using Figue 3 to conside the effect of kd eveals that fo any choice of the elative cente fequency, fo the signal alone, the pdf is heavily concentated nea a =, although lowe values of kd poduce moe tightly concentated pdfs. Fo the noise alone, the patten is less evident. Fo kd = π, the pdf is heavily concentated nea a =. This is expected since noise souces oiginating fom 9 ae exactly out of phase when kd = π, and theefoe have a tue coelation of. When the value of kd deviates fom this ideal situation, the noise-alone pdfs ae not necessaily concentated nea a =. Because the ultimate goal is to use as a decision vaiable in a hypothesis test, the system will pefom bette when the pdfs ae such that they occupy diffeent egions of the x- axis unde the two exteme conditions, with minimal ovelap of the pdfs between the cases of signal alone and noise alone. Theefoe, at fist glance, it might appea that selecting the elative cente fequency of kd = π is the optimal choice fo this paamete. Howeve, caeful examination of Figue 3 eveals that the noise-alone pdf fo kd = π spans a vey lage ange, with a tail in the positive a diection eaching values close to = +. Since ovelap of the signal-alone and noise-alone pdfs will advesely affect the pefomance of the hypothesis test, this long tail is an undesiable featue. Examining the noise-alone pdf fo kd = π/3,which is less concentated about a = but has less ovelap with the coesponding signal-alone pdf, indicates that this paamete setting should not be eliminated as a candidate. This suggests using the moments of the pdfs about the coesponding exteme values as appopiate metics to select the elative cente fequency paamete kd. The moment

8 A. Koul and J. E. Geenbeg 7 Figue 3: Pobability density functions of the estimated intemicophone coelation coefficient fo two souces in an anechoic envionment, f a W ( a W), computed fom (),fotheesnrs(,, and + db) and fo thee values of elative cente fequency (kd = π/3, π,π/3), with factional bandwidth =. and θ =. The fist ow epesents kd = /3π, the second ow epesents kd = π, and the thid ow epesents kd = /3π. The fist column epesents noise alone, the second column epesents SNR = db, and the thid column epesents signal alone. of the signal-alone pdf about + and the moment of the noise-alone pdf about will quantify how concentated each pdf is about the desied exteme value, while penalizing long tails deviating fom that value. Low values of the moment ae desiable, indicating moe concentated pdfs. Figue shows the second moments of the signal- and noise-alone pdfs as a function of kd fo seveal values of factional bandwidth. The lines in Figue (a)ae monotonic, indicating that educing kd always causes the signal-alone pdf to be moe concentated about +. Figue (b) shows that the moment of the noise-alone pdf has a local minimum fo kd.3π, with a slight vaiation due to bandwidth. The moments of the noise-alone pdf ae an ode of magnitude lage than those of the signal-alone pdfs, so in tems of optimizing the oveall pefomance, elatively geate weight should be given to the noise-alone pdfs. Based on Figue, the est of this wok consides two choices of elative cente fequency kd = π and kd = (/3)π. The value of kd=(/3)π is chosen because it is nea the minimum of the noise-alone pdf fo the lowe values of factional bandwidth. The value kd = π is selected since fo this value, the moment fo the noise-alone pdf is still within the elatively boad egion about its minimum, while being consideable lowe fo the signal-alone pdf. Figue also shows that fo the idealized scenaio of white Gaussian noise souces, inceasing the bandwidth paamete slightly inceases the moments. This will have a small but detimental effect on the pefomance. Howeve, in a pactical system, whee the desied signal is speech, a elatively wide bandwidth is equied to captue enough enegy fom the speech signal to minimize advese affectsdue to elative enegy fluctuations in diffeent fequency egions. The cuent theoetical analysis is necessaily based on idealized signals, while the final system will opeate on speech souces. Theefoe, the selection of the bandwidth paamete will be evaluated via simulations in Section... Effects of evebeation and theshold selection Figue shows the pdfs of the intemicophone coelation fo signal and noise computed by evaluating (3) fo thee values of SNR and thee levels of evebeation. Because the

9 8 EURASIP Jounal on Applied Signal Pocessing / /3 /6 7/6 /3 3/ kd/π =. =.33 (a) =.67 = / /3 /6 7/6 /3 3/ kd/π =. =.33 (b) =.67 = between signal-alone fom noise-alone cases; we wish to select a theshold that will minimize the pobability of eo when classifying combinations of signal and noise at vaious SNRs. Theefoe, to select the theshold, we conside the signal scenaio descibed in conjunction with the hypothesis tests in Section 3.. Figue 6 shows the conditional pdfs fo the hypothesis test as given by (9) fo thee levels of evebeation. Given equal pio pobabilities fo the two hypotheses, the optimum choice of the theshold is the value at which the pdfs coesponding to H and H intesect. Howeve, as seen in Figue 6, the value of at which this intesection occus is not constant; it vaies with the level of evebeation. A pactical system must use one theshold to opeate obustly acoss all levels of evebeation. The theshold cannot be selected to account fo the level of evebeation, which is an unknown envionmental vaiable. Figue 7 shows the pobability of eo given by (33) as a function of the theshold fo two values of kd. Fokd = π, any choice of theshold in the ange. minimizes the pobability of eo, egadless of the level of evebeation. Fo kd = (/3)π, the minimum pobability of eo vaies somewhat with theshold, but using = povidesneaoptimal pefomance fo all levels of evebeation.. SIMULATIONS Figue : Second moments of pdfs as a function of elative cente fequency kd, with θ =. The multiple cuves ae fo diffeent values of factional bandwidth. (a) Moment of signal-alone pdf about +. (b) Moment of noise-alone pdf about. system is dependent on the diectional infomation contained in the diect wave of the signals, it is not expected to pefom well in stong evebeation. Accodingly, we estict the level of evebeation to β, coesponding to DRRs geate than db. Compaing the top ow of Figue (anechoic) to the middle and bottom ows eveals that the effect of evebeation is to shift the cente-of-mass of the pdfs away fomtheextemevaluesof± andtowadsmoemodeate values of. This inceases the ovelap between the signalalone and noise-alone pdfs, theeby inceasing the pobability of eo of the hypothesis test. In the pevious section, candidate values of kd wee detemined based on the pdfs fo the anechoic case. Figue illustates that the signal-alone and noise-alone pdfs ae affected equally by the simple model of evebeation used in this wok, indicating that the analysis of the effect of kd in the anechoic case also applies to evebeation. The next step is to detemine the optimal ange fo the theshold. Because the effect of evebeation is to bing the signal-alone and noise-alone pdfs close togethe, we must include evebeation as we conside the theshold selection. Futhemoe, until now we have based ou analysis on the conceptually simple signal- and noise-alone pdfs shown in the ight and left columns of Figues 3 and.howeve, in this application, we ae not attempting to distinguish This section pesents the esults of compute simulations of the SNR-detection system shown in Figue. These simulations wee pefomed in Matlab (R). The sound souces wee sampled at khz. The bandpass filtes wee 8-point FIR filtes designed using the Paks-McClellan method. The filteed signals wee boken into fames of samples ( ms), which is appopiate fo tacking powe fluctuations in speech. Fo each fame, the sample coelation coefficient is computed accoding to (). This value is compaed to the theshold. If it exceeds the theshold, then the system declaes H (high SNR), othewise it declaes H (low SNR). The desied signal and intefeence souces wee fist convolved with thei espective souce-to-micophone impulse esponses and then added togethe. These impulse esponses wee geneated numeically using the image method [9, 3]. The simulated oom was m. The micophones wee centeed at the coodinates (.7,.,.6) m along the aay axis which was a line though the coodinates (.79,.3,.6) m. Thee intemicophone distances of d = 7,, and 8 cm wee used. All souces in the oom wee located on a cicle aound the aay cente in the hoizontal plane at height of.7 m. The fowad diection (θ =) is defined to be diectly boadside of the aay in the diection of positive coodinates, and inceasing the incident angle efes to clockwise pogession of souce angle when viewed fomabove. Theadius ofsoucelocations and coefficient of absoption fo the walls vay with the specified level of evebeation. Fo the anechoic envionment, the adius was. m and the absoption coefficient of all sufaces was.. Fo DRR = 3dB (β = ), the adius was.7 m and the absoption coefficient was.6. Fo DRR = db (β = ), the

10 A. Koul and J. E. Geenbeg 9 Figue : Pobability density functions of the estimated intemicophone coelation coefficient fo two souces in vaying levels of evebeation f β,w ( β, W)computedfom(3), fo thee SNRs (,,and+ db) and thee levels of evebeation (DRR=, 3, and + db epesents by the thee ows), with elative cente fequency of kd = π, factional bandwidth =., and θ =. The fist column epesents noise alone, the second column epesents SNR= db, and the thid column epesents signal alone. adius was.6 m and the absoption coefficient was again.6. The desied signal souce angle vaied between and and the intefeing noise souce angle vaied between 8 and 9,bothin incements. Fo each of the esulting 76 combinations of signal and noise souce angles, the system geneated pedictions of high and low SNRs fo each -millisecond fame. These esults wee then compaed to the tue SNRs fo each fame to detemine the detection and false alam ates... Simulations with white Gaussian noise Simulations wee pefomed using desied signal and intefeing noise souces consisting of 8-sample long segments of white Gaussian noise. The vaiance of the intefeing noise souce was constant at a value of one. The desied signal souce consisted of a seies of -sample intevals each with a constant vaiance; the vaiance inceased in steps of 3 db between intevals such that the SNR anged fom 9. db to 9. db. This input is stuctued so that the SNR is less than db fo the fist samples, and the SNR is geate than db fo the last samples. Thus, the fist half of the signal was used to detemine the false alam ate P F, and the second half was used to detemine the detection ate P D.ThevaluesofP D and P F wee aveaged ove all combinations of souce angles fo desied signals and intefeing noise. All of the simulations with white noise used an intemicophone spacing of d = cm togethe with two sets of system paametes. In the fist set, kd = π and =.. With d = cm, this esults in a cente fequency of f = 38 Hz. In the second paamete set, kd = (/3)π and =, esulting in a value of f = 6 Hz. Fo both paamete sets, the factional bandwidth vaied between. and., coesponding to actual bandwidths of Hz to 86 Hz fo the fist paamete set and 6 Hz to 7 Hz fo the second set. Figue 8 shows the esults of these simulations, displaying the detection, eo, and false alam ates as functions of factional bandwidth fo the two values of kd and thee levels of evebeation. This figue also includes the pobabilities

11 EURASIP Jounal on Applied Signal Pocessing H H (a) H H (b) PE PE Theshold DRR = db DRR = 3dB DRR = db (a) Theshold DRR = db DRR = 3dB DRR = db (b) H H (c) Figue 7: Pobability of eo P E as a function of theshold fo two values of elative cente fequency (kd = (a) π, (b)π/3) and thee levels of evebeation (DRR =, 3, and + db), with factional bandwidth =. and θ =. Figue 6: Conditional pobability density functions of the estimated intemicophone coelation coefficient fo the two hypotheses f H,β( H, β)and f H,β( H, β), computed as in (9) with elative cente fequency of kd = π, factional bandwidth =., and θ = fo thee levels of evebeation (a) DRR = +, (b) DRR=3dB,(c)DRR=dB. of detection, false alam, and eo as pedicted by the analysis in Section. The ageement between the analytic and simulation esults is quite good, especially fo the anechoic condition. Mino but systematic deviations ae appaent in the false alam and eo ates fo the evebeant conditions, which is not supising consideing the ovesimplified model of evebeation as a spheically diffuse sound field that was used in the analysis, but not in the simulations. Oveall, the best pefomance is obtained with low-tomodeate values of the factional bandwidth. As pedicted by Figue, lage values of the factional bandwidth incease the ovelap between the pdfs, theeby inceasing the eo ate. Howeve, the noise simulation esults indicate that pefomance is elatively constant fo a elatively wide ange of factional bandwidths. While both values of kd pefom compaably, thee is a slight benefit in using kd=(/3)π... Simulations with speech Moe ealistic simulations wee pefomed using speech as the desied signal and babble as the noise signal. The speech souce was 7-second long, fomed by concatenating two sentences [3] spoken by a single male talke. The noise souce consisted of -talke SPIN babble [3] timmed to the same length as the speech mateial and nomalized to have the same total powe. The tue SNR was calculated fo each -millisecond fame by taking the atio of the total powe in the speech segment to the total powe in the babble segment. The tue SNRs wee compaed to the system outputs to detemine the detection and false alam ates, which wee aveaged ove all combinations of signal and noise angles. The speech simulations investigated thee intemicophone spacings d =7,, and 8 cm, all with kd=(/3)π and =. This esulted in cente fequencies of f =33, 6, and 8 Hz fo d = 7,, and 8 cm, espectively. The factional bandwidth vaied between. and.. Fo d = 7cm, Speech simulations wee also pefomed with kd = π and =.. Howeve, since the effect of kd on pefomance was compaable fo both speech and noise simulations, those esults ae not pesented hee.

12 A. Koul and J. E. Geenbeg Figue 8: System pefomance as a function of factional bandwidth fo thee levels of evebeation (DRR =, 3, and + db) and two values of elative cente fequency (kd=π, π/3). The plots show detection ates (cicle), false alam ates (diamond), and eo ates (squae) fom the simulations with white noise along with the theoetical pobabilities of detection (dot), false alam (x), and eo (+) pedicted by the analysis in Section. The fist ow epesents DRR=, the second ow epesents DRR=3 db, and the thid ow epesents DRR=dB. The fist column epesents kd=π and the second column epesents kd=/3π. the lage factional bandwidths ( =. and.) wee not simulated because they coesponded to fequency anges that exceeded the signals khz bandwidth. Figue 9 shows the esults of these simulations, displaying the detection, eo, and false alam ates as a function of factional bandwidth fo thee values of d and thee levels of evebeation. Compaing the columns in Figue 9 confims that the oveall pefomance is elatively unaffected by micophone spacing when compaing systems based on the nomalized paametes kd and. The exception is the smalle micophone spacing (d = 7 cm), whee small factional bandwidths poduce elatively moe detections and false alams, leading to compaable oveall eo ates. Compaing the middle column of Figue 9 to the ighthand column of Figue 8 eveals that fo the same paamete settings, the use of speech signals leads to substantial eductions in system pefomance, as evidenced by highe eo and false alam ates and lowe detection ates. The discepancies between Figues 8 and 9 ae explained by the obsevation that in the case of the speech signals, the SNRs ae not unifomly distibuted in the ange db to db, as was assumed in the analysis. This assumption was tue fo the noise simulation. In the case of speech, values of the shot-time SNR tend to be concentated at less exteme values, whee the system does not pefom as well. In fact, the majoity of eos made by the system occu when the SNR is close to db, and theefoe in tansition between the two hypotheses. This is illustated in Figue, which shows the tue shot-tem SNRs fo a 3-second speech segment and the values of intemicophone coelation computed accoding to (), along with the locations of misses and false alams. Anothe majo diffeence between Figues 8 and 9 is the moe ponounced effectofbandwidth onspeechwhencompaed with noise souces. Fo the noise signals, the enegy was unifomly distibuted acoss the bandwidth, but this is not the case fo speech signals. As discussed in Section, selection of the bandwidth epesents a tadeoff between the theoetical consideations, which dictate smalle bandwidths, and pactical consideations, which equie that the system captues sufficient enegy fom the nonstationay speech signal to minimize advese affects of the elative enegy fluctuations in diffeent fequency egions. The simulation esults in Figue 9 suggest that fo speech signals, factional bandwidths in the ange.67 to. yield the best pefomance. 6. SUMMARY AND CONCLUSIONS This pape descibes a system fo detemining intevals of high and low signal-to-noise atios when the signal and

13 EURASIP Jounal on Applied Signal Pocessing Figue 9: System pefomance as a function of factional bandwidth fo thee levels of evebeation (DRR=, 3, and + db) and thee intemicophone spacings (d = 7,, 8 cm), with elative cente fequency (kd = π/3). The plots show detection ates (cicle), false alam ates (diamond), and eo ates (squae) fom the simulations with speech. The fist ow epesents DRR =, the second ow epesents DRR = 3 db, and the thid epesents DRR = db. The fist column epesents d = 7 cm, the second column epesents d = cm, and the thid column epesents d =8cm. noise aise fom distinct spatial egions. It uses the coelation coefficient between two micophone signals as the decision vaiable in a hypothesis test. The system has thee paametes: the cente fequency of the bandpass filte, the bandwidth of the bandpass filte, and the theshold fo the decision vaiable. We pefomed a theoetical analysis based on a signal scenaio that includes two spatially sepaated sound souces and a simple model of evebeation. By deiving conditional pobability density functions of the intemicophone coelation coefficient unde both hypotheses, we gained insight into optimal selection of the system paametes. Results of simulations using white Gaussian noise fo the sound souces wee in close ageement with the theoetical esults. Moe ealistic simulations using speech souces followed the same geneal tends and illustated the pefomance that can be obtained in pactical situations with the paametes detemined by the analysis, specifically, kd = (/3)π, =.67., and =. The contibutions of this wok ae twofold. Fist, it povides an example of how speech detection systems can be analyzed and optimized. Rigoous compaison of the many speech detection systems poposed in the liteatue is often hampeed by the diffeing conditions unde which they ae evaluated. If theoetical analyses simila to the one pefomed hee wee available, they would geatly facilitate the compaison of diffeent speech detection systems. Second, fo the paticula speech detection system consideed hee, the analysis povides simple and widely applicable guidelines fo the selection of paametes. The system consideed in this wok is only applicable in situations when two micophone signals ae available. It is futhe limited in that it is only expected to wok in mildto-modeate evebeation. The cuent study was esticted to a signal model consisting of a boadside aay configuation, micophones in fee space, a single intefeing noise souce, and simple models of evebeation. Futue wok should () conside endfie aay configuations; () investigate the effect of mounting the micophones nea the head fo the heaing-aid application; (3) assess the pefomance of the system in the pesence of multiple intefees; () quantify the degadation in pefomance with inceasing levels of evebeation; and () evaluate the system with ecoded (athe than simulated) sound signals. A study addessing these issues will moe completely establish the potential of

14 A. Koul and J. E. Geenbeg 3 SNR (db) Time (s) Missed detections False alams (a)... 3 Time (s) (b) Figue : Simulation esults fo a desied speech souce at 8 and intefeing babble at 86 azimuth, combined to poduce a longtem SNR of db. The souces wee in an anechoic envionment with cm micophone spacing. (a) Shot-time SNR as a function of time fo a 3-second segment of speech. (b) Estimated intemicophone coelation coefficient fo the same speech and babble segment as in (a), computed fo kd = /3π and =.. Using a theshold of =, the symbols in (a) indicate fames, whee thee wee missed detections ( + ) and false alams ( x ). the poposed system fo use in speech-enhancement and noise-eduction algoithms that equie identification of intevals when the desied signal is weak o absent. ACKNOWLEDGMENTS The authos ae gateful to Pat Zuek, who suggested the use of the Fishe Z-tansfomation and outlined potions of the deivation pesented in Section 3, and to thee anonymous eviewes, who povided valuable feedback on an ealie vesion of this pape. This wok was suppoted by the National Institute of Deafness and Othe Communicative Disodes unde Gant -R-DC7. REFERENCES [] R. Plomp, Auditoy handicap of heaing impaiment and the limited benefit of heaing aids, Jounal of the Acoustical Society of Ameica, vol. 63, no., pp. 33 9, 978. [] T. C. Smedley and R. L. Schow, Fustations with heaing aid use: candid epots fom the eldely, The Heaing Jounal, vol. 3, no. 6, pp. 7, 99. [3] S. Kochkin, MakeTak V: consume satisfaction evisited, The Heaing Jounal, vol. 3, no., pp. 38,. [] S. Kochkin, MakeTak V: why my heaing aids ae in the dawe : the consumes pespective, The Heaing Jounal, vol. 3, no., pp. 3,. [] D. Van Compenolle, Heaing aids using binaual pocessing pinciples, Acta Oto-Layngologica: Supplement, vol. 69, pp. 76 8, 99. [6] M. Kompis and N. Dillie, Noise eduction fo heaing aids: Combining diectional micophones with an adaptive beamfome, Jounal of the Acoustical Society of Ameica, vol. 96, no. 3, pp. 9 93, 99. [7] J. E. Geenbeg and P. M. Zuek, Evaluation of an adaptive beamfoming method fo heaing aids, Jounal of the Acoustical Society of Ameica, vol. 9, no. 3, pp , 99. [8] D. Van Compenolle, W. Ma, F. Xie, and M. Van Diest, Speech ecognition in noisy envionments with the aid of micophone aays, Speech Communication, vol. 9, no. -6, pp. 33, 99. [9] H. Kobatake, K. Tawa, and A. Ishida, Speech/nonspeech discimination fo speech ecognition system unde eal life noise envionments, in Poc IEEE Intenational Confeence on Acoustics, Speech, and Signal Pocessing (ICASSP 89), vol., pp , Glasgow, Scotland, UK, May 989. [] D. K. Feeman, G. Cosie, C. B. Southcott, and I. Boyd, The voice activity detecto fo the Pan-Euopean digital cellula mobile telephone sevice, in Poceedings of IEEE Intenational Confeence on Acoustics, Speech, and Signal Pocessing (ICASSP 89), vol., pp , Glasgow, Scotland, UK, May 989. [] M. Mazinzik and B. Kollmeie, Speech pause detection fo noise spectum estimation by tacking powe envelope dynamics, IEEE Tansactions on Speech and Audio Pocessing, vol., no., pp. 9 8,. [] C. Beining, P. Deiscitel, E. Hansle, et al., Acoustic echo contol. An application of vey-high-ode adaptive filtes, IEEE Signal Pocessing Magazine, vol. 6, no., pp. 69, 999. [3] J. Stegmann and G. Schode, Robust voice-activity detection based on the wavelet tansfom, in Poceedings of IEEE Wokshop on Speech Coding Fo Telecommunications Poceeding,pp. 99, Pocono Mano, Pa, USA, Septembe 997. [] R. Tucke, Voice activity detection using a peiodicity measue, IEE Poceedings. I: Communications, Speech, and Vision, vol. 39, no., pp , 99. [] J. Pencak and D. Nelson, The NP speech activity detection algoithm, in Poceedings of IEEE Intenational Confeence on Acoustics, Speech, and Signal Pocessing (ICASSP 9), vol., pp , Detoit, Mich, USA, May 99. [6] J. D. Hoyt and H. Wechsle, Detection of human speech in stuctued noise, in Poceedings of IEEE Intenational Confeence on Acoustics, Speech, and Signal Pocessing (ICASSP 9), vol., pp. 37, Adelaide, Austalia, Apil 99. [7] J. T. Sims, A speech-to-noise atio measuement algoithm, Jounal of the Acoustical Society of Ameica, vol. 78, no., pp , 98. [8] M. Akagi and T. Kago, Noise eduction using a small-scale micophone aay in multi noise souce envionment, in Poceedings of IEEE Intenational Confeence on Acoustics, Speech, and Signal Pocessing (ICASSP ), vol., pp. 99 9, Olando, Fla, USA, May. [9] M. W. Hoffman, Z. Li, and D. Khatania, GSC-based spatial voice activity detection fo enhanced speech coding in the pesence of competing speech, IEEE Tansactions Speech Audio Pocessing, vol. 9, no., pp. 7 78,.

15 EURASIP Jounal on Applied Signal Pocessing [] R. Le Bouquin-Jeannès and G. Faucon, Study of a voice activity detecto and its influence on a noise eduction system, Speech Communication, vol. 6, no. 3, pp., 99. [] M. Kompis, N. Dillie, J. Fancois, J. Tinembat, and R. Hausle, New taget-signal-detection schemes fo multimicophone noise-eduction systems fo heaing aids, in Poceedings of 9th Annual Intenational Confeence of the IEEE Engineeing in Medicine and Biology Society (EMBS 97), vol., pp , Chicago, Ill, USA, Octobe Novembe 997. [] R. J. M. van Hoesel and G. M. Clak, Evaluation of a potable two-micophone adaptive beamfoming speech pocesso with cochlea implant patients, Jounal of the Acoustical Society of Ameica, vol. 97, no., pp. 98 3, 99. [3] P. Janecek, A model fo the sound enegy distibution in wok spaces based on the combination of diect and diffuse sound fields, Acustica, vol. 7, pp. 9 6, 99. [] M. G. Bulme, Pinciples of Statistics, Dove, NewYok, NY, USA, 979. [] W. M. Hatmann, Signals, Sound, and Sensation, Spinge, New Yok, NY, USA, 998. [6] H. P. Hsu, Pobability, Random Vaiables, and Random Pocesses, McGaw-Hill, New Yok, NY, USA, 997. [7] H. Nélisse and J. Nicolas, Chaacteization of a diffusefield in aevebeantoom, Jounal of the Acoustical Society of Ameica, vol., no. 6, pp. 37 3, 997. [8] H. L. Van Tees, Detection, Estimation, and Modulation Theoy, Pat I, John Wiley & Sons, New Yok, NY, USA, 968. [9] J. B. Allen and D. A. Bekley, Image method fo efficiently simulating small-oom acoustics, Jounal of the Acoustical Society of Ameica, vol. 6, no., pp. 93 9, 979. [3] P. M. Peteson, Simulating the esponse of multiple micophones to a single acoustic souce in a evebeant oom, Jounal of the Acoustical Society of Ameica, vol. 8, no., pp. 7 9, 986. [3] IEEE, IEEE ecommended pactice fo speech quality measuements, Tech. Rep. IEEE 97, Institute of Electical and Electonics Enginees, Washington, DC, USA, 969. [3] D. N. Kalikow, K. N. Stevens, and L. L. Elliot, Development of a test of speech intelligibility in noise using sentence mateials with contolled wod pedictability, Jounal of the Acoustical Society of Ameica, vol. 6, no., pp , 977. Julie E. Geenbeg is a Pincipal Reseach Scientist in the Reseach Laboatoy of Electonics at the Massachusetts Institute of Technology (MIT). She also seves as the Diecto of Education and Academic Affais fo the Havad-MIT Division of Health Sciences and Technology (HST). She eceived a B.S.E. degee in compute engineeing fom the Univesity of Michigan, Ann Abo (98), an S.M. in electical engineeing fom MIT (989), and a Ph.D. degee in medical engineeing fom HST (99). He eseach inteests include signal pocessing fo heaing aids and cochlea implants, as well as the use of technology in bioengineeing education. She is a Membe of IEEE, ASEE, and BMES. Ashish Koul eceived the B.S. and M.Eng. degees in electical engineeing and compute science fom the Massachusetts Institute of Technology in and 3, espectively. While at MIT, he seved as a Reseach Assistant in the Sensoy Communications Goup within the Reseach Laboatoy of Electonics, whee he was involved in applications of digital signal pocessing in heaing-aid design. Cuently, he is employed as an Enginee woking on eseach and development in the Boadband Video Compession Goup at the Boadcom Copoation in Andove, Mass.