BLIND ESTIMATION OF REVERBERATION TIME IN OCCUPIED ROOMS

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1 14th Europea Sigal Processig Coferece (EUSIPCO 6, Florece, Italy, September 4-8, 6, copyright by EURASIP BLIND ESTIMATION OF REVERBERATION TIME IN OCCUPIED ROOMS Yoggag Zhag, Joatho A. Chambers, Fracis F. Li, Paul Kedrick, Trevor J. Cox The Cetre of Digital Sigal Processig, Cardiff School of Egieerig Cardiff Uiversity, Cardiff CF4 YF, UK. Departmet of Computig ad Mathematics Machester Metropolita Uiversity, Machester M1 5GD, UK. School of Acoustics ad Electroic Egieerig Uiversity of Salford, Salford M5 4WT, UK. ABSTRACT A ew framework is proposed i this paper to solve the reverberatio time (RT estimatio problem i occupied rooms. I this framework, blid source separatio (BSS is combied with a adaptive oise caceller (ANC to remove the oise from the passively received reverberat speech sigal. A polyfit preprocessig step is the used to extract the free decay segmets of the speech sigal. RT is extracted from these segmets with a maximum-likelihood (ML based method. A easy, fast ad cosistet method to calculate the RT via the ML estimatio method is also described. This framework provides a ovel method for blid RT estimatio with robustess to ambiet oises withi a occupied room ad exteds the ML method for RT estimatio from oise-free cases to more realistic situatios. Simulatio results show that the proposed framework ca provide a good estimatio of RT i simulated low RT occupied rooms. 1. INTRODUCTION Room reverberatio time is a very importat parameter that qualifies the room acoustic quality [1]. This parameter is defied as the time take by a soud to decay 6 db below its iitial level after it has bee switched off. May methods have bee proposed to estimate the RT durig recet years [][3][4][5]. The maximum-likelihood (ML estimatio method proposed i [5] which utilizes a passively received speech sigal has received a lot of attetio due to its simplicity ad efficiecy. I this method, a expoetially damped Gaussia white oise model is used to describe the reverberatio diffusive tail sigal. A ML estimatio method is the performed o segmets of the speech sigal to measure the time-costat of the decay. The most likely RT is idetified from a series of estimates by usig a orderstatistic filter. As show by the authors, it provides reliable RT estimates i a oise free eviromet. To estimate the RT i oisy eviromets, such as occupied rooms, where may oises are geerated by the occupats, this method potetially oly cosiders the sigal decay rage betwee the iitial maximum of the decay curve ad the poit where the decay curve itersects the backgroud oise. Whe the oise is large, for example comparable with the excited speech sigal, the results will be cotamiated or eve icorrect. Therefore this method is limited by the oise level ad ot suitable for occupied rooms. To make the ML RT estimatio method more robust ad accurate, a ituitive way is to remove the ukow oise sigal from the received speech sigal as much as possible before RT estimatio. A powerful tool for extractig some RT s( 1 oise s ( speech z( y ˆ ( ML RT Polyfit 1 - ANC y11( x 1( h11( h1( h1( h( Uobservable y ( 1 y ( 1 y ( x ( BSS Observable s ˆ 1 ( s ˆ ( Figure 1: Proposed blid RT estimate frame work for occupied rooms. oise iterferece sigal from a mixture of sigals is the covolutive BSS method [6]. Naturally, give two spatially distict observatios, BSS ca separate the mixed sigals to yield two idepedet sigals. Oe of these two sigals maily cosists of the excitatio speech sigal plus residue of oise ad the other sigal cotais mostly the oise sigal. Usig this estimated oise sigal as a referece sigal the oise cotaied i the received speech sigal ca the be removed by a ANC. Our ew framework is motivated by BSS ad ANC. Differet stages of this framework i a occupied room are show i Fig.1. The sigal s 1 (, which is assumed to be the oise sigal i this work, is idepedet with the excitatio speech sigal s (. The passively received sigals x 1 ( ad x ( are modelled as covolutive mixtures of s 1 ( ad s (. The room impulse respose h ji ( is the impulse respose from source i to microphoe j. BSS is used firstly to obtai the estimated excitatio speech sigal ŝ ( ad the estimated oise sigal ŝ 1 (. The estimated oise sigal ŝ 1 ( the serves as the referece sigal for the ANC to remove the oise compoet from x 1 (. The output of the ANC ŷ 1 ( is a estimatio of the oise free reverberat speech sigal y 1 (. As compared with x 1 (, it crucially retais the reverberat structure of the speech sigal ad has a low level of oise, therefore it is more suitable to estimate the RT of the occupied room. To remove the guess work of the widow legth selectio i the ML method ad reduce the variace of the RT estimates, we use a overlap polyfit method as a preprocessig step. The decay segmets i z( which cotai most of the free decay samples of the reverberat speech sigal are extracted by this preprocessig. The

2 14th Europea Sigal Processig Coferece (EUSIPCO 6, Florece, Italy, September 4-8, 6, copyright by EURASIP the ML estimatio method is performed oly o these decay segmets. Based o the idea of bisectio [5], a ew method to calculate the RT is also provided i the ML RT estimatio method. Compared with other calculatio methods this method has some advatages, as will be discussed later. The followig sectio itroduces the BSS process. The ANC is described i Sectio 3. The polyfit preprocessig is described i Sectio 4. Sectio 5 describes the ML method. A bisectio algorithm for the ML estimatio method is also itroduced. Simulatio results are give i Sectio 6. Sectio 7 summarizes the paper.. BLIND SOURCE SEPARATION As show by Fig.1, the goal of BSS is to extract the estimated oise sigal ŝ 1 ( from received mixture sigals x 1 ( ad x (. If we assume that the room eviromet is time ivariat, the received mixtures x 1 ( ad x ( ca be modeled as weighted sums of covolutios of the source sigals s 1 ( ad s (. Assume that N sources are recorded by M microphoes (here M=N= the equatio that describes this covolved mixig process is: x j ( = N P 1 i=1 p= s i ( ph ji (p (1 where s i ( is the source sigal from a source i, x j ( is the received sigal by a microphoe j, ad h ji ( is the P-poit respose from source i to microphoe j. Usig a T-poit widowed discrete Fourier trasformatio (DFT, time domai sigal x j ( ca be coverted ito the time-frequecy domai sigal X j (ω, where ω is a frequecy idex ad is a time idex. For each frequecy bi we have X(ω, = H(ωS(ω, ( where S(ω, = [s 1 (ω,,,s N (ω,] T ad X(ω, = [x 1 (ω,,,x M (ω,] T are the time-frequecy represetatios of the source sigals ad the observed sigals respectively ad ( T deotes vector traspose. The separatio ca be completed by the umixig matrix W(ω i a frequecy bi ω Ŝ(ω, = W(ωX(ω, (3 where ŝ(ω, = [ŝ 1 (ω,,,ŝ N (ω,] T is the timefrequecy represetatios of the estimated source sigals ad W(ω is the frequecy represetatio of the umixig matrix. W(ω is determied so that ŝ 1 (ω,,...,ŝ N (ω, become mutually idepedet. Exploitig the ostatioary of the speech sigal we defie the cost fuctio as follows: J(W(ω = argmi T K w=1 k=1 F(W(ω,k, (4 where K is the umber of sigal segmets ad F(W(ω,k is defied as F(W(ω,k = RŜ(ω,k diag[rŝ(ω,k] F (5 where RŜ(ω,k is the autocorrelatio matrix of the separated sigals ad F deotes the squared Frobeius orm, k is the block idex. The separatio problem is the coverted ito a joit diagoalizatio problem. Obviously, the solutio W(ω = will lead to the miimizatio of F(W(w,k. To avoid this some costraits should be added to the umixig matrix. I [6] a pealty fuctio is added to covert the costraied optimizatio problem ito a ucostraied optimizatio problem. The cost fuctio of pealty fuctio based joit diagoalizatio is as follows: J(W(ω = argmi T w=1 K k=1 F(W(ω,k λg(w(ω,k (6 where λ is the pealty weight factor ad g(w(ω,k is a form of pealty fuctio based o a costrait of the umixig matrix. With a gradiet-based descet method we ca calculate the umixig matrix after several iteratios from equatio (6. The separated sigals ŝ 1 ( ad ŝ ( ca the be obtaied from (3 after applyig a iverse DFT. 3. ADAPTIVE NOISE CANCELLER After BSS we obtai the estimated oise sigal ŝ 1 (. This sigal is the used as a referece i the ANC stage sigal to remove the oise compoet from the received sigal x 1 (. A ew variable step size LMS algorithm which is suitable for speech processig is used i the ANC. The updates of the step size ca be formulated as follows: e( = x 1 ( ŝ T 1 (w( (7 g( = e(ŝ 1 ( L[ ˆσ e ( ˆσ s (] (8 p( = βp( 1 (1 βg( (9 µ( 1 = αµ( γ p( F (1 where µ( is the variable step size, ŝ 1 ( = [ŝ 1 (,,ŝ 1 ( L 1] T, w( is the weight vector of the adaptive filter, L is the filter legth, ˆσ e ( ad ˆσ s ( are estimatios of the temporal error eergy ad the temporal iput eergy, < α < 1, < β < 1, γ >, g( is the square root ormalized gradiet vector, p( is a smoothed versio of g(. The recursio of the filter weight vector is as follows e(ŝ 1 ( w( 1 = w( µ( L[ ˆσ e ( ˆσ s (] (11 The square root ormalized gradiet vector g( i (8 is used to obtai a robust measure of the adaptive process. The first-order filter based averagig operatio i (9 removes the disturbace brought by the target sigal. The variable step size µ( i (1 is adapted to obtai a fast covergece rate durig the early adaptive process ad a small misadjustmet after the algorithm coverges. The adaptatio of the weight vector i (11 is based o the sum method i [7] which is desiged to miimize the steady state mea square error. Equatios (7(8(9(1(11 provide a ew variable step size LMS algorithm for the ANC stage. The output sigal of the ANC ŷ 1 ( should the be a good estimatio of the oise free reverberat speech sigal y 1 (. Next, estimatig of the RT from ŷ 1 ( must be cosidered.

3 14th Europea Sigal Processig Coferece (EUSIPCO 6, Florece, Italy, September 4-8, 6, copyright by EURASIP 4. POLYFIT PREPROCESSING I this stage, the iput sigal is the estimated oise free reverberat speech sigal ŷ 1 (. The overlap polyfit method is used to extract the decay segmets of this sigal. The output of this stage is the sigal z( which cotais the decay segmets of ŷ 1 (. I accordace with the ML estimatio of RT, we use the same expoetially damped Gaussia white oise model which has bee used i [5]. The mathematical formulatio is as follows: ŷ 1 ( = a(v( (1 where v( is a i.i.d. term with ormal distributio N(,σ ad a( is a time-varyig evelope term. Let a sigle decay rate τ describe the dampig of the soud evelope durig free decay, the the sequece a( is uiquely determied by where a( = exp( /τ = a (13 a = exp( 1/τ (14 I this stage, we first use a movig widow with a appropriate legth ad shift to obtai overlap speech frames. From the model of the reverberat speech tail i (1, which is assumed to hold i each frame, the logarithm of the evelope of the free decay segmet is a lie with egative slope. Because i reality the RT should have a reasoable spa, for example, s to 3s, such a slope should have a correspodig rage. A polyfit operatio is the performed o each frame to extract the slope. By discardig the frames whose slopes are outside such a rage, the speech sigal is divided ito several cotiuous decay segmets. The logest segmets cotaied i z( should cotai the most likely free decay segmets of the speech sigal. As a preprocessig stage for the ML RT estimatio method it has several advatages. At first it provides the widow legth for the ML RT estimatio method automatically. Although i [5] it has bee foud that icreasig widow legth reduces the variability i the estimates, the widow legth is limited by the duratio ad occurrece of the gaps betwee soud segmets. The choice of the widow legth is a trade off betwee the accuracy ad variace of the estimated. After the polyfit preprocessig the widow legth of the ML estimatio must be less tha the legth of the extracted sigal segmet. It is the chose automatically accordig to the segmet legth. Simulatio results show that half legth of the segmet legth will be a good choice of the widow legth. Secodly, the variace of RT estimates is reduced because most samples of these segmets are i agreemet with the Gaussia damped model, as will be cofirmed i later simulatios. 5. ML RT ESTIMATION METHOD The ML estimatio method is the performed o the chose segmets z(. From the defiitio of RT ad the sigal model, the relatioship betwee RT ad the decay rate τ is as follows [5]: T 6 = 3τ = 6.91τ (15 log 1 (exp( 1 The decay rate τ is extracted by the ML estimatio method. Deote the N-dimesioal vectors of z( ad a( (the same as that i (13 ad (14 by z( ad a( ad N is the estimatio widow legth, we ca obtai the logarithm likelihood fuctio N(N 1 E{L(z;a,σ} = l(a N l(πσ 1 N σ a z ( (16 =1 where σ is the iitial power of the sigal. With this fuctio the parameters a ad σ ca be estimated usig a ML approach. From each segmet we ca obtai a series of estimates of RT. All estimates are used to idetify the most likely RT of the room. By cosiderig the relatioship betwee a ad decay rate τ, we propose a ew bisectio method with respect to the RT rather tha with respect to a i [5]. The rage of the RT is set betwee 3s ad.1s. As the time-costat is ot required to be arbitrarily precise, the accuracy is limited to 1ms i our method. The update of our bisectio method is as follows: i. Iitializatio T 6 mi =.1;T 6 max = 3;accuracy =.1; iter = log ((T 6 max T 6 mi/accuracy where accuracy is the accuracy of the estimatio of RT ad iter is the iteratio umber.. Iteratio T (i = (T 6 mi T 6 max/ a(i = exp( 6.91/T (i g(i = L(y;a,σ a g(i > the T 6 mi = T (i g(i < the T 6 max = T (i As the authors poit out i [5], the disadvatage of the bisectio method is that it works poorly i regios ear the true value of a. From (14 ad (15 we kow that a is ot a liear trasform of RT. Our bisectio o RT is actually a o-equivalet bisectio with respect to a. Compared with the fast block algorithm proposed i [8] our algorithm has a umber of advatages: 1. No step size eeds to be selected.. No iitial value of a is eeded. 3. It always coverges ad coverges quickly withi a fixed umber of steps. 6. SIMULATION I this sectio we examie the performace of the proposed framework. The flow chart of the simulatios is show i Fig.1. The occupied room ad its impulse respose h ji betwee source i ad microphoe j are simulated by a image room model [9]. The room size is set to be 1*1*5 meter 3 ad the reflectio coefficiet is set to be.7 i rough correspodece with the actual room. The RT of this room measured by Schroeder s method [] is.7s. The excitatio speech sigal ad the oise sigal are two aechoic 4 secods male speech sigals with a samplig frequecy of 8kHz, ad scaled to make the sigal to oise ratio (SNR to be db over the whole observatio. The positio of these two

4 14th Europea Sigal Processig Coferece (EUSIPCO 6, Florece, Italy, September 4-8, 6, copyright by EURASIP sources are set to be [1m 3m 1.5m] ad [3.5m m 1.5m]. The positios of the two microphoes are set to be [.45m 4.5m 1.5m] ad [.55m 4.5m 1.5m] respectively. As show by Fig.1, BSS is performed firstly to extract the estimated oise sigal ŝ 1. This sigal cotais mostly the oise sigal ad a low level of the desired speech sigal. To evaluate the BSS performace we use a oise to sigal ratio (NSR which is the eergy ratio defied betwee the compoet of the oise sigal ad the compoet of the speech sigal cotaied i ŝ 1. The NSR of ŝ 1 i this simulatio is 38dB, therefore it has a strog correlatio with the oise sigal s 1 ad a slight correlatio with the speech sigal. This sigal is the used i the ANC model as a referece sigal. The filter legth of the ANC is set to be 5 ad the parameters α, β, γ are set to be.99,.9999, respectively. The last 1 samples of the filter coefficiets are used to measure the steady-state performace. The output sigal of the ANC cotais two compoets: the reverberat speech sigal ad the residue of the oise sigal. The sigal to oise ratio (SNR betwee these two compoets is 43dB. The first approximately 1s of this sigal will be used to estimate the RT. We plot the first approximately 1s of the received sigal x 1 ad the output sigal of ANC ŷ 1 i Fig.(a ad Fig.(b respectively. It is easy to see that after BSS ad ANC the oise cotaied i x 1 is reduced greatly..5 (a Received mixture sigal Sample umber x 1 4 (b Output sigal of ANC Sample umber x 1 4 (c Extracted segmets by polyfit process Sample umber x 1 4 Figure : The received mixture sigal, the output of ANC ad the extracted sigal by polyfit process At first we estimate the RT by usig the ML RT estimatio method [5] with the whole output sigal of ANC first. Accordig to the aalysis ad simulatios i [5], the widow legth is set to be 1, which is approximately equal to 4τ, to provide a good choice of the widow legth. The results are show i Fig.3(a. The the polyfit process is performed to extract the free decay segmets. The widow legth of our polyfit method is set to be 4 samples (.5s ad the shift is set to be 1 samples. Te segmets extracted by the polyfit stage are show 1 5 (a (b (c 4.9s.35s.3s Figure 3: (a The estimates of by ML method with the whole output sigal of ANC ad a widow legth of 1. (bthe estimates of by ML method with the output sigal of polyfit process ad a widow legth of 1. (cthe estimates of by ML method with the output sigal of polyfit process ad automatical decided widow legth. i Fig.(c. Note that three segmets are coected i the figure i the iterval 75, to 8,. Fially, two experimets are performed to show the two advatages of the polyfit process which we aalyzed i sectio 4. I the first experimet, the extracted sigal which is the output of the polyfit process is used to estimate the RT by usig the ML method with a widow legth of 1. The results are show i Fig.3(b. The secod experimet is the same as the first experimet except the widow legth of the ML method is decided automatically, which is half of the segmet legth. The results of this experimet are show i Fig.3(c. Compare Fig.3(a with Fig.3(b we ca see that the variace of the estimates of the RT is reduced greatly by usig the polyfit process, where most decay samples are extracted. The first peak i Fig.3(a is.9s, but it is ot clear ad the variace of the RT estimates is very large. I Fig.3(b the variace of the RT estimates is reduced greatly ad the first peak is.35s. Although both results i these two figures are larger tha the theoretical RT of.7s due to the lack of sharp trasiets i the clea speech, the bias of the model i ML method ad the ifluece of the iterferece, they are reasoable ad acceptable i most applicatios. Compare Fig.3(c with Fig.3(b we ca see that the variace of the RT estimates i both figures are comparable. The first peak i Fig.3(c is.3s, which is also a reasoable ad acceptable result. Thus we ca coclude that performace of the ML method with automatical decided widow legth is comparable, if ot better, with the performace of the ML method with a good choice of the widow legth. From all the simulatios above we ca see that the combiatio of BSS ad ANC ca remove the oise sigal greatly whilst retaiig the key reverberat structure to make the high-oise eviromet RT estimatio possible. Further

5 14th Europea Sigal Processig Coferece (EUSIPCO 6, Florece, Italy, September 4-8, 6, copyright by EURASIP more, the polyfit process has bee added before the ML RT estimatio method to reduce the variace of the results ad remove the guess work of the widow legth of the ML RT estimatio method. We have performed other experimets where oe of the speech sigals i the previous simulatios is replaced by a white oise sigal, as a simulated iterferece i the occupied room. Similar estimatio results are also obtaied. However limited by the room model ad the performace of frequecy domai BSS, this framework is desiged to estimate RT i the occupied room whose RT is less tha.3s. As show by our simulatios above, oetheless, reliable RT ca be extracted usig this framework withi a highly oisy occupied room, somethig that has ot previously bee possible. [7] J. E. Greeberg, Modified LMS algorithm for speech processig with a adaptive oise caceller, IEEE Tras. Sigal Processig, vol. 6, o. 4, pp , July [8] R. Ratam, D. L. Joes ad W. D. O Brie Jr., Fast algorithms for blid estimatio of reverberatio time, J. Acoust. Soc. Amer., vol. 11, o. 6, pp , Jue 4. [9] J. B. Alle ad D. A. Berkley, Image method for efficietly simulatig small-room acoustics, J. Acoust. Soc. Amer., vol. 65, pp , Apr CONCLUSION This paper proposes a ew framework for blid RT estimatio i occupied rooms. I this framework, BSS is combied with a ANC to remove the oise of the received speech sigal. A polyfit stage is added to improve the performace of the ML RT estimatio method. A bisectio method is used i the ML method which provides may advatages over the previous calculatio method. Simulatio results show that the oise is removed greatly from the reverberat speech sigal ad the performace of this frame work is good i a simulated low RT occupied room eviromet. Due to the motivatio of our framework BSS ad ANC ca be potetially used i may reverberatio time estimatio methods as a preprocessig. Although the mixig model used i this paper is ot suitable for may applicatios, this framework provides a ew way to overcome the oise disturbace i RT estimatio. However, limited by the performace of covolutive BSS, this framework is oly appropriate for the low RT estimatio case. Future work will focus o the theoretic aalysis of this blid RT estimate framework ad the improvemet of its stages, especially the improvemet of covolutive BSS uder log reverberatio eviromets. REFERENCES [1] H. Kuttruff, Room Acoustics 4th ed., Spo Press, Lodo,. [] M. R. Schroeder, New method for measurig reverberatio time, J. Acoust. Soc. Am, vol. 37, pp , [3] ISO 338, Acoustics-measuremet of the reverberatio time of rooms with referece to other acoustical parameters, Iteratioal Orgaizatio for Stadardizatio, [4] T. J. Cox, F. Li ad P. Darligto, Extractig room reverberatio time from speech usig artificial eural etworks, J. Audio. Eg. Soc, vol. 49, pp. 19 3, 1. [5] R. Ratam, D. L. Joes, B. C. Wheeler, W. D. O Brie Jr., C. R. Lasig ad A. S. Feg, Blid estimatio of reverberatio time, J. Acoust. Soc. Amer., vol. 114, o. 5, pp , Nov. 3. [6] W. Wag, S. Saei ad J. A. Chambers, Pealty fuctio-based joit diagoalizatio approach for covolutive blid separatio of ostatioary sources, IEEE Tra. Sigal Processig, vol. 53, o. 5, pp , May 5.