CHAPTER 4 SPEECH ENHANCEMENT USING MULTI-BAND WIENER FILTER. In real environmental conditions the speech signal may be

Transcription

1 55 CHAPTER 4 SPEECH ENHANCEMENT USING MULTI-BAND WIENER FILTER 4.1 Introducton In real envronmental condtons the speech sgnal may be supermposed by the envronmental nterference. In general, the spectrum of ths nose vares wth frequency. Snce envronmental nose s colored, orgnal speech spectrum wll not be affected unformly by ths nose. Recently researchers focussed on ths ssue and some fndngs are gven n [64-66]. Sub-band sngle channel speech enhancement systems are developed by dvdng the whole nosy speech spectrum nto frequency sub-bands [65], [67-68] and ths dvson s based on frequency response characterstcs of human ear. From the lterature, Bark scale s well suted for sub-bandng. The power spectral densty of colored nose s not constant, where as whte nose has constant value. Thereby dong speech enhancement by multplyng the nosy speech spectrum wth a same weghtng factor wll dstort the speech sgnal. Hence, t s necessary to perform speech enhancement usng dfferent weghtng factors for dfferent sub-bands. Thereby, speech dstorton wll be reduced whle most of the muscal nose s elmnated. Ths chapter deals wth mult-band nose suppresson technques, n whch dfferent weghtng factors are used n each sub-band. To resemblng the frequency response characterstc of human ear,

2 56 frequency spectrum nose speech s dvded nto sub-bands based on nonlnear Bark scale. 4. Mult-band Speech Enhancement In the earler proposed spectral subtracton [8], [39]. The authors have assumed that nose and speech sgnal are uncorrelated, then the cross correlaton terms between clean speech sgnal and nose sgnal are neglected. If we consdered speech wth background nose y (n), as combnaton of orgnal speech sgnal x (n), whch s addtvely affected by background nose d (n) then the nosy sgnal s gven by y( n) x( n) d( n) (4..1) Ths assumpton s true whle speech sgnal s statonary but t s not so n. By applyng the FFT to (4..1), at the th m frame and th k frequency bn, y(n) can be represented as: where ( Y, ( Y( X ( D( (4..) X and D( are the DFT coeffcents of speech wth background nose, clean speech and nose sgnals respectvely. The power spectrum nose corrupted speech sgnal s gven by Y( X ( D( X ( D ( X ( D( (4..3) where D ( and X ( denote ther complex conjugates. The functon s power spectrum of orgnal speech sgnal. X ( In spectral subtracton, s estmated from (4..3). In X ( equaton (4..3), the terms D (, X ( D ( and X ( D( are not possble to obtan ther values drectly and we use expected values

3 57 nstead of ther true values. D( E s obtaned usng method proposed n the chapter 3. In power spectrum subtracton, assumpton s made on d(n) as t s zero mean and ndependent to x(n) and then expected values of the terms X ( D ( and X ( D( wll be zero. Fnally based on those assumptons the orgnal speech sgnal can be obtaned as ˆ X ( Y( E D( (4..4) 4..1 Cross correlaton Terms n Spectral Subtracton The assumpton of the earler researchers that statstcal characterstcs of speech and nose are not correlated, lmts the performance of the spectral subtracton algorthm. Ths s not a vald assumpton n real world envronments. The autocorrelaton sequences of one frame of a clean speech, together wth the background and nosy verson of the same speech sgnal are shown n Fg.4.1. From the graphcal llustraton shown n Fg. 4.1, t s observed that autocorrelaton sequence of speech sgnal wth background nose s not same as that obtaned by summng the autocorrelaton sequences of the nose and orgnal speech sgnal. Fg.4.1 shows the exstence of the cross correlaton between the clean speech sgnal and nose sgnal [69-70]. * * Therefore, the terms X ( D ( and X ( D( cannot be neglected. By ncludng these terms, the muscal nose from the processed speech sgnal can be reduced. As the dscusson s on sngle

4 58 channel nose suppresson technques, t s not possble to have the samples of orgnal speech. In order to approxmate and nclude the cross correlaton terms, a spectrum of nosy speech s used to estmate Fg.4.1 Verfcaton of cross correlaton exstence between orgnal speech and nose sgnal. * * Y ( D ( and ( D( * * X ( D ( and ( D( Y nstead of X. Ths cross correlaton between spectra of speech sgnal wth background nose and nose sgnal s obtaned usng the cross correlaton coeffcent,. Ths coeffcent s gven by yd y. d,0 1 (4..5). y d

5 59 where yd M 1 1 N 0 Y( ) D( ) y M 1 1 N 0 Y( ) d M 1 1 N 0 Dˆ ( ) y M d M 1 1 N N 0 Y( ) Dˆ ( ) where M s length of the FFT frame. The value s proportonal to the degree of cross correlaton between clean speech and nose. 4.. Mel-scale Spectral Subtracton In most of the cases, the envronment nose has ts power spectral densty changng wth frequency and s unlke whte nose. Ths nose s known as color nose, whch affects the speech spectrum dfferently at dfferent frequency bands. Consderng machne nose, whch has characterstcs as low frequences, contans most of ts energy. A mult-band spectral subtracton was proposed by S.Kamath et al. [65], n whch nosy speech spectrum s dvded nto sub-bands based on lnear frequency spacng approach. However they dd not consder any cross correlaton terms. In ths approach, frequency spectrum of nosy sgnal s dvded by usng non-lnear spacng between sub-bands for spectral subtracton and cross correlaton terms are also ncluded n subtracton process. In ths work mel-scale s used for dvdng the human voce frequency range 31 sub-bands. Table 4.1 shows frequency ranges for sub-bands. y d

6 60 Usng (4..6) nput nosy speech sgnal frequency components are converted nto mel-scale. f 595log mf (4..6) And the sub-band nosy speech spectrum s obtaned by usng (4..7) Y ( m) Y(, 1,.., K k ( ) where s the sub-band number, K=31 s the total number of subbands and k() s the frequency ndex related to lower and upper boundares of the sub-band, dependng on the lower and upper frequency boundary of the crtcal band. Table 4.1 Sub-bands on mel-scale Sub-band Number of Bns Frequency(Hz)

7 Accordng to mel-scale, the speech spectrum s dvded nto K number of sub-bands and enhancement s done by subtractng the estmated nose n each sub-band. The orgnal speech sgnal spectrum can be obtaned n the th sub-band usng Xˆ ( Y ( Dˆ ( Dˆ (, otherwse Y ( Dˆ (, f Xˆ ( 0 (4..8) for k m k 1 where k and k 1are related to startng and endng frequences of the th sub-band and s the forgettng factor of the th sub-band. The choce of the value of parameter dctates the amount of nose elmnated. To provde the best trade-off between audble dstorton and resdual nose peaks, ths subtracton factor, should be selected approprately. If 1, then t ndcates over spectral subtracton and n ths case nosy speech spectrum s over attenuated. To avod ths over attenuaton, floorng parameter s used

8 6 and t wll gve the mnmum value to the gan of the subtracton flter but maskng occurs to the resdual nose. Equaton (4..8) represents estmated enhanced speech sgnal spectrum whch have to converge at the orgnal speech sgnal. However, enhanced speech sgnal of ths method s not convergng to the orgnal speech sgnal because of the non-statonary nature of speech sgnals. Ths spectral subtracton s also represented as a flter, wth flter gan G ( and value of ths gan s n the range 0 to 1. Now enhanced speech spectrum s obtaned by passng the nosy speech sgnal through ths flter and t s gven by X ˆ ( G(. Y( ; 0 G( 1 (4..9) comparng (4..4) and (4..5), we have G(, as ˆ D ( G( 1. (4..10) SNR Y ( post where SNR post w 1 mw w 1 mw Y ( Dˆ ( s a posteror SNR. Accordng to (4..10), ths flter gan functon s dependent on a posteror SNR. In the regons of estmated nose hgher than the nosy speech power spectru G( s equal to zero. Hence there s a trade-off between a posteror SNR and attenuaton of nosy speech. Whle a posteror SNR s ncreasng the attenuaton of the nosy speech reduces. Implementaton of ths approach s smple because a posteror SNR can be obtaned easly.

9 Mult-band Wener Flter Based on frequency response characterstcs of human ear, here a mult-band approach based on non-lnear sub-bands s proposed. Accordng to psychoacoustcs of human ear, a spectral gan for enhancement s proposed n [68]. Here Bark scale s used for dvdng the human voce frequency range nto 4 sub-bands whch s sutable to represent band pass flterng nature of human ear. The relatonshp between the nput frequency and Bark s gven n (4..11) and s also f b ( f ) 13arctan(0.76 f ) 3.5arctan. (4..11) 7.5 Graphcally representaton s gven n Fg.4.. Out of 4 sub-bands, Fg.4. (a) crtcal band rate and (b) frequency 18 sub-bands are suffcent to represent sampled speech sgnal wth samplng frequency 8 KHz. Nosy speech power spectrum on Bark scale s gven by Y ( b) Y( ( ), 1, K. (4..1) where ndcates ndex of sub-band, K=18 s the total number of subbands and () represents the frequency range of the sub-band. Now conventonal Wener flterng s used n each sub-band for nose elmnaton and nosy speech s multpled wth ths flter gan n each sub-band as

10 64 Xˆ ( GY ( (4..13) Wener flter s desgned by applyng MMSE crtera between clean speech sgnal and processed sub-band sgnals. To derve the Wener flter gan, cost functon s formulated n each sub-band, whch s gven by E Xˆ ( X (. (4..14) where Xˆ ( and ( denote the estmated and deal sub-band X speech sgnals n the th sub-band respectvely. By substtutng (4..13) n (4..14) and smplfyng, we get as G 1 EX ( G ED ( G 1G EX ( D (. (4..15) where D ( the estmated nose spectru s zero mean and assumed that t s uncorrelated wth X ( n each sub-band. The (4..15) can be smplfed to G 1 EX ( G ED ( (4..16) By the dfferentaton of (4..16) w.r.t weghtng factor G to zero and the weghtng factor G s found to be G E EX ( X ( ED ( S. (4..17) S D S Y Where, and S D Y ndcate estmated power of orgnal speech, background nose and speech wth background nose n the th subband respectvely.

11 65 By consderng cross correlaton between X ( and D ( and dfferentatng (4..15) w.r.t G we have EX ( EX ( D ( X ( ED ( EX ( D ( G. (4..18) E However t s not possble to estmate cross correlaton ter snce we are dealng wth sngle channel, no reference sgnal for orgnal speech s avalable but we have nosy speech sgnal Y (. Hence, cross correlaton between X ( and ( s estmated usng the avalable Y ( and estmated (, then D E E D Y D ( EX ( D (. ( D ( X ( D ( E Y ( D ( ED ( ) k. (4..19) By consderng the cross correlaton between Y ( and D (, E Y ( D ( Y ( D ( (4..0) where s the cross correlaton coeffcent whch relates the cross correlaton between nose corrupted speech and nose sgnals n a sub-band. Ths s gven n (4..5). By substtutng (4..0) and (4..19) n (4..18), flter gang can be obtaned as G E X ( Y ( D ( ED ( EY Y ( D ( ( 1 ED ( G (4..1) (

12 66 where ( s a pror SNR n a th sub-band and gven by E X ( ( and smlarly ( E D ( s a posteror SNR and defned as E Y ( (. Calculaton of a pror SNR s not possble drectly. E D ( Then t s estmated usng the approach gven n [34][71] and s gven by Xˆ ( ˆ ( 1 P ( 1. (4..) E Dˆ ( X E Dˆ ( s the estmaton of the nose power n the th where ˆ ( estmator of the orgnal speech s sgnal n the th subband, subband, P [] performs half wave rectfcaton and denotes smoothng factor. Intal a pror SNR s obtaned usng the ML estmate and s gven by ( E ( k 1). 4.3 Modfed A pror SNR Ths secton deals wth the modfed a pror SNR. Estmaton and updatng of ˆ ( k ) s controlled by the smoothng factor. Approach gven n [67] analyzed the estmaton a pror SNR and nose reducton based on smoothng factor. When closer to1, then less amount of resdual nose s remans n enhanced speech sgnal but transent dstorton wll be more. Balancng these effects researchers [8][7] set the value n the range If we choose the constant value,

13 67 then ˆ ( k ) fals to follow sudden changes n the speech sgnal magntude and after a certan tme delay t wll follow the a posteror SNR. Smlarly after a certan tme delay ˆ ( k ) wll follow the downfalls n the a posteror SNR, these downfalls correspond to the decrement n the speech sgnal magntude. It s convenent to use smaller values to n these transtonal areas. To get better performance wth the a pror SNR ˆ ( k ) an adaptaton method s proposed for smoothng parameter n [7], n whch authors made assumpton that the statstcal characterstcs of the background nose do not change wth frame and are statonary. Accordng to [7], s defned n terms of frame energy E m k Y ( and s gven by E E 1 max E, E 1 1 (4.3.1) In ths thess, a modfed smoothng factor s proposed whch s defned usng MMSE crtera. Ths factor s sutable for adaptvely changng the a pror SNR correspondng to changes n speech sgnal magntude. Modfed a pror SNR can be obtaned ˆ ~ ( ( ( m 1,. (4.3.) Where ~ ˆ ( m 1, X( m 1, / ED ( m 1, 1 ( P[ ( 1] and whch s smlar to a pror SNR (. Here cost functon J s formulated based on MMSE crtera to obtan modfed smoothng factor. ~ J ˆ E ( ( / ( m 1, (4.3.3)

14 68 Substtutng (4.3.) nto (4.3.3), an expresson for J can be obtaned as J ~ ( m 1, ( 1 ( ( ( 1) (. (4.3.4) Now dfferentatng J wth respect to ( and settng ths value to zero. Then smoothng factor ( has been modfed as opt 1 k ~. (4.3.5) (, ) ( 1, ) 1 m k m k (, 1) m k In the dervaton ( the followng terms are substtuted: E ( 1 ( ( 1 4 and EX ( / ED ( ( 4,t s the fourth order moment, dscusson on ths moment s gven n[69]. Intally, t s not possble to have ( then ( P ( 1 s substtuted for ( to get approxmated value of (. Ths modfed smoothng factor wll have smaller value, whle sudden changes n the speech sgnal magntude or n a posteror SNR. When speech sgnal has unform magntude varaton, then value of the smoothng parameter s nearer to 1. Fg.4.3 llustrates the comparson of varatons n a posteror wth obtaned smoothng parameter and parameter gven n [7]. The major dfference between the obtaned smoothng parameter wth parameter gven n [7] s that modfed factor changes for every frame and frequency bn. Ths characterstc s dfferng from parameter gven n [7].

15 Smulaton Results The evaluaton of mult-band sngle channel speech enhancement methods s dscussed n ths chapter. For ths evaluaton, smulatons are carred out wth the NOIZEUS, database [61] n MATLAB. Ths database provdes nosy speech samples at dfferent envronments at dfferent SNRs. For ths performance evaluaton arport, car, babble, tran, restaurant, ralway staton and street envronment noses are consdered at 0 db, 5dB, 10 db and 15dB SNR levels. Fg.4.3 Varaton of smoothng parameter ( ) (a) Nosy speech (b) Proposed ( (n dotted lne) and aposteror SNR, ( (n sold lne) (c) m of [65] (n dotted lne) and aposteror SNR, ( (n sold lne) (d) apror SNR, ( estmate usng proposed ( for k 37 (n sold lne) and apror SNR estmate usng. m The followng performance measures are used n ths evaluaton procedure: segmental SNR and Nose Reducton NR values. Hgher

16 70 values of these measures ndcate sgnfcant reducton n the background nose [54]. Detals of these performance measures are already dscussed n secton.6. The performance of the mel-scale spectral subtracton and mult-band Wener flter s compared wth power spectral subtracton and Wener flter. Table 4. shows the output average segmental SNR values of enhanced speech sgnals obtaned wth proposed method and wth other methods. The performance of the mult-band Wener flter method almost outperforms that of the power spectral subtracton, Wener flter and mel-scale spectral subtracton. Fg.4.4 llustrates graphcal representaton of the comparson of output average segmental SNR values for dfferent nose envronment condtons. Table 4.3 llustrates the comparson of nose reducton values. Form ths table t s clear that background nose reducton from nosy speech sgnal wth proposed method s better compared to other methods. Smlar comparson s gven n Fg.4.5. The tmng waveforms of the enhanced speech are gven n Fg.4.6, where orgnal speech sgnal s corrupted wth arport nose at 0 db SNR. Smlar comparson s gven n Fg.4.7 n terms of spectrograms. From these results and lstenng tests t s clear that mult-band Wener flter effcently removes the background nose compared to other methods.

17 71 Type of nose and SNR (db) Table 4. Output average segmental SNR values (db) Power Wener Mel-scale Spectral Flter Spectral Subtract (WF) Subtracton on (PSS) (Mel-scale SS) Mult-band Wener Flter (MWF) Arport Arport Arport Arport Babble Babble Babble Babble Car Car Car Car Street Street Street Street Tran Tran Tran Tran Restaurant Restaurant Restaurant Restaurant Staton Staton Staton Staton

18 7 Fg.4.4 Comparson of output average segmental SNR values for dfferent noses (a) arport (b) babble (c) car (d) restaurant (e) staton and (f) street

19 73 Type of nose and SNR (db) Table 4.3 Nose reducton values (db) Power Wener Mel-scale Spectral Flter Spectral Subtracton (WF) Subtracton (PSS) (Mel-scale SS) Multband Wener Flter (MWF) Arport Arport Arport Arport Babble Babble Babble Babble Car Car Car Car Street Street Street Street Tran Tran Tran Tran Restaurant Restaurant Restaurant Restaurant Staton Staton Staton Staton

20 74 Fg.4.5 Comparson of nose reducton values wth varous enhancement technques and mult-band Wener flter for dfferent noses (a) arport (b) babble (c) car (d) street (e) tran and (f) restaurant.

21 75 Fg.4.6 Tmng waveforms of (a) the orgnal speech (b) speech wth background nose and the enhanced speech usng (c) power spectral subtracton (d) Wener flter (e) mel-scale spectral subtracton and (f) mult-band Wener flter

22 76 Fg.4.7 Comparson of spectrograms of (a) the orgnal speech (b) speech wth background nose and the enhanced speech usng (c) power spectral subtracton (d) Wener flter and (e) mel-scale spectral subtracton (f) mult-band Wener flter 4.5 Concluson Ths chapter descrbed the development of a new mult-band speech enhancement system that consdered the affect on speech sgnal spectrum due to colored nose. In partcular, mel-scale spectral subtracton and mult-band Wener flter methods are examned. Performance of these methods s compared wth power spectral subtracton and Wener flterng methods. From smulaton results t

23 77 s observed that mult-band Wener flter method gves better performance than other methods. Chapter 5 descrbes reducton of harmonc dstorton caused durng mult-band wener flter speech enhancement.