A HYBRID NEAR-FIELD SUPERDIRECTIVE GSC AND POST-FILTER FOR SPEECH ENHANCEMENT

Transcription

1 2th Euopean Sgnal Poceng onfeence (EUSIPO 22) Buchaest Romana August A YBRID NEAR-FIELD SUPERDIRETIVE GS AND POST-FILTER FOR SPEE ENANEMENT Panaz Khaye Speech Poceng Reseach Lab Electcal and ompute Eng. Dept. Yazd Unvesty Yazd Ian panaz.khaye@gmal.com amd Reza Abutaleb Speech Poceng Reseach Lab Electcal and ompute Eng. Dept. Yazd Unvesty Yazd Ian habutaleb@yazdun.ac. Vahd Abootaleb Electcal and ompute Eng. Dept. Yazd Unvesty Yazd Ian abootaleb@yazdun.ac. ABSTRAT Ths pape deals wth the poblem of mcophone aay speech enhancement usng a hybd Genealzed Sdelobe ancelle (GS) Nea-Feld Supe-Dectve (NFSD) beamfome and post-flte. In ths eseach we employ a nea feld compensaton block befoe the blockng matx (of the GS) to pevent sgnal leakage n the efeence nose and a Lnea onstaned Mnmum Vaance (LMV) beamfome nstead of blockng matx to genealze the appopate pefomance of the system fo dffeent aval dectons of desed speech. We also consde the applcaton of the post-fltes on the beamfome output. A modfed veson of Mcowan post-flte s pesented by calculatng coheence functon fom mcophone-aay nputs. onsdeng smla dea we also popose a multchael veson of Shot-Tme Spectal Ampltude (STSA) post-flte. Ou evaluatons clealy demonstate the effectvene of the poposed modfcatons n the enhancement of the nosy speech. Index Tems- speech enhancement supedectve beamfome genealzed sdelobe cancelle lnea constaned mnmum vaance post-flte. INTRODUTION Much eseach has been done n ecent yeas on the use of mcophone aays fo the task of speech enhancement by spatal flteng. Whle adaptve beamfomes such as Genealzed Sdelobe ancelles (GSs) ae especally sutable fo the suppeon of sngle dectonal nose souces [] supe-dectve beamfomes have shown supeo nose educton pefomance n the case of dffuse nose felds [2]. Many eal-lfe envonments nclude dffuse ncoheent and dectonal noses smultaneously. To acheve a poweful mult-mcophone speech enhancement system fo such cases a hybd adaptve beamfome and post-flte was poposed that employs a Nea Feld SupeDectve (NFSD) beamfome as the fxed beamfome n the fst path of the GS [34]. oweve thee s stll one ue emaned to be solved: The best pefomance of NFSD occus n endfe stuaton (whee the desed souce s at ). On the othe sde due to the employed Jm and Gffth s blockng matx [] the GS suffes fom the leakage of the desed sgnal when the sgnal souce s not n boadsde stuaton (o at 9 ); Ths s because of the sgnal leakage n the ntefeence cancelle block of the GS. As a emedy n ths eseach we popose a novel blockng matx to exclude the desed sgnal fo evey desed decton wthout the sgnal leakage. Futhemoe the nput sgnals ae paed though a nea feld compensaton block befoe the blockng matx. The utlzaton of the compensaton block s neceay accodng to the blockng matx stuctue; the nput sgnals of the blockng matx should be the same (n ampltude and phase chaactestcs) to pevent sgnal leakage n the efeence nose (output of ntefeence cancelle block). Fnally we also popose some post-fltes to be appled on the beamfome output. We modfy Mcowan post-flte [56] by calculatng coheence functon fom mcophoneaay nputs. onsdeng the dea behnd the modfed Mcowan post-flte we also popose a modfed veson of STSA post-flte [78]. The est of ths pape s oganzed as follows: In Secton 2 we explan the basc NFSD-GS and pesent the poposed modfcatons. Secton 3 explans post-fltes and ou poposed methods fo post-flteng. In Secton 4 we explan the expements and evaluaton esults. Fnally Secton 5 contans some concludng emaks. 2. ADAPTIVE BEAMFORMING 2.. Employng NFSD n GS Stuctue (NFSD-GS) The basc GS system has two paths: ) a standad fxed beamfome wth constants on the desed decton and 2) an adaptve nose cancelle to mnmze the nose powe at the output. In tun the second path ncludes a blockng matx that emoves the desed sgnal fom the nosy nputs EURASIP 22 - ISSN

2 and an Intefeence ancelle (I) whch s updated usng an unconstaned adaptve algothm such as the Least Mean Squae (LMS) []. The so-called NFSD-GS [3] uses an NFSD beamfome as the fxed beamfome n uppe path Nea-Feld ompensaton In fa-feld condtons the desed souce s fa enough fom the aay so that the eceved desed sgnal on mcophones can be consdeed as the same; howeve n nea-feld condtons the ampltude/ phase of the eceved desed sgnal on mcophones ae not the same Thus n nea-feld condtons even fo the boadsde sgnal souce the sgnal leakage s occued n the lowe path of GS. As shown n Fg n the case of a nea-feld desed souce a nea-feld compensaton should be fstly appled on the nput sgnals to algn the desed sgnal on all chaels (befoe the blockng). To ensue full cancellaton we have to compensate fo both phase msalgnment and ampltude scalng of the desed sgnal aco mcophones by [3]: X '' = X d NF () whee X s nput vecto X '' s nput of blockng matx and d NF s steeng vecto fo nea-feld condton that s gven by: d NF = exp( 2πf )... exp( 2πf c M M T ) c whee s the space between mcophone and sgnal souce f s fequency ndex and c s the sound velocty. (2) blockng matx column beampatten(db) Fa.feld -7 Uncomp.Nea.feld comp.nea.feld angle(degee) Fg. 2.The beampatten of Jm and Gffths blockng matx (fst ow) n fa- nea- compensated nea-feld cases. whee s nose feld coheence matx. The (m)-th component of s the coheence between the nose sgnals that s calculated based on nose PSDs and co spectal denstes between mcophones and ( ϕ ) [5]: Ω Ω Ω = ϕ e ϕ e ϕ e. (5) In the case of dffuse nose feld the coheence functon s expeed by: Ω sn( Ωf slm c) ( e ) = (6) dffuse Ωf slm c whee l m s mcophone spacng f s s samplng fequency Ω s fequency ndex and c s the sound velocty. The output of blockng matx (B) s: ' '' X = B X. (7) If A denotes the adaptve fles of I block the output of lowe path s gven by: Fg.. Block dagam of NFSD-GS Fg. 2 shows the dectvty patten at 4kz fo the fst ow of the Jm and Gffths blockng matx [] fo an aay wth 5 mcophones wth nte-mcophone dstance of 4 cm. As shown n the nea-feld condtons the fa-feld chaactestcs of the blockng matx can be appoxmated by the use of a nea-feld compensato (equaton ()). The pefomance of ths system can be summazed as follows. If aay has M mcophones and X denotes the sgnals eceved by aay afte tme algnment the output of uppe path s gven by: y = ( M) W X (3) whee s the weghtng fltes of NFSD that ae typcally fomulated to maxmze the aay gan as: W { d } [ + I ] d d [ + εi ] = NF NF NF ε (4) y A = A. X. (8) It should be noted that the adaptve fltes ae updated usng the standad unconstaned LMS algothm as follows: A k + = Ak + µ yk X k (9) whee µ s the adaptaton step sze and k s the fame ndex. Fnally the system output s calculated fom the outputs of the uppe and lowe paths as: Y = y y A. () 2.3. Poposed Blockng Matx Thee s an ue n basc NFSD-GS that should be esolved somehow: The best pefomance of NFSD occus n endfe stuaton. On the othe sde due to the employed Jm and Gffth s blockng matx [] the GS suffes fom the leakage of the desed sgnal when the sgnal souce s not n boadsde stuaton. In ths eseach we popose the use of Lnealy onstaned Mnmum Vaance (LMV) beamfome [2] 266

3 to elease the above-mentoned lmtaton of the decton of desed sgnal. The weghts (flte coeffcent) of LMV ae calculated so that mnmze the output powe (output vaance) whle mposng multple lnea constants on the output sgnal (fo pesevng desed sgnal and emovng dectonal undesed sgnals) [2]. Optmal coeffcent vecto s calculated as []: W opt =R - x ( R - x ) - F () whee R x s nput covaance matx W opt s weght vecto and and F ae constant matx and vecto espectvely. ee we explot the LMV as a blockng matx to extact the desed sgnal comng fom a specfc decton; thus the constant matx and vecto should be detemned such that fulfll a null towads desed decton and unty value towads dectonal nose(s). In ths way LMV povdes a sgnal-fee nput fo the I block n any abtay decton of desed sgnal. In the followng we efe to the above-mentoned stuctue as NFSD-Lnealy onstaned GS o befly NFSD-LGS. 3. POST-FILTERING Post-flteng denotes the poceng of beamfome output by a sngle chael nose suppeon flte. The postflteng can sgnfcantly mpove the SNR and speech qualty [7]. When the equed statstcal and spectal nfomaton of the speech and the nose ae pesent Wene post-flte (PF) s the optmum PF that povdes a Mnmum Mean Squaed Eo (MMSE) estmaton of the desed sgnal. The tansfe functon of Wene flte s estmated by: h = ϕ ϕ + ϕ ) (2) w ( whee ϕ and ϕ ae powe spectal denstes (PSDs) of the (sngle-chael) desed sgnal and nose espectvely. Obvously the estmates of the sgnal and nose PSDs ae equed to fomulate the PF tansfe functon. Thee ae two man appoaches fo ths pupose: ) nose PSD s estmated fom slent fames of nput sgnal and PF coeffcents ae calculated by an teatve algothm []. 2) speech and nose PSDs ae estmated by the use of the autoand co-spectal denstes of the mult-chael nput sgnals (afte the tme algnment module) [567]. The latte s efeed to as the Zelnsk PF. PFs ae called sngle-chael when the PF coeffcents ae calculated fom output of a beamfome and called mult-chael when the PF coeffcents ae estmated fom aay nput sgnals. 3.. Modfed Mcowan Post-Flte Unde the aumptons: ) the speech and nose ae uncoelated ( ϕ n s = ) and 2) the nose powe spectum s the same on all mcophones ( ϕ n n = ϕ ) the auto and co-spectal denstes of the algned sgnals can be calculated and updated usng Welsh ecusve update fomula as [56]: * ˆ ϕ ˆ x x = αϕ x x + α x x (3) whee ˆϕ x x and ˆϕ ae the spectal estmates fo the x x pevous and cuent fames espectvely and * s the complex conugate opeato. Also α s a facto close to unty. If aay has M mcophones the speech PSD can thus be estmated as [56]: R{ ˆ ϕ } R{ ˆ }( ˆ ϕ ˆ + ϕ ) ( ) ˆ ϕ 2 = R ˆ { } M M ( ) = (2 M ( M )) = = + ˆ ϕ ˆ ϕ (4) whee ˆϕ s nose co spectal densty between x x mcophones and and Ĉ s coheence functon of nose feld (equaton(5)). The PF denomnato ( ϕ + ϕ ) n equaton (2) can n tun be estmated by aveagng ˆ ϕ x x ove all unque mcophone combnatons. The esultng PF s [56]: hˆ ˆ ϕ =. (5) pf M ( M ) = ˆ ϕ x x onsdeng equatons (4) and (5) coheence functon has a fundamental ole n the above equatons. Mcowan pesented a PF by modfyng the aumpton of zeo coelaton between the noses n dffeent chaels [56]. Mcowan PF s calculated by consdeng dffuse nose felds (snc functon n equaton (6)). Although Mcowan PF s appopate n some condtons but n ealstc nose stuatons (whee smultaneously nclude dffuse ncoheent and dectonal noses) the use of snc coheence functon s some msleadng. In ths eseach we pesent Modfed Mcowan (o Mod-Mcowan) PF by use of the pactcal coheence functon of nose feld that can be calculated and updated n slent fames of nput sgnals (that ae specfed by means of a Voce Actvty Detecto (VAD)). It s expected that the PF pefomance s mpoved due to a moe accuate estmaton of coheence functon Spectal Ampltude MMSE Post-Fltes A mao categoy of the PFs ae based on MMSE estmaton of Shot-Tme Spectal Ampltude (STSA). onsdeng the mao mpotance of the spectal ampltudes the STSA of the enhanced sgnal s estmated and combned wth the shot-tme phase of the nosy (nput) speech. By usng ths PF at the output of beamfome ( T (X ) ) the spectal ampltude of the clean speech s estmated by [78]: 267

4 u u u u sˆ = R. Γ(.5).exp. ( + u) I + ui (6) MMSE STSA γ whee R = T( X) Γ denotes the gamma functon and I and I denote the modfed Beel functons of zeo and fst odes espectvely. Also u s defned by u = ( ζ ( + ζ )). γ whee ζ and γ ae a po and a posteo sgnal-to-nose ato of T (X ) espectvely: 2 ζ = ϕ ϕ γ = R ϕ. (7) Geneally n spectal ampltude MMSE γ s calculated fom equaton (7) usng nose PSD estmaton; But ζ s gven by a ecusve algothm as [7]: 2 ζ = β. h SA ( l ). γ ( l ) + ( β ).max( γ ( l) ) (8) whee h denotes PF tansfe functon l s fame numbe SA β s a constant between zeo and one and max s the sgn of maxmzaton. In ths eseach we have consdeed a mult-chael veson of the STSA PF. ee we use the algothm descbed n sub-secton 3. to estmate powe spectal denstes of sgnal and nose (to be used n the calculaton of STSA PF). So the PF coeffcents ae estmated fom aay nput sgnals. Also ζ s calculated by equaton (7) usng desed sgnal PSD that s specfed n equaton (4) and nose PSD. The latte s estmated fom slent fames of nput sgnals and can be updated. The poposed PF s called Pop. STSA. 4. EXPERIMENTS AND RESULTS Fo the evaluaton of the poposed modfcatons we have fstly compaed the pefomance of the NFSD-LGS wth that of basc NFSD-GS. Then we have evaluated the effect of dffeent descbed PFs been at the output of NFSD- LGS. Thee obectve measues have been consdeed n these evaluatons: SSNR (Segmental SNR) LLR (Log Lkelhood Rato) and PESQ (Peceptual Evaluaton of Speech Qualty) []. Fo the evaluaton of methods we smulated the souces and mcophone aay setup shown n Fg. 3 (wth d=4 cm). Fg. 3. Aay and nose souces stuaton Accodng to the boad-band chaactestc of speech sgnal we have taken advantage of nested sub-aay technque [] fo the mplementaton of the methods. Ths facltates appopate poceng on each fequency subband. The mplemented sub-aay technque dvdes the boadband sgnal nto thee subband sgnals. A lnea unfom aay wth 5 mcophones has been used n each subband as follows: f < kz : mcophones and 9 kz < f < 2 kz : mcophones and 8 2 kz < f < 4 kz : mcophones and 7 The desed speake was consdeed n nea-feld stuaton. As shown n Fg. 3 thee wee thee dectonal nose souces n thee dffeent angles wth espect to the aay axs whch ae n the fa-feld: An ntefeng speake at the angle of 65 ; A whte Gauan nose souce at the angle of 6 ; and a snusodal (3 kz) nose souce at 45. Fo the desed sgnal and ntefee speake we used seveal segments of speech fom the TIMIT database [2]. To make the nosy nputs we also consdeed the ncoheent and dffuse noses. Fo modelng ncoheent nose whte Gauan noses wth the same ampltude ae ndependently added to each mcophone. Also dffuse nose s geneated usng equally spaced nose souces unfomly dstbuted on the sphee whose adus s much lage than senso dstance (d) [3]. Dffuse dectonal and ncoheent nose components wee added to each nput sgnal at a popoton of 3 3 and espectvely. All the sgnals wee at the samplng ate of 8 kz. To examne the effect of the poposed LMV blockng matx the beam-patten of ts fst ow has been depcted n Fg. 4. The beam-pattens wee calculated at the fequency of kz and n the case of dffeent aval dectons of desed sgnal ( 3 6 and 9 ). ampltude(db) endfe angle(degee) Fg. 4. The beam-patten of poposed LMV blockng matx (fst ow) n the case of dffeent desed dectons onsdeng the cuves n Fg. 4 the poposed blockng matx has poduced a tue null n the decton of desed sgnal. Ths guaantes a sgnal-fee nput fo the I block and consequently no sgnal cancellaton at the output of NFSD-LGS. In othe wod ths has genealzed NFSD- GS fo evey desed decton wthout any sgnal leakage n efeence nose. In the next step a set of expements was done to compae the pefomance of basc NFSD-GS (n boadsde condton) and NFSD-LGS (n endfe condton) n 268

5 vaous nput SNR values (-5 db db and 5 db). The compaatve esults have been lsted n Table along wth those fo the nosy nput. The esults show that the poposed NFSD-LGS s consstently supeo to the basc NFSD- GS n tems of SSNR LLR and PESQ. Ths can be ustfed by consdeng that n the poposed stuctue both uppe and lowe paths ae n the best pefomance howeve n basc NFSD-GS only the lowe path s n ts best pefomance. It s noted that n ths evaluatons both NFSD-GS and NFSD-LGS stuctues have been n the best wokng stuatons. In the next set of the expements we compaed the pefomance of dffeent PFs that wee appled to the output of NFSD-LGS. Table 2 summazes the esults of these expements n vaous nput SNR values. The esults show that the Mod. Mcowan PF s supeo to the Mcowan PF n tems of SSNR LLR and PESQ. Futhemoe Mod. Mcowan PF has a bette pefomance compaed to snglechael Wene PF n tems of LLR and PESQ; howeve t s not bette n SSNR measue. Also whle the Pop. STSA PF pefoms bette compaed to the STSA PF n tems of SSNR t s slghtly wose n LLR cteon. 5. ONLUSION In ths pape we ntoduced a new beamfomng stuctue that ncopoates NFSD n uppe path of GS usng nea-feld compensaton and genealzed ths system fo dffeent desed dectons. The latte was done by eplacng the blockng matx wth an LMV flte. The poposed NFSD-LGS obvously outpefoms basc NFSD-GS n the suppeon of dffuse ncoheent and dectonal noses. Futhemoe we poposed some modfcatons fo the post-fltes that ae appled on the output of NFSD-LGS. The evaluaton esults demonstate the supeoty of the Modfed Mcowan PF athe than the Mcowan PF. Also the mult-chael Pop. STSA PF showed slghtly bette pefomance n compason wth ts sngle-chael veson (STSA PF). 6. REFERENES [] J. Benesty J. hen and Y. uang Mcophone Aay Sgnal Poceng Beln Gemany: Spnge-Velag 28. [2] D. ommnello M. Scapnt R. Pas and A. Uncn A Novel Affne Poecton Algothm fo Supedectve Mcophone Aay Beamfomng n Poc. of 2 IEEE Intenatonal Symposum on cuts and Systems Jun. 2 pp [3] I. Mcowan D. Mooe And S. Sdhaan Speech Enhancement Usng Nea-Feld Supedectvty wth an Adaptve Sdelobe ancelle and Post-Flte n Poc. of 2 Austalan Inenatonal ofeence On Speech Scence and Technology Dec. 2 pp [4] I. Mcowan. Mao and L. Mauuay. Robust Speech Recognton Usng Neafeld Supedectve Beamfomng wth Post-Flteng n Poc. of IASSP- vol. 3 2 pp [5] I. Mcowan and. Boulad Mcophone Aay Post-Flte Based on Nose Feld oheence IEEE Tans. on Speech and Audo Poceng vol. no. 6 pp Nov 23. [6] S. Lefkmmats and P. Maagos A Genealzed Estmaton Appoach fo Lnea and Nonlnea Mcophone Aay Post- Fltes Speech ommuncaton vol. 49 pp Feb 27. [7] T. Lotte. Benen and P. Vay Mutchael Speech Enhancement Usng Bayesan Spectal Ampltude Estmaton n Poc. of IASSP-3 23 pp. I88-I883. [8] L.. Km M.. Johnson and S. Koeng-Mo Genealzed Optmal Multmcophone Speech Enhancement Usng Sequental Mnmum Vaance Dstotonle Response (MVDR) Beamfomng and Post-Flteng n Poc. of IASSP-6 vol. 3 July 26. [9] M. Souden J. Benesty and S. Affes A Study of the LMV and MVDR Nose Reducton Fltes IEEE Tans. on Sgnal Poceng vol. 58 no. 9 pp Sept. 2. [] J. ansen B. Pellom An Effectve Qualty Evaluaton Potocol fo Speech Enhancement Algothms n Poc. of ISLP Dec. 998 pp [] W. Taweesangungo and R. Suleesatha Equalze and Sub- Aay Beamfome fo Speech Enhancement n Poc. of AS Automatc ontol onfeence 25. [2] J. S. Gaofolo et al. TIMIT Acoustc-Phonetc ontnuous Speech opus Lngustc Data onsotum Phladelpha 993. [3] E. abets and S. Gaot Geneatng senso sgnals n sotopc nose felds ul: 27. Table : ompason of basc NFSD-GS and pop. NFSD-GS SNR_n = -5 db SNR_n = db SNR_n = 5 db SSNR LLR PESQ SSNR LLR PESQ SSNR LLR PESQ nput basc NFSD-GS NFSD-LGS SNR_n = -5 db SNR_n = db SNR_n = 5 db Table 2: Evaluaton of dffeent post-fltes appled to the output of NFSD-LGS NFSD-LGS Mod. Mcowan Wene PF Mcowan PF (no PF) PF STSA PF Pop. STSA PF SSNR LLR PESQ SSNR LLR PESQ SSNR LLR PESQ