Enhancement of Noisy Speech Using Sliding Discrete Cosine Transform

Transcription

1 Enhancemen of Noiy Speech Uing Sliding Dicree Coine Tranform Vialy Kober Deparmen of Compuer Science, Diviion of Applied Phyic CICESE, Enenada, B.C. 860, Mexico Abrac. Denoiing of peech ignal uing a liding dicree coine ranform (DCT) i propoed. A minimum mean-quare error (MMSE) eimaor in he domain of a liding DCT i derived. In order o provide peech proceing in real ime, a fa recurive algorihm for compuing he liding DCT i preened. The algorihm i baed on a recurive relaionhip beween hree ubequen local DCT pecra. Exenive eing ha hown ha bacground noie in acual environmen uch a he helicoper cocpi can be made impercepible by proper choice of uppreion parameer. Inroducion Proceing of peech degraded due o addiive bacground noie i of inere in a variey of a. For example, many peech ranmiion and coding yem, whoe deign i predicaed on a relaively noie-free environmen, degrade quicly in qualiy and performance in he preence of bacground noie. Thu, here i a coniderable inere in and applicaion for he developmen of uch yem, which compenae for he preence of noie. In many cae, inelligibiliy i affeced by bacground noie o ha a principal objecive of a peech proceing yem may be o improve inelligibiliy. Numerou yem have been propoed o remove or reduce bacground noie [-8]. Thee yem provide an apparen improvemen in ignal-onoie raio, bu inelligibiliy i in fac reduced. In hi paper, an approach o peech denoiing on he bae of a liding DCT i ued. In many filering and pecral analyi applicaion, he ignal uch a peech have inherenly infinie lengh. Moreover, ince he ignal properie (ampliude, frequencie, and phae) uually change wih ime, a ingle orhogonal ranform i no ufficien o decribe uch ignal. A a reul, he concep of hor-ime ignal proceing wih filering in he domain of an orhogonal ranform can be ued [9]. The hor-ime orhogonal ranform of a ignal x i defined a n= + n ( n ) = x w ψ,, () where w n i a window equence, ψ(n,) repreen he bai funcion of an orhogonal ranform. Equaion () can be inerpreed a he orhogonal ranform of x +n a n A. Sanfeliu and J. Ruiz-Shulcloper (Ed.): CIARP 003, LNCS 905, pp. 9 35, 003. Springer-Verlag Berlin Heidelberg 003

2 30 V. Kober viewed hrough he window w n. diplay he orhogonal ranform characeriic of he ignal around ime. Noe ha while increaed window lengh and reoluion are ypically beneficial in he pecral analyi of aionary daa, for ime-varying daa i i preferable o eep he window lengh ufficienly hor o ha he ignal i approximaely aionary over he window duraion. We aume ha he window ha finie lengh around n=0, and i i uniy for all n [- N, N ]. Here N and N are ineger value. Thi lead o ignal proceing in a liding window [0]. In oher word, local filer in he domain of an orhogonal ranform a each poiion of a moving window modify he orhogonal ranform coefficien of a ignal o obain only an eimae of he pixel x of he window. The choice of orhogonal ranform for liding ignal proceing depend on many facor. The DCT i one he mo appropriae ranform wih repec o he accuracy of power pecrum eimaion from he oberved daa ha i required for local filering, he filer deign, and compuaional complexiy of he filer implemenaion. For example, linear filering in he domain of DCT followed by invere ranforming i uperior o ha of he dicree Fourier ranform (DFT) becaue a DCT can be conidered a he DFT of a ignal evenly exended ouide i edge. Thi conequenly aenuae boundary (emporal aliaing) effec caued by circular convoluion ha are ypical for linear filering in he domain of DFT. In he cae of DFT, peech frame are uually windowed o avoid emporal aliaing and o enure a mooh raniion of filer in ucceive frame. For he filering in he domain of DCT, he windowing operaion can be ipped. In uch a manner he compuaional complexiy can be furher reduced. The preenaion i organized a follow. In Secion, we preen compuaionally efficien algorihm for compuing he liding DCT. In Secion 3, an explici filer formula minimizing he MMSE defined in he domain of he liding DCT i derived. We alo e he filer performance in acual environmen uch a he helicoper cocpi. Secion 4 ummarize our concluion. Fa Algorihm for Compuing he Sliding DCT The dicree coine ranform i widely ued in many ignal proceing applicaion uch a adapive filering, video ignal proceing, feaure exracion, and daa compreion. Thi i becaue he DCT perform cloe o he opimum Karhunen- Loeve ranform for he fir-order Marov aionary daa, when he correlaion coefficien i near 0.9 []. Four ype of DCT were claified []. The DCT dicued in he paper i referred o he ype-ii. The ernel of he DCT i defined for he order N a DCT = ( n / ) + co π, () N

3 Enhancemen of Noiy Speech Uing Sliding Dicree Coine Tranform 3 if = 0, where n, =0,,, N-; =. For clariy, he normalizaion oherwie. facor N for he forward ranform i negleced unil he invere ranform. The liding coine ranform (SCT) i defined a N n= N ( n + N ) + = x + n co π, (3) N where N=N +N +, { ; =0,,, N-} are he ranform coefficien around ime. The coefficien of he DCT can be obained a { C 0 = 0 ; C =, =,, N-}. We now derive fa algorihm for he SCT on he bae of a recurive relaionhip beween hree ubequen local DCT pecra [3]. The local DCT pecra a he window poiion - and + are given by + = = N n= N N + n= N+ ( n + N + ) π x + n co π +, (4) N N ( n + N + ) π x+ n co π. (5) N N Uing properie of he coine funcion and equaion (4) and (5), we can wrie + π π = co + co x N N. (6) ( x x + ( ) ( x x ) N N + N + + N We ee ha he compuaion of he DCT a he window poiion + involve value of he inpu equence x a well a he DCT coefficien compued in wo previou poiion of he moving window. The number of arihmeic operaion required for compuing he liding dicree coine ranform a a given window poiion i evaluaed a follow: he SCT for he order N wih N=N +N + require (N-) muliplicaion operaion and N+5 addiion operaion; he DCT require one exra operaion of muliplicaion. Table li numerical reul of compuaional complexiy for he propoed algorihm and nown fa DCT algorihm. Noe ha fa DCT algorihm require he lengh of a moving window o be of a power of, N= M. In conra, he lengh of a moving window for he propoed algorihm i an arbirary ineger value deermined by he characeriic of he ignal o be proceed. We ee ha he propoed algorihm yield eenially beer reul when he lengh of he window increae.

4 3 V. Kober Table. Number of muliplicaion and addiion for compuing he liding DCT M Fa DCT[4, 5] Propoed algorihm Mul. Add. Mul. Add The invere algorihm for he liding DCT can be wrien a follow. x N = N = ( N / ) + + co π, (7) N 0 where N=N +N +. The compuaional complexiy i N muliplicaion operaion and N addiion operaion. If x i he cenral pixel of he window, ha i, N =N and N=N +, hen he invere ranform i implified o N = ( ) + x 0. (8) N = We noe ha in he compuaion only he pecral coefficien wih even indice are involved. The compuaion require one muliplicaion operaion and N + addiion operaion. 3 Denoiing of Speech Signal in he Sliding DCT Domain The objecive of hi ecion i o develop a noie uppreion echnique on he bae of he liding DCT, and o e he algorihm performance in acual noie environmen. We deign locally adapive filer o enhance noiy peech. Aume ha a clean peech ignal {a } i degraded by zero-mean addiive noie {v } where {x } i a noiy peech equence. Le {, A, V, x = a + v, (9) Â ; =0,,, N-} be he DCT ranform coefficien around ime of noiy peech, clean peech, noie, and filered ignal, repecively. Here N=N + i he lengh of he DCT. Noe ha N i an arbirary ineger value, which i deermined by pich period of peech. One can be choen o be approximaely a he maximum expeced pich period for adequae frequency reoluion.

5 Enhancemen of Noiy Speech Uing Sliding Dicree Coine Tranform 33 Variou crieria can be exploied for he filer deign. In he following analyi we ue he crierion of he MMSE around ime which i defined in he domain of DCT, aing ino accoun (8), a follow: MMSE N = 0 [ A A ] = E ˆ α, (0) where E. denoe he expeced value. A we menioned above, he lengh of he window i choen in uch a way ha noie can be conidered a aionary in he window. Le P = E V denoe he power pecrum of noie in he domain of DCT. Suppoe ha A ˆ = H, here filer o be deigned around ime. By minimizing MMSE wih repec o arrive o a verion of he Wiener filer in he domain of DCT: H i he H, we H P P = =. () The MMSE eimaion of he proceed peech in he domain of he liding DCT i given by P ˆ, if > = P A. () 0, oherwie The obained filer can be conidered a a pecral ubracion mehod in he domain of liding DCT. In general, pecral ubracion mehod [], while reducing he wideband noie, inroduce a new muical ' noie due o he preence of remaining pecral pea. To aenuae he muical noie, one can ugge overubracion of he power pecrum of noie by inroducing a nonzero power pecrum bia. Finally, he MMSE eimaion of he proceed peech in he domain of he liding DCT can be wrien a follow: P ˆ, if > + = P B A, (3) 0, oherwie where B i a peech-dependen bia value. The filered peech ignal can be obained wih ue of (8). I alo follow from (8) ha in he eimaion only he pecral coefficien wih even indice are involved.

6 34 V. Kober A e peech ignal recorded in helicoper environmen i preened in Fig.. The daa wa ampled a 6.00Hz. In our e he window lengh of 76 ample i ued. The liding quared DCT coefficien averaged over all poiion of he running window for noiy peech i preened in Fig.. The power pecrum of noie i obained by acual meauremen from bacground noie in inerval where peech i no preened. I i hown in Fig. 3. We ee he difference in pecral diribuion of he peech and he helicoper noie, which will help u o uppre he helicoper noie. Fig.. Time wavefron of helicoper peech Fig.. Average quared DCT magniude of noiy peech Fig. 4. Enhanced peech ignal Fig. 3. Average quared DCT magniude of noie The reul of filering by uing he propoed filer i hown in Fig. 4. I i clearly ha he yem i capable of ignifican noie reducion. Numerou formal ubjecive e are hown ha he helicoper noie can be made impercepible by proper choice of he filer parameer in (3). In hi ecion we derived a filer for noie uppreion on aumpion ha peech i alway wa preened in he meaured daa. However, if a given frame of daa coni of noie alone, hen obviouly a beer uppreion filer can be ued [5, 6]. In general, an opimal algorihm hould include a deecor of voiced and unvoiced peech ignal. Afer deecing, differen raegie of proceing hould be applied o voiced and unvoiced peech ignal.

7 Enhancemen of Noiy Speech Uing Sliding Dicree Coine Tranform 35 4 Concluion In hi paper, we have preened a new echnique for enhancing peech degraded by addiive noie. The echnique uilize he liding DCT. A MMSE eimaor in he domain of he liding DCT ha been derived. In order o provide peech proceing in real ime, a fa recurive algorihm for compuing he liding DCT ha been uggeed. The algorihm require eenially le operaion of muliplicaion and addiion comparing wih nown fa DCT algorihm. Exenive eing ha hown ha bacground noie uch a in he helicoper cocpi can be ignificanly reduced by proper choice of uppreion parameer. Acnowledgmen. Thi wor wa uppored by he gran A from CONACYT Reference. Boll S.F., Suppreion of acouic noie in peech uing pecral ubracion, IEEE Tran. Acou. Speech Signal Proce., Vol. ASSP-7, (979) Lim J.S. and Oppenheim A.V., Enhancemen and bandwidh compreion of noiy peech, Proc. IEEE, Vol. 67, (979) McAulay R.J., Malpa M.L., Speech enhancemen uing a of-deciion noie uppreion filer, IEEE Tran. Acou. Speech Signal Proce., Vol. ASSP-8, (980) Ephraim Y. and Malah D., Speech enhancemen uing a minimum mean-quare error hor-ime pecral ampliude eimaor, IEEE Tran. Acou. Speech Signal Proce., Vol. ASSP-3, No. 6, (984) Ahmed M.S., Comparion of noiy peech enhancemen algorihm in erm of LPC perurbaion, IEEE Tran. Acou. Speech Signal Proce., Vol. 37, No., (989) Chen Y.M. and O Shaughney D., Speech enhancemen baed concepually on audiory evidence, IEEE Tran. Signal Proce., Vol. 39, No.9, (99) Ephraim Y., A Bayeian eimaion approach for peech enhancemen uing hidden Marov model, IEEE Tran. Signal Proce., Vol. 40, (99) Hu H.T., Robu linear predicion of peech ignal baed on orhogonal framewor, Elecronic Leer, Vol. 34, No 4, (998) Oppenheim A.V., Shafer R.W., Dicree-ime ignal proceing, Prenice Hall, Englewood Cliff, NJ (989). 0. Viu R.Y., and Yarolavy L.P., Recurive algorihm for local adapive linear filraion, in: Mahemaical Reearch., Ed.: Yarolavy L.P., Roenfeld A., and Wilhelmi W., Academy Verlag, Berlin, (987) Jain A.K., A inuoidal family of uniary ranform, IEEE Tran. Paern Anal. Machine Inell., Vol. PAMI-, No 4, (979) Wang Z., Fa algorihm for he dicree W ranform and for he dicree Fourier ranform, IEEE Tran. Acou. Speech Signal Proce., Vol. ASSP-3, No 4, (984) Kober V. and Criobal G., Fa recurive algorihm for hor-ime dicree coine ranform, Elecronic Leer, Vol. 35, No 5, (999) Hou H.S., A fa recurive algorihm for compuing he dicree coine ranform, IEEE Tran. Acou. Speech Signal Proce., Vol. ASSP-35, No 0, (987) Briana V, On he dicree coine compuaion, Signal Proce., Vol. 40, No -3, (994)