AN EFFICIENT ALGORITHM FOR REAL-TIME SPECTROGRAM INVERSION. Gerald T. Beauregard Xinglei Zhu Lonce Wyse. Research, Singapore

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1 AN EFFICIENT ALGORITHM FOR REAL-TIME SPECTROGRAM INVERSION Gerald T. Beauregard Xngle Zhu Lonce Wyse muvee Technologes Insttute for Infocomm Research, Sngapore Insttute for Inforcomm Research, Sngapore ABSTRACT We present a computatonally effcent real-tme algorthm for constructng audo sgnals from spectrograms. Spectrograms consst of a tme sequence of short tme Fourer transform magntude (STFTM) spectra. Durng the audo sgnal constructon process, phases are derved for the ndvdual frequency components so that the spectrogram of the constructed sgnal s as close as possble to the target spectrogram gven real-tme constrants. The algorthm s a varaton of the classc Grffn and Lm [] technque modfed to be computable n real-tme. We dscuss the applcaton of the algorthm to tme-scale modfcaton of audo sgnals such as speech and musc, and performance s compared wth [three] other methods. The new algorthm generates comparable or better results wth sgnfcantly less computaton. The phase consstency between adjacent frames produces excellent subjectve sound qualty wth mnmal fame transton artfacts.. INTRODUCTION Magntude and power spectra, and ther tme sequences n the form of spectrograms, are wdely used to represent the tmefrequency structure of audo sgnals such as speech and musc. By combnng the real and magnary part of each spectral frequency component nto a sngle number, they provde a valuable vsualzaton tool wth a strong correspondence to how sgnals are heard n terms of frequency content. However, they do so at the expense of nformaton whch must be provded n order to convert the representaton back nto an audo sgnal. Frequency magntude representatons are also used computatonally n a number of applcatons (such as nose reducton, sgnal enhancement, sgnal source separaton etc.), where the frequency doman representaton of a sgnal s modfed before beng transformed back nto a tme-doman sgnal. In general however, a modfed (or arbtrary) magntude spectrum s not a vald representaton of an audo sgnal n the sense that there may be only a complex, but no real sgnal whose STFTM exactly matches the modfed one. In such cases, we would lke to fnd a sgnal wth an STFTM as close as possble to the modfed or target STFTM. Grffn and Lm [][] developed an teratve least squares error method for estmatng a real audo sgnal from a modfed STFTM (that we abbrevate G&L ). Ther algorthm monotoncally reduces the dfference between the target magntude spectrum (MS) and the MS of the reconstructed sgnal. The error measure reaches a plateau for most sounds after between 0 and 00 teratons. Though computaton s becomng less of an ssue as computers get faster, G&L s nherently not real-tme snce each teraton must loop over all tme frames n the sgnal before the next teraton s computed. As t was orgnally formulated, the method s unusable for applcatons wth real-tme requrements such as nose reducton n real speech transmsson, or any applcaton requrng nteractve manpulaton of the analyss and synthess parameters. Slaney [] also developed technques to reconstruct tme-doman audo sgnals from cochleagrams and correlograms explotng the G&L technque. Tme-scale modfcaton (TSM) s a process for modfyng the rate of sgnals such as speech or musc whle keepng other characterstcs such as ptch or formants unchanged. TSM s useful n a varety of applcatons such as musc playback. In meda producton for example, TSM s frequently used to synchronze the audo sgnal wth the vdeo sgnal. TSM s typcally mplemented n the tme-doman for computatonal effcency, but we wll demonstrate some advantages to usng a frequency doman method. The rest of the paper s organzed as follows. In Secton we revew the G&L algorthm and show the detals of our Real-Tme Iteratve Spectrogram Inverson algorthm (RTISI) to reconstruct the tme-doman sgnal from a gven spectrogram. In Secton 3 we brefly ntroduce the synchronzed overlap and add (SOLA) method and apply the RTISI algorthm to the tme-scale modfcaton of audo sgnal. In Secton 4 we evaluate our method and compare the results wth three other methods. In Secton 5 we make conclusons.. RECONSTRUCTION OF TIME-DOMAIN SIGNALS FROM THE MSTFTM A dscrete sgnal x(n) can be represented as a sequence of STFT s as follows: X jϖ n ( ms, ϖ ) = x( n) w( n ms ) e () n = where w s the analyss wndow, S s the analyss step sze and m s the ndex of the frames of STFT s. The STFT can be consdered to be generated by sldng a wndow w across the tme doman sgnal wth step sze S. From X(mS,ω) we can exactly reconstruct the tme-doman sgnal x(n). However n many applcatons we need to recover the tme-doman from the magntude spectrum X(mS,ω), or a modfed verson X (ms,ω). In Secton. we take a bref look at the G&L method and n Secton. we present the detals of our algorthm. DAFX-

2 .. The Grffn and Lm (G&L) Algorthm Startng wth an ntal estmate x 0 (n) of the orgnal tme-doman sgnal x(n), the G&L algorthm teratvely renews the estmate x (n) at the th teraton so that the STFTM of the new estmate s monotoncally closer to the STFTM of the orgnal sgnal x(n) n terms of the dstance measure functon D. The M [ x( n), x ( n)] dstance measure s defned as π DM [ x( n), x ( n)] = [ X ( ms, ϖ ) X ( ms, ϖ ) ] dϖ π ϖ π m () = = where X(mS,ω) s the STFTM of orgnal sgnal x(n) and X (ms,ω) s the STFTM of the th estmate x (n). G&L uses the followng functon to update the estmate n each teraton, x jϖ n w( n ms ) X ( ms, ϖ ) e dϖ π + m = ϖ = π ( n) = m = π w ( n ms ) where X (ms,ω) s the STFT of x (n) wth the magntude constrant: X( ms, ϖ ) (4) X ( ms, ϖ) = X ( ms, ϖ) X ( ms, ϖ ) By the magntude constrant, X (ms,ω) has the same phase as X (ms,ω) and the same magntude as X(mS,ω). A Hammng wndow wth L=4S s used, wth scalng such that the sum of the squares of the overlappng wndows s always. Ths smplfes the update functon n Equaton (3), as the denomnator wll be for all n. By the normalzaton of the wndow functon, the update functon of x (n) n Equaton (3) can be smplfed, because the denomnator s equal to for all n. Although Grffn and Lm [] showed that the dstance measure functon monotoncally decreases wth the ncreasng number of teratons, t was not proven that the algorthm converges to a soluton wth the globally mnmum possble error. Convergence to a local mnmum s possble dependng on the ntal estmate x 0 (n). The ntal estmate also determnes the number of teratons requred. In practce, however, wthn 00 teratons ths algorthm generally gves a hgh qualty reconstructon [4]... The Real-Tme Iteratve Spectrogram Inverson (RTISI) Algorthm In order to enable the use of magntude spectra n nteractve and real-tme applcatons, the G&L algorthm needs to be modfed so that a gven frame s dependent only upon the current and prevous frames of the target spectrogram. G&L could also be sped up sgnfcantly by fndng a better ntal estmate of phases for each frame. We accomplsh both of these goals by employng a G&L teraton strategy on the current frame alone, usng nformaton from the audo frames already reconstructed that overlap wth the current frame to construct an ntal current frame phase estmate. Suppose we already have reconstructed the frst m- frames of the synthess sgnal, whch we denote as y m- (n), let us consder the problem of generatng frame m. The sgnal frames already generated at ths pont are llustrated n Fgure. (3) S s S s S s S s Frame m Fgure. An llustraton of the partally reconstructed frames of sgnal y(n). Before frame m s estmated, there exsts an overlap-added result of the frames m-, m-, m- 3 n the range of the frame m wndow. The sold lne shows the magntude contour of the prevously syntheszed sgnal and the dashed lnes ndcates the ndvdual frames. As shown n Fgure, for m> before we estmate the frame m, the overlap nterval s partally flled by the former frames. We use a fxed 75% synthess wndow overlap (.e. S = L/4) n our system so that the m th partal frame comes from the overlap-added results of the estmaton of the frames m-, m-, m-3 of y(n), whle the 4 th quarter of frame m s all zero. The partal frame wll be used to estmate the ntal phase n our system as dscussed below. To dstngush the partally flled frame from the fully constructed frame m, we notate the former as y m- (n)w(n-ms),where w(n) s the wndow functon. Now we estmate frame m and overlap-add t wth the partal frame y m- (n)w(n-ms) to generate y m (n). To generate an ntal estmate for the phases of frame m, we compute the phase of the partally reconstructed sgnal usng an analyss wndow postoned at the partally constructed frame m. Ths ensures that even the ntal phase estmate for frame m wll provde good phase contnuty wth the partally-reconstructed sgnal. The Fourer transform of ths partal frame s calculated wth the same normalzed Hammng wndow as n Secton.. We then apply the magntude constrant of Equaton (4) to ths Fourer transform keepng the phase unchanged. Next we calculate the nverse Fourer transform of ths new frequency doman sgnal to get a new estmate of frame m. If the maxmum teraton number s not reached, we add frame m to the partal frame y m- (n)w(nms), apply the wndow, and calculate the Fourer transform of the wndowed summaton to get a new estmate of the phase. We thus use the update Equaton (3) from the G&L algorthm n our teratve process but nstead of updatng the estmate of the whole sgnal x(n), n each step we update the estmate of the current frame only. The teratve process s llustrated n Fgure. There s a specal case at the begnnng of the sgnal, where we do not have a partal frame to be added to our estmate. Any ntal phase can be used as the ntal phase estmaton for the frst frame. In our experments we smply use a zero ntal phase estmate wth the target magntude spectrum and follow the above teratve process to generate the frst frame of y(n). When the teratve process ends, frame m s combned wth the partal frame y m- (n)w(n-ms) and the process contnues wth advancng frames untl the spectrogram frames are exhausted. We wll refer to ths method as the Real-Tme Iteratve Spectrogram Inverson (RTISI) algorthm. DAFX-

3 FFT wndow + y m- (n) w s (n-ms) N th phase estmaton phase IFFT wndow th estmaton of frame m maxmum teraton number reached? Y overlap-add magntude spectrum magntude chronzed overlap and add algorthm (SOLA) [4] and ts varous modfcatons such as WSOLA[5]/SAOLA[6] /PSOLA[7], the phase vocoder algorthm [8] and some methods for buldng specfc models of speech processes such as the vocal tract model[9] and a probablstc nference model[3]. To acheve tme-scale modfcaton, for polyphonc sgnals the phase vocoder method [8] s a common choce. For monophonc sgnals, a tme-doman process of overlap and add (OLA) s often used as follows. The orgnal sgnal s frst wndowed at length L wth an analyss step sze S a. Then for each wndowed frame a reconstructon sgnal of the same length s generated and all the regenerated sgnal segments are overlap-added wth approprate weghts for the synthess step sze S s. However a smple tmedoman OLA method does not generally work well because the sgnal segments beng overlap-added may not be consstent when the audo modfcaton rate (S s /S a ) s other than. Dfferent OLA varants modfy the basc process to mprove qualty. For example n the SOLA method, the reconstructed frame vares wthn a small range to maxmze a correlaton functon to mprove the consstency of the scaled result. Fgure. Frame-by-frame teratve phase estmaton process Where G&L uses partally reconstructed audo nformaton from frames m-3 through m+3 to reconstruct frame m, the RTISI method uses nformaton from prevous frames only. Also, the partal nformaton used to construct frame m wth G&L changes wth each teraton, whereas n the RTISI method, each frame s estmated strctly n tme order. The frame-by-frame method admts an obvous source of error n that the computaton of frame m s based only on part of the sgnal that the target frame m s based upon. For ths reason, RTISI cannot be expected to match the spectral error measure acheved by G&L. The overlap-add procedure adds audo to frame m from future frames m+, m+ and m+3 after frame m has already been estmated. Ths wll change both the magntudes and the phases of the gven frame when t s analyzed followng the complete constructon of the sgnal. Ths can cause the addton of spectral energy where the magntude has already been closely matched. However, the future frames overlappng wth frame m can also compensate for the error resultng from any nablty to approach the target magntude spectrum due to frequency content not present n the partal sgnal used n the estmaton of frame m. Thus, the error n the resultng spectrogram s n practce not great, and n any case, nter-frame phase consstency s mantaned durng future frame overlap, whch prevents a common source of perceptual degradaton. Furthermore, n the trade-off we gan n speed of convergence gven the greater nformaton for the ntal phase estmate avalable usng RTISI. 3. TIME-SCALE MODIFICATION OF AUDIO SIGNALS Tme-scale modfcaton (TSM) of sgnals has long been a subject of nterest n the audo and speech processng doman. A key challenge n TSM s to change the audo rate, whle preservng other characterstcs such as ptch and tmbre. There have been several approaches reported to modfy the tme-scale of an audo sgnal. Such approaches nclude the G&L method [], the syn- The reconstructon of the wndowed sgnal can be mplemented n ether the tme-doman wth a method such as SOLA, or n frequency doman wth a method such as the phase vocoder or the RTISI algorthm do. Because tradtonal magntude-spectraonly reconstructon methods n [][] requre a large number of teratons of the analyss-synthess cycle to acheve good performance, the tme-doman methods are consdered to be economcal n computaton and have been appled n many commercal mplementatons. The tme-doman TSM methods work well when the modfcaton factor s close to and when the sgnal source s monophonc, but the performance s often degraded when they are appled to polyphonc sounds or when the modfcaton factor s large [0]. The RTISI method s applcable to both monophonc samples and polyphonc samples. The relatvely small amount of calculaton requred by RTISI and the consstency between the adjacent regenerated frames make t applcable to real-tme applcatons. In Secton 3. we descrbe the use of synchronzed overlap and add (SOLA) for TSM. In Secton 3., we dscuss the mplementaton of TSM usng the RTISI approach, and then compare the methods n the evaluaton secton. 3.. Synchronzed Overlap and Add Method SOLA s a modfcaton of the smple OLA method and t provdes more consstency between the reconstructed adjacent frames. Consder a pulse tran across two adjacent wndowed frames n the source sgnal. If the TSM rate s other than, the pulses n neghbourng frames do not lne up for the overlap and add. Ths creates artfacts such as addtonal clcks, false frequences, and reverberaton effects. The addtonal synchronzaton step n SOLA provdes a more a more consstent soluton across frames. SOLA algns the adjacent frames n a way that they are of hghest smlarty where the wndows overlap durng reconstructon n order to mantan the orgnal character of audo sgnal such as ptch nformaton. It s acheved by sldng the new analyss frame along the sgnal reconstructed as so far, whch s noted as DAFX-3

4 y(n), by an algnment offset k p n a range of [k mn, k max ] that maxmzes the followng normalzed cross-correlaton functon: R [ k] = m L q= 0 yms ( + k+ qxms ) ( + q) s L L ( s ) ( q= 0 q= 0 yms + k+ q x ms + q) where L s the length of analyss wndow, S s s the synthess step sze, S a s the analyss step sze, m s the ndex of current frame, and y(n) s the reconstructed sgnal as so far. After the best synchronzaton poston k p s found, the wndowed frame m s overlap-added to the synthess sgnal wth offset k p and the process s repeated for the next frames untl the whole sgnal s exhausted. 3.. The RTISI Method for Tme-Scale Modfcaton The way we apply RTISI to tme-scale modfcaton follows the tradtonal frequency doman method: for a modfcaton rate α, we use an analyss step sze S a to obtan the STFTM and use a synthesze step sze S s such that S a = S s /α. The frame lengths n the analyss and synthess process are both L. Here we use a fxed synthess step sze S s = L/4, whch keeps computatonal requrements consstent for varous modfcaton rates. Gven α, we use an analyss step sze of S s /α to acheve the modfcaton rate. The process s shown n Fgure 3. a a (5) 4. EVALUATION The evaluaton secton s dvded nto two parts: the evaluaton of the phase reconstructon performance and the evaluaton of the TSM applcaton. 4.. Phase Reconstructon Performance We evaluate the phase reconstructon result usng an SNR functon smlar to the one n [3] comparng the spectrogram of the reconstructed sgnal to that of the target: SNR = 0log E ( w f w s ( f ) s ( f ) ) E w f w w E s ( f ) where S w (f) s the STFTM of the orgnal sgnal, S w(f) s the STFTM of the reconstructed sgnal, E s the total energy n the reconstructed sgnal, summatons over w and f are over all wndows and frequences respectvely. We appled the frame-by-frame tme-doman sgnal reconstructon algorthm on a set of 4 test audo samples ncludng chrp samples, frequency modulaton samples, pulse tran samples, male speech samples, female speech samples and musc samples. The average SNR computed by Equaton (6) s shown n Table for dfferent numbers of teratons. (6) Sa Sa Sa L orgnal sgnal Iteraton number Average SNR(dB) Table. Average SNR measures for RTISI spectra Table shows a comparson of RTISI wth G&L on the same test set. We run G&L wth 5, 0 and 50 teratons, and we run RTISI wth 5 and 0 teratons. Fgure 4 llustrates the error n the frequency magntude doman for a typcal data (taken from a vowel sound n male speech). S s S s S s L tme-scale modfed sgnal SNR (db) G&L (5 teratons) 0.37 G&L (0 teratons).6 G&L (50 teratons) 5.50 RTISI (5 teratons) 7.7 RTISI (0 teratons) 8.4 Fgure 3. Tme-scale modfcaton n RTISI. Table. Average SNR results for G&L and RTISI on a test set of 4 sgnals for dfferent levels of teraton. RTISI can effcently acheve excellent nter-frame consstency thereby removng the prmary obstacle to applyng a frequencydoman method to TSM. DAFX-4

5 qute slow, and reasonable stoppng crtera can be chosen to lmt computatonal cost. Fgure 4. Magntude spectra at a partcular frame of a male speech vowel. Shown are comparsons between the orgnal magntude spectra and (a) RTISI at 5 teratons, (b) G&L at 5 teratons, and (c)g&l at 00 teratons. Fgure 5. Dstance from target magntude spectra for dfferent numbers of teratons. Achan[3] recently ntroduced a method of probablstc nference for computng an estmate of reconstructed sgnals gven a spectrogram. To compare RTISI wth ther method, we downloaded the female speech example publshed by the authors on the webste Both the orgnal sgnal and the reconstructon result of the method descrbed n that paper were provded. A comparson of the two methods s shown n Table 3. The SNR fgures show some mprovement usng RTISI, however, there are clck artfacts apparent n the result of the Achan method, the perceptual salence of whch s not adequately reflected n the SNR numbers. SNR (db) Achan s method 7.05 Achan wth AR model 7.04 RTISI (5 teratons) 0.68 RTISI (0 teratons).86 Table 3. SNR from dfferent methods for a specfc sample The RTISI algorthm converges quckly compared wth G&L. Fgure 5 shows the change of the dstance calculated by the Equaton () for dfferent numbers of teratons for the RTISI algorthm. It can be seen that the dstance decreases fast when we ncrease the teraton number from to 5 before stablzng. Fgure 6 shows the dstance between the orgnal sgnal and the reconstructed sgnal usng the measure n Equaton () for both the RTISI method and for G&L. The ntal error of the G&L algorthm s large because of the zero phase ntalzaton n every frame. Because we use the partally constructed frame as our startng pont, we get a much smaller ntal error. Usng only a few teratons, the dstance measure for RTISI decreases to a stable value. The error for G&L decreases monotoncally and t typcally becomes smaller than that of RTISI after about 5 teratons. After the pont at whch the error functons of the two methods cross, the reducton n error for further teraton of G&L s Fgure 6. Change of dstance between the orgnal sgnal and the reconstructed sgnal. The trangle lne s from G&L and the cross lne s from the RTISI algorthm. An obvous extenson to the standard G&L algorthm for nonreal-tme applcatons s to run RTISI for one or two teratons to produce ntal sgnal and phase estmates, and then proceed wth G&L thereafter f a further reducton n error s stll requred. Comparng the tradeoffs n detal s part of our current research. 4.. Tme-Scale Modfcaton Performance For TSM applcatons, we appled the SOLA and RTISI to a varety of audo sgnal types ncludng speech, musc and generated sgnals such as chrp and pulse tran. For a pulse tran, whch s the knd of sgnal SOLA was specfcally desgned to address, SOLA generates better results than RTISI. But for almost all other sound samples, SOLA performs worse than RTISI and the computaton tme of SOLA s much longer because t calculates several dozens cross correlaton functons for each ndvdual frame n the orgnal sgnal. DAFX-5

6 When appled to polyphonc sgnals such as pop musc, there are perceptually obvous artfacts wth SOLA, even wth a modfcaton rate close to. Such artfacts nclude warblng, transent doublng and skppng and tempo modulaton. Informal lstenng tests show that RTISI works well for speech as well as for polyphonc sgnals such as musc, even at modfcaton rates far from. For TSM, there are no reference magntude spectra to compare wth the modfed sgnal so we do not provde an objectve evaluaton functon here, but the artfacts and dstortons from RTISI are far less audble than those from SOLA. There s slght phasness that can be perceved for smple nonstatonary sgnals such as a chrp, but for complex real audo sgnals t s not obvous. Another advantage of RTISI over many tme-doman TSM methods s that there s no need to estmate ptch or make perodc-versus-nose decsons. The straght-forward overlap-and-add process of RTISI generates hgh qualty results and the consstency between successve frames remans even at modfcaton rates far from one. The most salent artfact produced by RTISI audo constructons s a smearng of transent nformaton. The sub-frame sample-rate temporal nformaton from the orgnal sgnal s not used n the method, and the phase choces are made to enforce nterframe consstency rather than any knd of transent pattern. Thus, there are less dstractng artfacts lke clcks and reverberaton n RTISI than SOLA, but musc loses some ts punch and speech loses a small degree of artculaton. The effect s most notceable n hghly transent sgnals such as clck trans or the sound of a cracklng fre. Many examples are avalable for lstenng at 5. CONCLUSIONS The Real-Tme Iteratve Spectrogram Inverson (RTISI) algorthm for constructng real audo sgnals from a sequence of magntude spectra was presented. The method s based a strategy presented by Grffn and Lm [], but s modfed to estmate audo frames n sequence rather than n parallel. In addton to makng the method applcable to real-tme audo sgnal constructon, the modfcaton allows for better ntal phase estmates whch sgnfcantly speed up the convergence toward target spectra. The RTISI method can approach, but not match the performance of G&L run at 00 teratons n terms of magntude spectrum error, however, the perceptual qualty of RTISI after 5 teratons s qute good. If a magntude spectrum error better than that whch RTISI can delver s necessary, the RTISI approach wth one or two teratons can be used to produce an ntal phase estmate for the G&L provdng a sgnfcant speed mprovement. When appled to tme-scale modfcaton, RTISI compares favourably wth the SOLA tme-doman method of sgnal modfcaton n terms of computatonal complexty, and favourably n terms of perceptual results on all but a few specally constructed sgnals. RTISI provdes consderable mprovement at both small and large scalng factors n terms of the absence of the clckness, ptch and reverberaton artfacts that plague tme-doman methods of TSM. Future work s necessary to quantfy the frame transton artfacts that are not reflected n spectral SNR measures. The RTISI method wll also be explored further n the context of other sgnal modfcaton applcatons, and for mprovng the ablty to capture and ncorporate transent behavor from source sgnals n applcatons where such nformaton s avalable. 6. REFERENCES [] D.W. Grffn, J.S. Lm, Sgnal Estmaton from Modfed Short-Tme Fourer Transform, IEEE Transactons on Acoustcs, Speech, and Sgnal Processng, vol.3, no., Apr, 984. [] S.H. Nawab, T.F. Quater, J.S. Lm, Sgnal Reconstructon from Short-Tme Fourer Transform Magntude, IEEE Transactons on Acoustcs, Speech, and Sgnal Processng, vol.3, no. 4, Aug 983. [3] K. Achan, S.T. Rowes, B.J. Frey, Probablstc Inference of Speech Sgnals from Phaseless Sepctrograms, Neural Informaton Processng Systems 6, pp , 003. [4] S. Roucos, A. M. Wlgus, Hgh Qualty Tme-Scale Modfcaton for Speech, IEEE Internatonal Conference on Acoustcs, Speech, and Sgnal Processng, vol.0, pp , Apr 985. [5] W. Verhelst, M. Roelands, An Overlap-Add Technque Based on Waveform Smlarty(WSOLA) for Hgh Qualty Tme-Scale Modfcaton of Speech, IEEE Internatonal Conference on Acoustcs, Speech, and Sgnal Processng, vol., pp Apr 993. [6] D. Dorran, R. Lawlor, E. Coyle, Hgh Qualty Tme-Scale Modfcaton of Speech Usng a Peak Algnment Overlap- Add Algorthm(PAOLA), IEEE Internatonal Conference on Acoustcs, Speech, and Sgnal Processng, vol., pp. 6-0, Apr 003. [7] E. Moulnes, F. Charpenter, Ptch Synchronzed Waveform Processng Technques for Text-To-Speech Synthess Usng Dphones, Speech Communcaton, vol. 9, pp , 990. [8] J. Laroche, M. Dolson, Improved Phase Vocoder Tme- Scale Modfcaton of Audo, IEEE Transactons on Speech, and Audo Processng, vol. 7, No.3, May 999. [9] T.F. Quater, R.J. McAulay, Shape Invarant Tme-Scale and Ptch Modfcaton of Speech, IEEE Transactons on Sgnal Processng, vol. 4, no. 3, Mar 99. [0] E. Moulnes, J. Laroche, Non parametrc technques for ptch-scale and tme-scale modfcaton of speech, Speech Communcaton, vol. 6, pp , Feb 995. [] M. Slaney, D.Naar, R.F. Lyon, Audtory Model Inverson for Sound Separaton, IEEE Internatonal Conference on Acoustcs, Speech, and Sgnal Processng, vol., pp , Apr 994. DAFX-6