APPLICATION OF CEPSTRUM ANALYSIS IN SPEECH CODING. Vahid Abolghasemi, Hossein Marvi

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1 ICSV4 Cairs Australia 9- July, 7 APPLICATION OF CEPSTRUM ANALYSIS IN SPEECH CODING Vahid Abolghasemi, Hossei Marvi Faculty of Electrical & Robotic Egieerig, Shahrood Uiversity of Techology vahidabolghasemi@yahoo.com, marvi_hossei@yahoo.co.uk Abstract A simple Code Excited Liear Predictio Coder based o Cepstral-Aalysis to decrease the bit-rate of coder has bee proposed. The proposed method first applies Cepstral aalysis to the iput speech sigal ad the attempts to remove isigificat coefficiets of the cepstrum. These modified coefficiets rather tha the iput speech samples, are fed to our simple CELP coder to be ecoded. At the decoder side, we compute iverse cepstrum of the decoded coefficiets ad obtai the recostructed speech sigal. Our experimetal results approve the reductio of bit-rate.. INTRODUCTION Speech codig is the compressio of speech (ito a code for trasmissio with speech codecs that use audio sigal processig ad speech processig techiques. I additio, most speech applicatios require low codig delay, as log codig delays iterfere with speech iteractio [].Speech codig algorithms ca be classified ito waveform coders, vocoders ad hybrid coders. I a waveform coder, i the ecoder, a reductio of the sigal dyamics ca be achieved by a fixed or adaptive quatizatio. Better results are obtaied if a (fixed or adaptive predictio filterig, accordig to the correlatio properties of the sigal, is employed. Uder certai presumptios, a predictio gai ca be used to reduce the bit rate, if the predictio error (residual sigal is quatized istead of the origial sigal. The predictio filter parameters may be adapted usig the recostructed sigal []. I vocoders, (or parametric coders ot the sigal samples but the parameters of a source filter speech model are quatized ad trasmitted. This source-filter sythesis represetatio closely follows the model of speech productio. The time-varyig sythesis filter correspods to the vocal tract ad may iclude a model of the acoustic tube ad the lip radiatio. I approximatio, a all-pole model ca be used. The usage of this filter correspods to the priciple of Liear Predictive Codig (LPC. Pure vocoders are particularly used for low bit rate applicatio (below.5 bits per sample. The third type of speech (hybrid coder is the itermediate class betwee waveform coder ad vocoder. This type of coders is workig for medium bit rates (.5... bits per sample with relatively high quality. Similar to a parametric coder, it relies o a speech productio model

2 ICSV4 9- July 7 Cairs Australia durig ecodig. Additioal parameters of the model are optimized i such a way that the decoded speech is as similar as possible to the origial waveform. The majority of moder hybrid speech coders is based o the priciple of liear-predictive aalysis-by-sythesis codig also kow as CELP (Code-Excited Liear Predictio. [][]. I this paper we propose a ovel approach to CELP desig. The proposed method attempts to apply cepstral aalysis to a simple CELP coder, to reduce bit rate. For this purpose the iput speech sigal first is divided ito frames ad the the cepstral coefficiets of every frame is computed. After that, these coefficiets are fed to the CELP coder, istead of the speech frames. Before feedig the frames to the CELP coder, the frame legth has bee decreased by removig some samples (cepstrum coeffs. to reduce the bit rate. This idea is based o the fact that the most importat iformatio of the vocal tract is laid i low qu-frequecies ad pitch iformatio i high qu-frequecies, ad the middle regio of qu-frequecy domai does ot ivolve much speech iformatio [3]. This paper is orgaized as follows. After itroductio, the CELP cocept ad also the basic parts of a simple CELP coder is discussed i sectio. Sectio 3 describes our proposed method usig Cepstral-Aalysis. Experimetal results are give i sectio 4 followed by a coclusio i sectio 5.. THE CELP (CODE EXCITED LINEAR PREDICTION CONCEPT CELP codig ca be itroduced by cosiderig log-term ad short-term liear predictio models. Figure. demostrates a block diagram of the speech productio model icludig a excitatio codebook. As ca be foud from this figure, the extracted excitatio is multiplied with a suitable gai at first. The this scaled sigal is passed through the cascade coectio of pitch ad format sythesis filters to yield the sythetic speech. The advatage of usig this pitch sythesis filter is that the periodicity of the speech sigal is produced associated with the fudametal pitch frequecy. Also the spectral evelope is geerated usig the format sythesis filter []. CELP coders have bee classified ito the aalysis-by-sythesis category. Figure shows a fudametal CELP diagram. As ca be see form the figure, a closed-loop search routie selects the excitatio sigal ad feed it to the sythesis filters. The sythesized sigal is the compared with the origial speech frame followed by a distortio measuremet. This process is repeated for all excitatio codevectors stored i a codebook []. After this procedure the idex of the best excitatio sequece is set to the decoder. Usig this idex, the excitatio codevectors stored i a codebook is reproduced at the decoder. Figure 3 shows more details about the block diagram of the CELP. I the followig these details are described briefly.. Liear Predictio (L model Figure: The CELP Model of speech productio The vocal-tract ca be modelled as a all pole filter usig liear predictio aalysis. This filter geerates the spectral evelope of the speech sigal. The filter coefficiets ca be obtaied by implemetig a lattice filter actig both as a forward ad backward error predictio filter [4].

3 ICSV4 9- July 7 Cairs Australia Eq. shows the time domai equatio that relates the previous samples to the curret oe. Take the advatage of Eq., we ca defie frequecy domai equatio for the filter. p yˆ ( = a y( i ( i= i Figure : Basic CELP scheme, miimize error by selectig best codebook etry. So H( defies as the IIR recostructio filter used to reproduce speech. H ( = = p i + a z i= i. Perceptual Weightig Filter The desiged Liear Predictio filters output the sythetic speech frames. I order to evaluate the differece betwee the origial ad the sythesized speech as a error criterio, these two sigals are subtracted []. The error sequece is passed through a perceptual error weightig filter with system fuctio ( w( = z / c = c M ( p ( cp ( p ( cp...( p...( cp M M (3 Where c is a parameter i the rage < c < that is used to cotrol the oise spectrum i weightig. The coefficiets of the filter A ( z / c are aic which ca be see from M M M z / c = a ( z / c... am ( z / c = ( ac z... ( am c z (4.3 Excitatio sequece The codebook is made up of vectors whose compoets are cosecutive excitatio samples. Each vector cotais the same umber of excitatio samples as there are speech samples i a frame. The codebook is kow to the ecoder as well as the decoder [5][6]. The sigal e( used to excite the LP sythesis filter / is determied every several millisecods withi the frame uder aalysis. A excitatio sequece d k ( is selected from a codebook of stored sequeced, where k is the idex. Excitatio codebook search is the most computatioally itesive part of CELP codig. Throughout the years, may ideas have bee proposed to reduce this complexity issue []. I geeral, differet types of codebooks ca be foud. The most widely used are adaptive codebooks i cojuctio with the fixed codebook []. I our experimet the fixed codebook, which is a collectio of Gaussia sigals, is used. 3

4 ICSV4 9- July 7 Cairs Australia.4 The Pitch Sythesis Filter Figure 3: Block diagram of CELP ecoder As for voiced speech frames, the excitatio sequece demostrates a sigificat correlatio from oe pitch period to the ext, a log-delay correlatio filter is used to geerate the pitch periodicity i voiced speech [][3]. Therefore the filter with system fuctio J ( = (5 P bz describig the effect of the log-term predictor i sythesis, is kow as the log term sythesis filter or pitch sythesis filter..5 Error Miimizatio As metioed above, the excitatio sequece e( is modeled as a sum of a Gaussia codebook sequece d k (, ad a sequece from a iterval of past excitatio, that is e( = Gdk ( + be( (6 The excitatio is applied to the vocal-tract respose / to produce a sythetic speech sequece give by Let, F( =, sˆ = e( * f ( = Gdk ( * f ( + be( * f ( (7 Where the parameters G, k, b, ad P are selected to miimize the eergy of the perceptually weighted error betwee the speech s( ad the sythetic speech over small block of time i.e. E( = w( *( s( sˆ( (8 Let I ( = F( W ( (9 The the error sigal ca be writte as E( = w( * s( Gdk ( * I( be( * I( = E( GE (, k be (, ( Where E ( = w( * s( ( E (, k = dk( * I( ( 4

5 ICSV4 9- July 7 Cairs Australia E (, = e( * I( (3 Note here that sice P ca be greater tha sub frame legth, we eed to buffer previous values of e( to use at this poit. To simplify the optimizatio process, the miimizatio of the eergy of error is performed i two steps. First, b ad P are determied to miimize the error eergy Y ( P, b ] = [ E ( be (, (4 Thus, for a give value to P, the optimum value of b is give by differetiatig the equatio with respect to b ad puttig equal to zero. We get the result bˆ( = E ( E (, E (, Which ca be substituted for b i the equatio for Y ( P, that is Y ( ( P, bˆ = E E ( E (, E (, b Hece the value of P miimizes Y ( P or, equivaletly, maximizes the secod term i the above equatio. The optimizatio of P is performed by exhaustive search, which could be restricted to a small rage aroud the iitial value obtaied from the LP aalysis. Oce these two parameters are determied, the optimum choices of gai G ad codebook idex k are made based o the miimizatio of the error eergy betwee E (5 (6 = E ( be ˆ (, Pˆ ad GE (, (7 3 ( k Thus P ad k are chose by a complete search of the Gaussia codebook to miimize [ E ( GE (, k ] Y (8 ( k, G = 3 which is solved i a similar maer as above. Note, that the output of the filters because of the memory hagover (i.e. the output as a result of the iitial filter state, with zero iput of previous itervals must be icorporated ito the estimatio process. Ad so we eed to store fial coditios of the filters, the previous values of b ad e( to be used i the later frames..6 Quatizatio I our experimet for quatizatio we use uiform scalar quatizatio for the four parameters i.e. Gai, Pitch Delay, Pitch Filter coefficiets, Liear Predict coefficiets ad Excitatio Sequece Idex [][]. 3. PROPOSED METHOD BASED ON CEPSTRAL-ANALYSIS Homomorphic aalysis is based o the cepstrum, which is the iverse Fourier trasformatio of the logarithm of the speech spectrum magitude [7]. 5

6 ICSV4 9- July 7 Cairs Australia By cosiderig the speech spectrum it ca be realized that a speech segmet is cosist of two major parts. Oe is a smooth varyig portio which correspods to the vocal tract, ad the secod part is a rapidly varyig fie structure which is related to the periodic excitatio of the speech sigal [3]. If we represet the spectrum as the product of the vocal tract evelope ad the pitch harmoics, the the cepstrum is computed as the iverse Fourier trasform of the logarithm of the magitude. Sice the vocal tract evelope varies smoothly, it cotais low frequecy compoets, while the fie structure varies more rapidly ad cotais high frequecy compoets [7]. Of course after trasformatio, the low ad high frequecy compoets correspod to low time (qu-frequecy ad high time (qu-frequecy as show i Figure 4 (a Note that the periodic pitch compoet is trasformed to a high time (qu-frequecy peak [3]. From Figure 4 (a it ca be cocluded that Cepstrum, compresses ad separates the vocal tract iformatio i low qu-frequecies ad the pitch iformatio i high qu-frequecies, so there is a gap betwee these two parts which does't iclude sigificat iformatio. Of course these compoets which are laid i medium qu-frequecies correspod to uvoiced iformatio which i compariso with vocal tract ad pitch compoets, have low amplitude. Thus, it is expected that by removig a reasoable umber of these compoets the total bitrate will decrease, which is a promotio i speech codig. It is also clear that the quality of recostructed waveform will decrease, too. Usig this characteristic to reduce the frame legth, i our proposed method, after computig the cepstral coefficiets of the iput speech frames (Figure 4 (a, we decrease the frame legth by removig the coefficiets ivolved the gap (Figure 4(b. The we feed the retaied coefficiets, istead of the speech evelopes, to the CELP coder which described i the previous sectio. Figure 5 shows block diagram of this modified CELP which we call it "CEPS-CELP". (a (b Figure 4: (areal Cepstrum for oe frame of the iput speech sigal. (b Real Cepstrum for oe frame of the iput speech sigal after removig isigificat samples We ca select a wider gap to remove more coefficiets, but as metioed before, the more coefficiets have bee removed; the poorer quality of recostructed speech is achieved. So there is always a tradeoff betwee the quality of decoded speech ad umber of rejected coefficiets. At the decoder side, after sythesis of these coefficiets from the codebook, we compute iverse-cepstrum for every frame ad obtai the recostructed speech sigal. At the decoder side, it is observed that the bit-rate reduced, but a bit degradatio of speech quality also is produced. By applyig log-cepstrum for every frame we have: ( F { log F{ s( } } c( = Re (9 Where s( is the iput speech sigal ad F is the Fourier operator. At the decoder, the recostructed speech sigal is obtaied by applyig 6

7 ICSV4 9- July 7 Cairs Australia ( F { exp( F{ c ( } sr = Re r ( Where c r ( is the recostructed Cepstral coefficiets for every frame. 4. EXPERIMENTAL RESULTS Experimets have bee coducted to evaluate ad approve the proposed method. I our implemetatio vocal-tract filter has L = 5 coefficiets ad the fidelity criterio is MSE The speech sigal is sampled at 8 khz, the frame size is 3ms (4 samples, the block duratio for the excitatio sequece selectio is 5 ms (4 samples. Furthermore, the codebook has 4 sequeces which require bit to sed the idex k. ad the lag of the pitch filter, P, is searched i the rage 6 to 6 (equivalet to 5Hz to 5H which require 8 bit to represet. It should be oted that usig uiform quatizatio at least 4 bits are required to represet every sample. I CEPS-CELP Sice we have made zero coefficiets located i the iterval (5 for 4 frame legth, o-zero samples per frame would be 6. These zeroed samples are ot set s ( Cepstrum c( Aalyzer Code Book Excitatio G bz P Sythesis Filters LP Aalysis sˆ ( A ( + - z / c e(k Perceptual Weightig toward the decoder. Therefore just 6 o-zero samples per frame are set. At the decoder with the kowledge about the umber ad locatio of zeroed samples, we rearrage them ito each decoded frame. It leads to resize the frame legth, up to 4. I fact this procedure is a lossy compressio. Thus the bit allocatio for above parameters chages as follows: -Vocal tract filter L = coefficiets - Pitch filter coeff. = 5 - Gai = 5 - Pitch Delay = 8 MOS scale Speech quality Bad Poor 3 Fair 4 good 5 Excellet Table : The MOS scale We applied both Persia ad Eglish speeches of male ad female to the proposed coder ad foud that, quality of the recostructed speech sigal for Eglish speakers is better, compared to Persia speakers. Aother experimet has bee doe usig MOS stadard test. MOS (Mea Opiio Score scale has bee show i Table.. The utteraces which are used i this experimet are "Exercise oe", "coversatio", "liste ad practice", which has bee obtaied from twelve MMSE Figure 5: Block diagram of the proposed coder: CEPS-CELP 7

8 ICSV4 9- July 7 Cairs Australia listeers The results has bee summarized i Table.. From Table, it ca be realized that the quality of recostructed speech sigal i CELP is comparable with that of i CEPS-CELP which cofirms the capability of the proposed method. A compariso of bit rate betwee CELP ad CEPS-CELP is show i Table 3. As ca be see from this table, the bit rate is cosiderably reduced i CEPS-CELP. But the MOS test is decreased too. CELP CEPS-CELP Average MOS Score Table : MOS test for utterace "Exercise oe", "Coversatio", "Liste ad practice". Symbol Bit allocatio Bit allocatio CELP CEPS-CELP Codebook idex k x4 x4 Pitch delay P x4 8x4 Pitch filter coeffs b 7x4 5x4 Gai G 7x4 5x4 LP coeffs a 5x5 x4 Total bit rate 7.3 kbps 5. kbps Table 3: Compariso of two type of CELP 5. CONCLUSION I this paper, the CELP cocept has bee preseted. A basic CELP coder has bee desiged ad implemeted i MATLAB. The, a improved approach to reduce bit rate based o cepstral aalysis proposed. We compared the performace of both basic CELP ad our coder "CEPS-CELP". Experimetal results show outperformace of suggested method to origial CELP. REFERENCES [] Adreas S. Spaias. Speech Codig: A Tutorial Review, Proceedig of the IEEE Vol. 8, No., pp , October 994 [] WAI C. CHU. Speech Codig Algorithms Foudatio ad Evolutio of Stadardized Coder. Joh-Wiley,, pp , 3 [3] Paos E.Papamichalis, Practical Approaches To Speech Codig,, Pretice-Hall,, pp. 9-74, 987 [4] Lawrece R.Rabier ad Roald W.Schafer, Digital Processig Of Speech Sigals. Pretice-Hall, Ic. pp , 978 [5] K. Koishida, K. Tokuda, T. Kobayashi ad S. Imai, CELP codig system based o melgeeralized cepstral aalysis, Proc. ICSLP 96, pp.38 3, 996. [6] K. Koishida, G. Hirabayashi, K. Tokuda ad T. Kobayashi, A widebad CELP speech coder at 6 kbit/s based o melgeeralized cepstral aalysis, Proc. ICASSP 98, pp.57 6, 998. [7] CLIFFORD J. WEINSTEIN, ALAN V. OPPENHEIM, Predictive Codig i a Homomorphic Vocoder, IEEE Tras. Audio Ad Electro acoustics. Vol. AU-9, NO. 3, 97 8