A Time-Frequency Way for Improving the Quality of the ... - Wseas.us

A **Time**-**Frequency** **Way** **for** **Improving** **the** **Quality** **of** **the** Syn**the**sized SpeechSignal in Classical LPC Compression MethodCERNAIANU LEONARDO, SERBANESCU ALEXANDRU, QUINQUIS ANDRETelecommunication SectionEIAMilitary Technical AcademyENSIETAGeorge Cosbuc Street, 81-83, Bucharest 2, rue François Verny 29806 Brest CEDEX 9ROMANIAFranceAbstract: - The LPC method is classical in speech compression, never**the**less it presents a bad sound quality. But, even withthis drawback, **the** LPC method is currently **us**ed beca**us**e **of** its sound compression capacity. We have looked **for** a way **of**improving **the** quality **of** **the** syn**the**sized speech signal.Key-Words: - Adaptive, Wavelet Packets, Huffman, LPC, Speech, Compression1 IntroductionThe classical LPC method is a beginning step in **the**world **of** speech processing. The LPC filter, **the** LPCcoefficients, Levinson and Durbin algorithms are wellknown ([1], [2] and [3]). A lot **of** applications **us**e,today, this method **of** speech syn**the**sis such as LPCvocoders and mobile phones. But **the** quality **of** **the**syn**the**sized speech was never very good. That’s **the**reason why we propose a speech syn**the**sis methodhaving as start point **the** LPC method, but with a goodsyn**the**sized sound given to **us** by **the** time-frequencyalgorithms we **us**e : **the** Wavelet Packetsdecomposition.2 Problem FormulationThe LPC method computes **the** coefficients in **the** ARmodel by minimizing **the** mean square error between**the** input and syn**the**sized signals. The resultingprediction error tend to a decorrelated signal as **the**AR model order increases. We propose to transmitalso a compressed version **of** this error. The length **of****the** prediction error is **the** same as **the** initial signal soit can be said that **the**re is no gain in transmitting errorinstead **of** original signal. Indeed, **the** proposedmethod gives better results if applied directly on **the**speech signal. With **the** LPC-Wavelet Packets method**the** compression rate decreases but **the** gain is animprovement **of** **the** syn**the**sized signal quality.3 Problem SolutionThe main idea **of** **the** algorithm is to send acompressed **for**m **of** **the** prediction error. To do that,we **us**ed a modified **for**m **of** Wavelet Packets (WP)algorithm combined with an adaptive Huffmancompression.3.1 The adaptive Wavelet Packets algorithmThe classical WP algorithm **us**e two types **of** filters **for**signal filtering – a low-pass filter syn**the**sized **us**ing **the**wavelet mo**the**r function and **the** associated mirrorfilter. This is done at each decomposition level,beginning with level 1 and finishing with level N.Each cell at **the** level k has 2 N −kWP coefficients.That means that, at each level, **the** spectrum portionsconsidered are twice smaller than at **the** previo**us** level.In most applications, **the** decompositionalgorithms reach **the** level 3 or 5. In practice, **the**spectrum properties **of** **the** prediction error can vary alot. So, **the** decomposition level can not be **the** same**for** all signals. It have to be determined from one inputspeech word to ano**the**r.

We have developed an automatic leveldecomposition algorithm. We have made manyexperiments consisting in Wavelet Packetsdecomposition on **the** best basis **us**ing vario**us** kind **of**signals, mo**the**r functions and cost functions. For astrict control **of** **the** syn**the**sized sound quality, wehave **us**ed **the** Donoho thresholding method which willbe presented in **the** next sub-section.We observed that **the** thresholded coefficientsnumber variation in function **of** **the** decompositionlevel follow a convex parabolic law. That means that**the**re is an optimal decomposition level **for** each inputsignal we have and we can determine this level bymaking step by step **the** decomposition until we findthat **for** **the** level k, **the** necessary coefficients numberis bigger that by **us**ing **the** k-1 level. This algorithm isill**us**trated in fig. 1. The syn**the**sized signal quality is**the** same **for** each level decomposition we **us**e beca**us**e**of** **the** Donoho thresholding method, but **the**compression varies from one level to ano**the**r.3.1.1 The Donoho thresholding methodThe Donoho thresholding method [4] idea is to have asyn**the**sized signal carrying only a percentage (α) **of****the** original signal energy (E). We keep **the** greatestcoefficients until **the** energy or regarded coefficients isαE . For choosing α value, we can approximate **the**signal to noise ratio **us**ing **the** followed equation:ESNR = 10*log = −10*log( 1−α ) (1)E − αEAs you can observe, ano**the**r advantage **of** **the**proposed method is that we can impose **the** desiredsignal to noise ratio. This is very important **for** signaltransmission beca**us**e we can choose **the** quality **of** **the**received signal. We did not consider **the** channel noise,but **the** difference between **the** input and syn**the**sizedsignals.Fig.1 The best decomposition level determinationalgorithmEven with Donoho thresholding method, **the** number**of** WP coefficients is equal to **the** length **of** **the** inputsignal after we complete with zeros to a length power**of** two (zero padding). We cannot eliminate **the**coefficients we do not keep beca**us**e, in **the** syn**the**sisalgorithm, we need **the** initial position **of** **the** holdedcoefficients in **the** decomposition table. So, we put all**the** values **of** **the** canceled coefficients zero and try tocompress this vector. We also need a vector toindicate **the** position **of** **the** coefficients in **the**decomposition table. Beca**us**e we **us**ed **the** best basisdetermination algorithm, this vector (bb) keeps **the**in**for**mation about **the** best basis localization in **the**decomposition table. If we look at **the** decompositiontable, from left to **the** right and from up to down, tobuild **the** bb vector we add a 1 if **the** field belongs to**the** best basis and a 0 if not. There**for**e, we have tocompress **the** thresholded coefficients vector (wpth)and **the** bb vector.

3.1.2 The Wavelet Packets coefficients compressionmethodWe can multiply **the** wpth vector without changing **the**signal in**for**mation nei**the**r in **for**m nor in frequency.Knowing this, we normalized **the** input signal between–1 and 1. Doing this operation, we obtain sub-unitaryWP coefficients. Then, we multiplied **the** WPcoefficients vector by 100 and we syn**the**sized **the**signal. The syn**the**sized signal was **the** input signalamplified by 100.We apply **the** Donoho thresholding method,amplify by 100 **the** wpth vector, round all values to **the**nearest integer and syn**the**size **the** signal. The resultingerror is very small (under 0.2 dB). There**for**e we canbuild a amplified version **of** **the** wpth vector (wptha)which has integer values and we can still compress thisvector **us**ing one **of** **the** classical compressionalgorithms without significant deterioration. We **us**edtwo compression methods : **the** RLC (Run LengthCoding) and Huffman algorithms [5].To eliminate **the** bb vector, we compress **the** wpthavector **us**ing a modified **for**m **of** RLC method. Weobtain a vector which has two kinds **of** elements – **the**normal ones (we named **the**m **the** elements **of** **the**wptha vector) and some number-zero groups. Themethod we **us**e to build this vector is very simple : **for**all **the** parts from **the** wptha vector which contain j**us**tzeros, we count **the** number **of** zeros, delete **the**respective part and put instead **the** counted valuefollowed by one single zero as in **the** next example:vector so we have j**us**t positive values. We do this byadding to each element **of** **the** wpthac vector **the**absolute value **of** **the** greatest negative element pl**us**one. We will not touch **the** number zero-zero groups(see fig. 3 **for** example)!Fig.3 The wpthac translation methodIf we have in mind that we made a amplification by100, we can change each coefficient **of** **the** wpthactvector into an even one. The error resulting from thisoperation is insignificant. Afterwards, we add **the** bestbasis vector to **the** resulting vector like in **the**following example:Fig.4 The combination **of** **the** wpthactp and bb vectorsFig.2 The RLC compression algorithmAfter **the** RLC compression we want to add **the** bbvector to **the** wpthac vector to keep only 1 vector. But**the** wpthac vector have also negative values. It cancontain an –1 so, if we add **the** best basis vector to **the**wpthac vector, we can obtain ano**the**r zero and wecan’t distinguish anymore **the** number-zero groups. Tosolve this, it is necessary to translate **the** wpthacAs you can see in fig.4, we can extract **the** bbvector in **the** syn**the**sis process by looking at **the** evenoddpropriety **of** **the** wpthactpb elements.We still have a vector which has j**us**t integernumbers. So we can compress it by **us**ing **the** Huffmanalgorithm. The main problem is that we m**us**t consideras data some delimiters between **the** coefficients. Inmost cases, a blank character is considered.Proceeding like this, **the** quantity **of** data we need tocompress becomes double and we have ten characters(from 0 to 9) **for** compression and **the** blank character.

To eliminate blank characters from compression,we imagine **the** following method : we complete **the**wpthactpb vector with **the** length in digits **of** eachnumber which it contains and eliminates all **the** blankcharacters as ill**us**trated in fig.5.Fig.7 The correlation between **the** input signal andsyn**the**sized LPC signal (top) and between **the** inputsignal and **the** syn**the**sized LPC-Wavelet Packets-RLC-Huffman signal (bottom)Fig.5 The way we eliminate **the** blank characterNow, we can per**for**m **the** Huffman compressionalgorithm to **the** wpthactpbc vector. The advantage isthat we will generate **the** Huffman tree **us**ing j**us**t tencharacters (from 0 to 9). All **the** additionally data weneed (which includes **the** length **of** **the** vector we addin blank character elimination step) **for** syn**the**sisalgorithm can be send or memorized as a header (in**the** transmission).In fig.6, we show an example **of** signal syn**the**sizedwith this method compared with **the** input signal (**the**romanian word “shase”) and **the** signal syn**the**sized**us**ing **the** classical LPC method.In fig.7 and fig.8 we draw **the** correlation andcoherence functions calculated between **the** inputsignal and **the** syn**the**sized LPC-WP-RLC-Huffmansignal and between **the** input signal and syn**the**sizedLPC signal respectively.Fig.8 The coherence between **the** input signal andsyn**the**sized LPC signal (top) and between **the** inputsignal and **the** syn**the**sized LPC-Wavelet Packets-RLC-Huffman signal (bottom)4 The LPC-WP-RLC-Huffmancompression algorithm stepsFig.6 The input signal “shase” (top), **the** LPC-Wavelet Packets- RLC-Huffman syn**the**sized signal(middle) and **the** LPC syn**the**sized signal(bottom)Fig.9 The compression algorithm

5 Practical resultsThe syn**the**sized sound quality and **the** compressionrate may be chosen by selecting **the** α parameter. If weselect a greater value **for** α, we’ll have a wellapproximation **of** **the** input signal, but a smallercompression rate. For “shase”, **the** compressedversion **of** **the** input sound we need 4.24 times lessmemory than **the** original signal.The variation **of** **the** compression rate (C) infunction **of** **the** α parameter is almost linear as shownin fig. 10.[3] A. Gersho, R.M. Gray, Vector quantization andsignal compression, Kluwer Academic Publishers,1992[4] Donoho, D., WaveLab reference manual, San**for**dUniversity, 1995[5]Thomas J. Lynch, Data Compression – Techniquesand applications, Van Nostrand Reinhold, 1985Fig. 10 The variation **of** **the** compression rate infunction **of** **the** α parameter **for** **the** “shase”6 Concl**us**ionThe syn**the**sized signal we obtain is closer to **the** inputsignal that in **the** classical LPC method and wepreserve a good compression rate. The syn**the**sizedsound quality and **the** compression rate can be strictlycontrolled. This algorithm can be **us**e in both LPC-WP-RLC and LPC-WP-RLC-Huffman **for**m, **the**second one being recommended **for** data stocking.References:[1] J.D. Markel, A.H. Gray, Linear prediction **of**speech, Springer-Verlag, 1976[2] L.R. Rabiner, R.W. Schafer, Digital processing **of**speech signals, Prentice Hall, 1978