Recognition of Human Speech using q-bernstein Polynomials

Transcription

1 Iteratioal Joural of Computer Applicatios ( ) Volume o.5, Jue 00 Recogitio of Huma Speech usig -Berstei Polyomials Abdulkadir Karacı Kastamou Uiversity Departmet of Computer ad Istructioal Techology ducatio, ducatio Faculty, Turkey İbrahim Büyükyazıcı Gazi Uiversity Departmet of Mathematics Turkey Muharrem Aktüme Ahi vra Uiversity, Departmet of Mathematics ducatio, ducatio Faculty, Turkey ABSTRACT Recogitio of huma speech has log bee a hot topic amog articial itelligece ad sigal processig researchers. I this paper, Patter recogitio ad -Berstei polyomials have bee combied to create computer software desiged for the recogitio of huma speech, ad the mai priciples of speech recogitio have bee explaied i a systematic cotet. - Berstei polyomials, which are mathematical operators, have bee applied for patter recogitio, ad a ew method has thus bee developed. Software has bee prepared usig the Delphi 7 programmig laguage, ad with this software, this method has bee applied for the processig of verbal expressio recogitio. I the program as developed, samples of 8-bit stereo images were computerized. Speech recogitio tests were coducted for six words, ad ormatio related to the results of this test is provided i this paper. Keywords Speech recogitio, patter recogitio, -Berstei polyomials. ITRODUCTIO Recogitio of huma speech is a problem with may solutios, but is still a ope problem because oe of the curret methods are fast ad precise eough to be comparable with the recogitio capability of huma beigs. Several methods exist for recogitio of huma phoemes, icludig hidde Markov models (HMMs) [], time-delay eural etworks [], support vector classiers with HMM [3], idepedet compoet aalysis [4], HMM ad eural-etwork hybrids [5], ad more. Speech commad recogitio provides importat advatages for commuicatio betwee huma ad computer. Obtaiig speech commad data is very easy ad does ot reuire ay special talet such as keyboard skills, i cotrast to other data storage methods. Usig speech commads, trasferrig texts to electroic form ca be extremely fast. This method provides the users with freedom of movemet ad the possibility of usig their hads for other purposes [6]. The first step i recogizig speech commads by computer is to trasform voice sigals ito statistical form to take icidetal characteristics of the soud out of the sigal ad to make a recogitio procedure possible by providig it with the ormatio obtaied. I coveyig the speech commad to the recogitio procedure, the trasfer of the speech commad to the computer by microphoe is the first step. By trasformig the voice sigal ito statistical form, it is made ready for widowig, filterig, ad other aalyses. By these procedures, ay oise existig i the voice sigal is removed, ad the sigal is separated out from the elemets which are depedet o the perso or o the geographical area [7]. Two voice vectors are extracted i the patter recogitio method. The similarities ad dfereces betwee the vectors are determied usig various distace measuremet methods. The first step i the patter recogitio procedure is to apply preparatory procedures to the raw voice data. I this study, i cotrast to the usual patter recogitio procedure, after the voice data have bee acuired ad prepared, -Berstei polyomials are applied to the statistical voice data. The statistical voice data which have bee processed through - Berstei polyomials come to resemble each other more closely, ad this situatio icreases recogitio performace. I this paper, -Berstei polyomials, which are mathematical operators, have bee applied to patter recogitio, ad a ew method has thus bee developed. Software has bee developed usig the Delphi 7 programmig laguage, ad with the aid of this software, the method has bee applied to process verbal expressios for recogitio. Moreover, i the program as developed, samples of 8-bit stereo images were computerized, speech recogitio tests were coducted for six words, ad results were obtaied as reported later i this paper. We state that this study is a experimetal work.. -BRSTI POLYOMIALS I recet years, -Berstei polyomials have attracted a great deal of iterest because of their potetial applicatios i approximatio theory ad umerical aalysis, ad may properties of these polyomials have bee discovered [8, 9, 0,, ]. Let 0. For each oegative iteger, the -iteger [ ] ca be defied as [ ] ad the -factorial ]! as [ ]! [ ] [ [ ] [] ( ) /( For the itegers ad k, with 0 k, the -biomial coefficiets are the defied as follows [9]: 0 )

2 Iteratioal Joural of Computer Applicatios ( ) Volume o.5, Jue 00 k [ ]! [ k]![ k]! I 997, Phillips [] geeralized Berstei polyomials to - Berstei polyomials: [ k] k k s B, ( f ; x) f x ( x), () k 0 [ ] k s 0 0 x,,,3,... where a empty product is take to eual. xplicit expressios r for B, ( t ; x) for r 0,, ca be obtaied by direct calculatio, givig B, (; x) B, ( t; x) B, ( t ; x) x x x( x) [ ] ote that f (x) 0 o [ 0,], this implies that B, ( f ; x) 0 o [ 0,] for 0. These properties of -geeralized Berstei operators eable the use of the Korovki theorem [3] to obtai covergece results. Because for a fixed value of with 0, lim of (), [ ], to esure the covergece properties will be assumed to be a seuece such that as for. 0 Theorem. Let ( ) be a seuece of real umbers such that 0 ad lim. The, for f C[0, ], B ( f ; x), coverges uormly to f (x) o [ 0,]. The proof ca be foud i []. Theorem. Let ( ) be a seuece of real umbers such that 0 ad lim. The, for f C[ a, b], xample. For,5,0, 0, 30, the covergece of B, ( f ; x) to f ( x) xcos x is illustrated i Fig.. Fig.. Covergece of B, ( f ; x) to f (x). 3. PRPARATIOS FOR SPCH RCOGITIO Much processig is eeded betwee acuirig the voice sigal ad achievig speech recogitio, which costitutes the speech recogitio procedure. The recogitio procedure ca be approached by providig a basic overview of the preparatios for speech recogitio. The method obtaied is illustrated i Fig. 3, step by step ad geerally [7]. Start Acuire the voice sigal as a computerized statistical form Preemphasis Filter 3 B, ( f ; x) f k 0 a [ k] [ ] ( b a) x ( k b a k k ) ( a s 0 s x b a ), a Widowig coverges uormly to f (x) o [ a, b]. Theorem ca be proved i the same way as Theorem. xample. For,5,0, 0, 30, the covergece of B, ( f ; x) to six f ( x) is illustrated i Fig.. x Fast Fourier Trasform Patter Recogitio d Fig. 3. A geeral view of speech recogitio. Fig.. Covergece of B, ( f ; x) to f (x) DSIG OF TH SPCH RCOGITIO SOFTWAR The software developed i this study recogizes the limitatio that spoke words vary from oe perso to aother by icorporatig -Berstei polyomials ito the patter recogitio method. I the software, the user first creates a dictioary database with the words that he or she wats to be recogized. The software applies the Berstei fuctio to the words that the speaker said ad all the words i the database 3

3 Iteratioal Joural of Computer Applicatios ( ) Volume o.5, Jue 00 durig word recogitio. The it performs a compariso procedure, calculatig a recogitio percetage for all the words i the database oe by oe ad returig the word for which the measuremet is most like the observed word. If further procedures eed to be performed for the particular word foud, the software executes them. The geeral seuece of the software as developed is show i Fig. 4. Fig. 4. Geeral schematic of the software as developed. 4. Voice Acuisitio The voice sigal is acuired usig a Philips SHM3300 microphoe. While the voice sigal is beig acuired, the codes described below are etered i the audio compoet of the data record. Moreover, i the software as developed, samples are stored i the database as 8-bit stereo recordigs. procedure TForm.AudioRecord(Seder: TObject; LP, RP:poiter;BufferSize: ); begi Start Process the voice sigal ad calculate statistics Calculate the voice sigal power Determie the begiig of the voice sigal Determie the ed of the voice sigal Apply Preemphasis Filter Apply Widowig Procedure Apply Fast Fourier Trasform Apply Autocorrelatio Fuctio defa:=defa+; defa= the liste.items.add('başla') else liste.items.add(ittostr(buffersize)); gercekses:=lp; Veriyikutupla(lp,sosize); kutupkot.checked=true the Veriyigorutule(sayisalsessiyali,image,sosize); erji; sesyakala; ed; -Berstei Compare with the words i database Was the word foud? Yes Write the ame of word d o Write The word caot be foud 4. Data Polarizatio Data polarizatio is used for processig the data samples from the voice card i a way which is idepedet of the 8-bit or 6- bit samplig procedure. The data as received are kept i 3-bit form for further processig. The data polarizatio subprocedure used here deducts 7 from the voice sigal i the case of 8-bit data. This is ecessary to idety the positive ad egative oscillatios of the voice. The results ca be coverted ito 3-bit data ad processed i a way which is idepedet of 8-bit or 6- bit processig. The subprocedure for data polarizatio is preseted below. procedure veriyikutupla(data:poiter;size:iteger); var p:array[ ] of iteger; b:pbytedizi; i:iteger; z:iteger; begi b:=data; for i:=0 to epebuyukluk- do p[i]:=ocekiveri[i]; for i:=epebuyukluk to size- do p[i]:=b^[i-epebuyukluk]-7; for i:=size-epebuyukluk to (size-) do ocekiveri[i-(sizeepebuyukluk)]:=p[i]; sayisalsessiyali:=@p; for z:= to do pheryerde[z]:=p[z];ed; 4.3 Voice Sigal Power Calculatio Procedure To detect the start ad ed of the voice sigal, the itesity that represets the eergy of the voice sigal must be determied. Sice 970, eergy parameters have bee used to determie the ed poit of the voice sigal. Oe of the basic characteristics of the voice sigal is its power. A sigal evaluatio method freuetly used i speech recogitio systems determies the wave power as the sum of suared power values for every poit of the wave or its desity i a arbitrary time widow [4]. This eergy is calculated usig a short-term eergy formula. This eergy value is used to calculate the eergy i the voice sigal over a arbitrary time period [5]. Sum of suares of eergy: x i) i ( () Short-term eergy Short-term eergy is the eergy that the voice sigal has over a certai period of time. There are three dferet defiitios used i short-term eergy calculatios [5]: Logarithm of eergy: log x( i) (3) i Sum of suares of eergy: x i) i ( (4) 4

4 Iteratioal Joural of Computer Applicatios ( ) Volume o.5, Jue 00 Sum of absolute eergy: x i) i ( (5) 4.4 Procedure for Capturig the Voice Sigal It is very importat to determie the voice sigal accurately i oisy locatios. A wrog determiatio of the voice edig poit i speech recogitio has two egative effects: first, a recogitio failure occurs because of the false determiatio of the voice edig boudary; secod, whe the voice boudary is determied wrogly, the computatio time icreases because o-voice segmets of the sigal must be processed [6] Procedure for establishig begiig ad ed of the voice sigal To establish the begiig ad ed of a voice sigal, it is ecessary to look at the eergy values calculated. The value of the miimum eergy threshold ad the umber of samples over which values greater tha this threshold must be maitaied must be determied. I the procedure used here, the umber of samples is set to 50 ad the threshold value to 40. The best threshold value ca be foud by experimetatio. The program examies the voice eergy value begiig at a predetermied poit; the eergy reaches a value of 50 ad the remais above that level for the ext 40 samples, it meas that the begiig of the voice sigal has bee foud. Whe the ed of the voice sigal is foud, the eergy values are looked at agai. A reductio of eergy to less tha the maximum eergy threshold value determied earlier idicates that the voice sigal has fiished ad defies the umber of samples to be provided to the program. These two parameters are optimized usig a voice capture cotrol widow i the program. The default values of these parameters are 30 ad 40, meaig that over 30 samples, the eergy remais less tha 40, this meas that the ed of the voice sigal has bee established. 4.5 Preemphasis Filter Spoke utteraces have high eergy values at low freuecies. The preemphasis filter is used to esure that low-freuecy compoets do ot mask the high-freuecy oes. The preemphasis filter is usually described usig the relatio i euatio 6: P ( z) z, (6) where µ suared varies betwee 0.9 ad 0.95 [7], ad z represets a stadard delay [7]. The followig program code implemets a preemphasis filter: Procedure preemphasisfilter(rawdata:poiter;size:iteger; coefficiet:real); var preemphasisdata:poiteritegerdizi; i:iteger; begi preemphasisdata:=rawdata; preemphasisdata^[0]>0 the preemphasisdata^[0]:=0; for i:=0 to size- do begi preemphasisdata^[i+]:=roud(preemphasisdata^[i+]- coefficiet*preemphasisdata^[i]); ed; ed; The poiter variable i the preemphasis filter procedure poits to the voice data to which the preemphasis filter is beig applied. Whe the preemphasis filter is applied, the first elemet of the umeric voice data vector is greater tha the cutoff value, it is zeroed by preemphasis^[0]:=0;. The i a For loop, the coefficiet is multiplied by the previous sample data (preemphasisli^[i-]) ad erred from the sample data of that time period (preemphasisli^[i]), ad the data vector with preemphasis filtratio applied is thus obtaied. This procedure cotiues util the sample umber is -. Figure 5 illustrates the applicatio of a preemphasis filter to the voice sigal correspodig to the word. ( Fig.5. (a) Raw voice sigal. (b) Voice sigal after applicatio of preemphasis filter. 4.6 Widowig A captured voice sigal must be widowed ad a certai part selected for maipulatio by Fourier aalysis. The part selected must correspod to the smallest uit of meaig ad eable Fourier aalysis calculatios to be performed i a short time (geerally 30 ms [7]). Voice sigal graphs, the applied raw voice sigal, ad Hammig widowig are show i Fig. 6. Widowig meas the multiplicatio of the voice sigal y() by a time-varyig fuctio W(). Widowig ca be implemeted by startig a widow at the poit where the previous widow fiishes, so that the two adjacet widows do ot overlap, or else the later widow ca be started a bit earlier, so that the two widows overlap. I this way, the hard limits i the procedure ca be softeed. I the software developed here, dferet types of widowig such as Suare, Blackma, Haig, Hammig or Bartlett ca be used accordig to the choice of the user. I this study, the Hammig widowig method has bee used because it yields better results. (a) (a) Fig.6. (a) Raw voice sigal. (b) Voice sigal with applied widowig. (b) (b) 5

5 Iteratioal Joural of Computer Applicatios ( ) Volume o.5, Jue Fast Fourier Trasform (FFT) The Fast Fourier Trasform (FFT) divides a voice sigal ito its costituet freuecies. A ormal voice sigal is formed by combiig voice compoets of various freuecies, like the colors i a raibow. The voice sigal i its raw form ca create dferet impressios, although various speakers are sayig the same word. It is dficult to characterize a voice sigal usig oly its raw properties (time ad amplitude). For this reaso, the voice sigal is maipulated i various ways to make recogitio easier. FFT is oe of these techiues [8]. The Fast Fourier Trasform (FFT) has a log ad iterestig history. It was origially discovered by Gauss ad the rediscovered by Cooley ad Tukey ad became widely kow. The FFT is a algorithm for uick calculatio of the Discrete Fourier Trasform (DFT). The DFT is oe of the mai procedures used i digital sigal processig for liear filtratio, which is used i may applicatios. However, the calculatio time reuired i DFT for a voice sigal of fiite size is greater tha i other methods [9]. FFT is a efficiet method for calculatig the DFT. The reaso that this model is cosidered efficiet is that it ca be used to solve a variety of problems, ad therefore this techiue has received great attetio. Procedures ca be implemeted more uickly with FFT tha with DFT. FFT has a computatioal complexity of order log for sample size, whereas DFT has a complexity of order. For istace, =04, FFT will reuire time Log =0 40, but DFT will eed time = [0]. The DFT fuctio is defied i euatio (7) []: jk X ( j) A( k) W, j 0,,...,, (7) k 0 where i / W e. The raw voice sigal ad the voice sigal after applicatio of FFT are show i Fig. 7. Fig.7. (a) Raw voice sigal. (b) Voice sigal after applicatio of FFT. 4.8 Autocorrelatio Fuctio The autocorrelatio fuctio ideties the mai freuecies i a sigal ad makes recogitio easier [7]. Discoverig characteristic freuecies i oisy eviromets is a key techiue for correct voice recogitio. I may existig voice recogitio systems, the recogitio of characteristic freuecies depeds o the uality of the voice data after the correctio procedure. The autocorrelatio fuctio has bee foud to provide the best performace i oisy eviromets []. I the speech recogitio program developed here, the Blackma-Tukey autocorrelatio distace is used. The Blackma-Tukey autocorrelatio distace is described by euatio 8 [3]: (a) (b) k R( k) (/( k)) x( i). x( i k). (8) i Recogitio This is the step where the maipulated voice sigal from the speaker is compared with source sigals saved i a database after previous maipulatios. I this sectio, i cotrast with the usual patter recogitio approaches, the -Berstei fuctio is applied both to all the referece sigals i the database ad to the voice sigal from the speaker. The a compariso procedure is performed i a effort to fid the closest referece sigal. If the correspodece is lower tha 80 percet, this meas that the word has ot bee foud. A subprogram which applies the - Berstei fuctio to voice data is give below. Procedure Tformyakalaa.berstei(size:iteger); var pecere,pecsay,tuti,x,e:iteger; iyerie:iteger; s,k,i,j:iteger; carp:double; toplamf,toplamg:real; begi pebuy:=; pecere:=size div pebuy; for pecsay:=0 to pecere do begi for x:=pebuy*pecsay to pebuy+pebuy*pecsay do begi toplamg:=0;toplamf:=0; for j:=0 to pebuy do begi carp:=; for s:=0 to pebuy-j- do begi ed; carp:=carp*(-(power(-/pebuy,s)*(xpebuy*pecsay)/(pebuy+pebuy*pecsay))); toplamg:=toplamg+biomial(pebuy,j)*power((xpebuy*pecsay)/(pebuy+pebuy*pecsay),j)*carp*fftalaoku a[j+x]; toplamf:=toplamf+biomial(pebuy,j)*power((xpebuy*pecsay)/(pebuy+pebuy*pecsay),j)*carp*fftala[j+x]; ed; topl[x]:=toplamf; topg[x]:=toplamg; ed;ed;ed; Various distace measuremets ca be used to calculate the degree of resemblace betwee voice sigals. I the program developed here, the Oclid measuremet is used. The Oclid measuremet fids the geometric distace betwee two poits i a vertical coordiate system ad ca be defied as: d X, Y) oclid ( xi i yi ) (. (9) The voice sigal beig recogized is compared with a referece sigal i the database usig the Oclid measuremet. I this procedure, the Oclid measuremet for every widow is calculated by dividig the two voice sigals ito a widow eight 6

6 The Widows umber which is foud Recogitio percetage Recogitio percetage Recogitio percetage The Widows umber which is foud The Widows umber which is foud The Widows umber which is foud The Widows umber which is foud The Widows umber which is foud The Widows umber Recogitio which is foud percetage Recogitio percetage The Widows umber which is foud The Widows umber which is foud Recogitio percetage Recogitio percetage The Widows umber which is foud The Widows umber which is foud Recogitio percetage Recogitio percetage The Widows umber which is foud times larger tha the ormal widow size. If the calculated Oclid value is smaller tha the acceptace threshold value determied by the program, the widow size for the observed sigal is icreased by oe. The procedure is repeated for every widow. Fially, the recogitio percetage is calculated as follows: ObservedWidowSize*00 Recogitio Percetage (0) TotalWidowSize These procedures are repeated for all the words stored i the database. After these procedures, the program returs whether or ot the voice sigal has bee idetied, the recogitio percetage associated with the ideticatio, ad which word has bee idetied. If desired, further processig specic to the idetied word ca be performed. For example, for the word word, a routie specic to this word ca be performed. Furthermore, the program lists the recogitio percetage for every referece cotaied i the database. I Fig. 8, the recogitio percetage of the word word as determied by the program is show. Iteratioal Joural of Computer Applicatios ( ) Volume o.5, Jue 00 developed without usig the -Berstei fuctio are show i Fig.0. As it is show i Fig.0, i accordace with the acuired test results from the voice recogitio program which has bee developed without the -Berstei fuctio, the recogitio rates of the words are low. Besides, some words are ot recogized eve false recogitios have bee occurred. Due to the uormly covergece, shape-preservig ad -geeralizatio of the Bézier curves, givig them a practical applicatio features of the -Berstei fuctio, the problems like false recogitio of words the or o-recogitio of words are preveted Ope Widows 4 Ope Widow Repeat umber umber Repeat umber umber 0 0 Ope Fig. 8. Recogitio percetage of the word word as determied by the program. 5. XPRIMTAL RSULTS I this study, software has bee developed for the recogitio of spoke utteraces usig the -Berstei mathematical fuctio as the patter recogitio method. At the ed of the tests, it was see that the voice recogitio rate achieved by the software proved to be higher tha that achieved by the patter recogitio method without -Berstei. Moreover, i may patter recogitio methods, words are sometimes cofused with each other, but i the patter recogitio method with -Berstei, words are ot cofused. If the voice sigal as recogized 0 by the voice recogitio software is similar to the real voice sigal at a level of more 0 tha 80%, it meas that the word is 0 recogized. The similarity ratio is obtaied by comparig the widow values to a 0 threshold value. As a result of the 0 tests, it was determied that the threshold value yieldig the best result is 5. I this software, at the ed of the tests held separately with sigle samplig, the miimum recogitio rate was 00%. Moreover, 4 it was observed that the greater the umber of samples i the database, the higher 4the similarity ratio, which icreases 4 recogitio performace. Usig the software as developed, the words 4,, Widows,,, 4ad Ope were recorded i a database, ad te tests were carried out for each word. It ca be see that the style of prooucig the words ad the toe of voice have a impact o recogitio. The experimetal results belogig to voice recogitio program which has bee developed by usig the -Berstei fuctio are show i Fig.9 ad the experimetal results belogig to voice recogitio program which has bee Repeat umber Repeat umber Widows Widows Ope 4 Fig. Ope 9. The experimetal Widows results belogig to voice recogitio program which Widows has bee developed by usig the -Berstei Widows fuctio. Widows Ope Repeat umber 9 0 Repeat umber 4 4 Ope Ope Ope Widows 0 4 Repeat umber Repeat umber umber Ope Widows Repeat 3umber Repeat 9 0 umber Repeat umber 0 Repeat umber Repeat umber Repeat 7 umber 8 9 0Repeat umber Repeat umber Repeat umber Repeat umber 0 Ope Widows 7 Ope Wid xce Ope Wido

7 Recogitio percetage Recogitio percetage Recogitio Repeat umber percetage Recogitio percetage Recogitio percetage Recogitio percetage Iteratioal Joural of Computer Applicatios ( ) Volume o.5, Jue Repeat umber Repeat umber Repeat Widows umber Widows Repeat umber Repeat umber Fig. 0. The experimetal results belogig to voice recogitio program which has bee developed by ot usig the -Berstei fuctio. 6. COCLUSIOS AD FUTUR WORK I this study, -Berstei polyomials, which are mathematical operators, have bee applied to patter recogitio, ad thus a ew method has bee developed. This method was applied to six words usig the software developed i this research. The data obtaied have show that the huma speech recogitio rate was higher usig this method tha with the patter recogitio method without -Berstei polyomials. Use of the same method for voice ad figerprit recogitio techologies is uder cosideratio. 7. RFRCS [] B. Babaali, H. Sameti, The Shar speaker-idepedet large vocabulary speech recogitio system. Proceedigs, d Workshop o Iformatio Techology ad its Disciplies, Kish Islad, Ira, 004. [] M.R. Berthold, A time-delay radial basis fuctio etwork for phoeme recogitio. Proceedigs of the I Iteratioal Coferece o eural etworks, 7, Orlado, , 994. [3] S.. Golowich, D.X. Su, A support vector/hidde Markov model approach to phoeme recogitio, ASA Proceedigs of the Statistical Computig Sectio, 5 30, 998. [4] O.W. Kwoa, T.W. Lee,. Phoeme recogitio usig ICAbased feature extractio ad trasformatio. Sigal Process. 84(6) (004), [5] P. Schwarz, P. Matejka, J. Cerocky, Phoeme recogitio based o TRAPs, Proceedigs of the Workshop o Multimodal Iteractio ad Related Machie Learig Algorithms, Switzerlad, 004. [6]. Megüşoğlu, Rule-based desig ad realizatio of a Turkish verbal expressio recogitio system. Master s Thesis, Hacettepe Uiversity, Istitute of Sciece, Akara, Repeat umber Ope Ope Repeat umber Recogitio percetage [7] S. Doğa, Recogitio of verbal istructios i PC medium. Master s Thesis, Marmara Uiversity, Istitute of Sciece, İstabul, 999. [8] W. Hepig, X.Z. Wu, Saturatio of covergece for - Berstei polyomials i the case. J. Math. Aal. Appl. 337() (008), [9] V. Kac, P. Cheug, Quatum Calculus. Spriger, ew York, 00. [0] S. Ostrovska, -Berstei polyomials ad their iterates. J. Approx. Theory 3() (003), [] G.M. Phillips, Berstei polyomials based o the - itegers, A. umer. Math. 4 (997), [] V.S. Videskii, O some classes of -parametric positive operators, Operator Theory Adv.Appl. 58 (005), 3. [3] F. Altomare, M. Campiti, Korovki Type Approximatio Theory ad Its Applicatios, de Gruyter Series Studies i Mathematics, Vol.7, Walter de Gruyter, Berli-ew York, 994. [4] B. Akçay, Recogitio of Turkish speech through articial eural etworks. Master s Thesis, Hacettepe Uiversity, Istitute of Sciece, Akara, 994. [5] H. Qiag, Z. Youwei, O prefilterig ad edpoit detectio of speech sigals. Fourth Iteratioal Coferece o Sigal Processig (ICSP 98), , 998. [6] G.S. Yig, C.D. Mitchell, L.H. Jamieso, dpoit detectio of isolated utteraces based o a modied Teager eergy measuremet, Proceedigs of the I Iteratioal Coferece o Acoustics, Speech ad Sigal Processig (ICASSP 93) (993), [7] L.T. Burrows, Speech processig with liear ad eural etwork models. Upublished thesis, Cambridge Uiversity, Uited Kigdom, 996. [8] Ö. Aydı, Developmet of a voice recogitio system by usig articial eural etworks. Master s Thesis, Trakya Uiversity, Istitute of Sciece, dire, 005. [9] S. Oraitara, Y.J. Che, T.Q. guye, Iteger fast Fourier trasform. I Trasactios o Sigal Processig 50(3) (00), [0] W.T. Cochra, J.W. Cooley, What is the Fast Fourier trasform? Proceedigs of the I, 55(0), , 967. [] J.W. Cooley, J.W. Tukey, A algorithm for the machie calculatio of complex Fourier series, Math. Comput. 9 (965), [] H. Kobayashi, T. Shimamura, A weighted autocorrelatio method for pitch extractio of oisy speech, Proceed. I Iter. Coferece o Acoustics, Speech ad Sigal Processig 3, , 000. [3] M. Dedrios, G. Carayais, Spectrum aalysis usig a ew autocorrelatio measure.acoustics, Speech ad Sigal Processig 4(998),