A Novel Postfiltering Technique Using Adaptive Spectral Decomposition for Quality Enhancement of Coded Speech

Transcription

1 Hassan ars A Novel Postflterng Technque Usng Adaptve Spectral Decoposton for Qualty Enhanceent of Coded Speech HASSAN ARSI Dept. of Electronc and Electrcal Eng., aculty of Eng., Unversty of Brjand, Brjand, IRAN. hfars@brjand.ac.r Abstract: - An adaptve te-doan postflterng technque based on the synthess LP flter factorsaton s proposed. Inforaton s gathered about the relaton between the LP flter poles and forants for ths factorsaton. Ths technque shapes the an forant dfferently fro the other forants. Pole locatons representng the an forant are odfed and optu shapng constants for each forant are searched to ae ore narrower an forant bandwdth whle antanng other forant nforaton and ore attenuaton n valley regons. Key-Words: - Speech spectru, postflter, forant frequency, synthess flter. Introducton or speech percepton, speech forant regons are perceptually ore portant than spectral valley regons. Snce t s possble to push the quantsaton nose under an naudble threshold n both forant and valley regons at low encodng rates [] a good strategy s to allow ore quantsaton nose, yet lower than the naudble threshold, at the forant regons whereas sacrfcng the aount of quantsaton nose ntroduced n the valley regons. Ths technque s perfored n analyss-by-synthess coders by ncorporatng subjectve weghtng factors nto the error nsaton procedure []. Ths causes the nose coponents n soe of the valley regons to exceed the threshold. However, these nose coponents can be ade naudble by attenuatng the wth a postflter at the decoder. In [], a postflter consstng of a long-ter postflter secton n cascade wth a short-ter postflter secton was proposed. The long-ter secton ephasses ptch haroncs and attenuates the spectral valleys between ptch haroncs. On the other hand, the short-ter postflter antans forant nforaton and attenuates the spectral valleys between the forants. The followng sectons present the shortter postflter and thus we use postflter for splcty. The postflter s desgned based on the quantsed speech spectru. Due to varatons of the local characterstcs of the speech spectru, use of an adaptve postflter s preferred to the fxed one. The adaptve postflterng attepts to suppress the nose coponents by attenuatng the valleys and not alterng the forant nforaton. In perforng such attenuaton the speech coponent n the valley regon wll also be attenuated. Generally, the ntensty of the spectral valley can be attenuated by as uch as wthout any audble effect []. Therefore, by attenuatng the coponents n the spectral valleys, the postflter ntroduces a nu perceptual dstorton n the speech sgnal. However, t also acheves a substantal nose reducton. Ths paper s organsed as follows: In the next secton, we deonstrate the shortcongs of conventonal postflterng ethods. These probles are resolved usng the proposed odfed conventonal postflter. The new schee uses the synthess LP flter factorsaton whch s based on forant locatons and searchng the optu shapng constants for each forant. Ths procedure s perfored for each frae and thus the optu constants are updated nter and ntra frae. Secton 3 detals the new postflter desgn procedure. nally, n secton 4, the new and the conventonal postflters are evaluated n cobnaton wth the full-rate GSM-AMR proposed standard based on ACELP coder operatng at bt rates between 8.5 to 3.65 b/s [].. Conventonal postflterng The frequency response of an deal short-ter postflter should follow the peas and valleys of the spectral envelope of speech. Snce the LPC spectru contans the spectral envelope nforaton, t s natural to derve the short-ter postflter fro the LPC predctor. A conventonally used short-ter ISSN: Issue 5, Volue 4, May 8

2 Hassan ars postflter s gven by []: P( p α a z A( z / α ( µ z ( µ z p A( z / β β a z Where the odfed synthess flter ( A( z / β attepts to odel the speech spectral envelope through ephassng the forant regons and achevng the quantsaton nose reducton n the valley regons. The second flter structure A( z / α tres to flatten the spectru and reove the low pass spectral tlt ntroduced by the synthess flter for voced speech. Ths tlt has the sde effect of ang the postfltered speech sound uffled. The dfference between α and β deternes the flterng effect. (a forants to be weghted n the sae way. Snce lowfrequency forants play a ore portant role n perceptual speech qualty than the other forants, t s requred that these forants and the relatve valleys are shaped dfferently fro the other forants and valleys. As shown n gure (a, a possble sde effect of the LPC paraeters quantsaton s broadenng of the forants where the LP/LS coeffcents are quantsed usng a splt vector quantser [3]. Magntude ( Quantsed Modfed # Modfed # Modfed #3.9.8 Quantsed.7 # : (α.6, β.7 # : (α.6, β.8 #3 : (α.6, β.9 (b requency Noralsed by PI 9 6 Quantsed requency gure.: The orgnal and the correspondng quantsed LP spectrus Subjectvely, a large dfference wll gve a dsturbng deep voce effect wth ufflng of the hgher frequences. If the dfference s not large enough then there s no subjectve proveent n the speech qualty. or nstance, g. shows three dfferent choce of ( α.6, β.7, ( α.6, β.8 and ( α.6, β.9 where the enhanced spectru s noralsed such that the frst forant agntude s antaned dentcal to orgnal one. In fact, usng the sae constants for all of the forants causes the (c 8 4 gure : (a The orgnal and the correspondng quantsed LP spectrus,(b The correspondng frst two LS s, (c The correspondng pole locatons. 7 3 ISSN: Issue 5, Volue 4, May 8

3 Hassan ars Ths occurs when LSs representng the relatve forant becoe further apart than the orgnal one (g.b or equvalently, the rad of the poles representng the forant decrease (g..c. In fact, ncreasng the bandwdth undesrably aplfes quantsaton nose around the an forant and therefore affects speech qualty. In the followng secton we desgn a new postflter, whch factorses the LP synthess flter to ult-polynoals based on the forant nforaton and the optu shapng constants are then searched. 3. Proposed postflterng The conventonal postflters encounter two probles. rstly, weghtng the forants by the sae constants wthout consderng the role of the an forant on perceptual speech qualty, secondly aplfyng quantsaton nose around the forant frequences. Thus, the proposed postflter perfors the followng tass: I Soothng the an forant agntude varatons for both nter and ntra frae, II producng a narrower bandwdth for the an forant, III antanng other forant nforaton, IV attenuatng valleys regons n the speech spectru n order to acheve nose reducton and hence produce better speech qualty. 3. The LP flter factorsaton We propose a novel postflterng ethod, whch s based on LP synthess flter factorsaton. In order to control the shape of each forant, we calculate a polynoal representng the forant. Ths s perfored usng the relaton between the poles of the synthess flter and the forants. Snce the forants frequences appear as local axus n the speech spectru and consderng flat resdual spectru, we assue that pole angles n a LPC spectru contan nforaton about the forant locatons. Gven that a LPC spectru s defned as: Where H ( A( ( M A( a z (3 and M s the order of the LPC predctor, the poles can be found by solvng for the roots of A(. Snce ost speech coders use th order LPC flter, we consder M. Egenvalue ethod s used n solvng for the roots A( [4]. In ths ethod, the coeffcents { a },, L, M a are placed nto a copanon atrx whose egenvalues are the roots of A(. (a (b Magntude ( P P P requency Noralsed by PI 5 P P P4 P9 gure 3: (a The LP spectru and the correspondng poles, (b The pole locatons. Snce the coeffcents of A( are real, ts roots are n coplex conjugate pars, although two real poles ght exst. If two real poles exst, they always have an angle of and π. Notng ths syetrcal property, the poles can be dvded nto a group of postve angles and a group of negatve angles. In the postve angle group, the angles of the poles are arranged n ascendng order whereas for the other group the arrangeent s based on descendng order. Wth ths arrangeent r and r 6 have the sae radus and occur n conjugate angles when there are no real roots. To analyse the relaton between poles and the forants, a typcal LPC spectru s plotted wth the pole angles located on the noralsed frequency axs as shown n g. 3. In ths fgure, the locatons of poles through 5 are noted by P through P 5. Poles P 3, P 4 and P 5 ndcate the exact locatons of the forant peas. However, the poles are not always 7 P P8 P3 P7 P5 6 P P6 P 3 ISSN: Issue 5, Volue 4, May 8

4 Hassan ars located at the peas as shown n the exaple. In general, a wde forant bandwdth has two or three poles that are close together. Ths can be observed n g. 3 where the bandwdth of the frst forant s wder than the second forant. The frst forant has poles P and P that are close together whereas the other forants only have a sngle pole. Wth nowledge of the poles, estaton of the forants and the valleys regons can begn and the poles representng the forants are coputed. In order to estate forant and valley regons, the agntude response of the synthess flter for any gven angle, ω s coputed usng pole locatons as: H ( M + r π r cos θ N,, L, N (4 Where r and θ are the radus and the angle of pole P, respectvely and M s the order of the synthess flter and N ndcates frequency resoluton. Next, the forants and the valleys are searched fro the resultng agntude response usng the property that the forants and the vallys appear as local axu and nu, respectvely. Each pole s then allocated to the nearest forant based on L nor as follows: Q ( n ( P Z, n M (7 Where P ndcates the th pole allocated to the th forant. As an exaple g. 4 shows the decoposton of the speech spectru envelope based on the forants and the poles locaton orant # orant # orant #3 orant # Noralsed requency P ω M, L f θ ω < θ ω L, (5 Where ω s th forant, L and ndcate the nu and axu nuber of forants. In our experent L and 5 were consdered. The exceptons are for real poles where the poles wth angles and π are allocated to the frst and last forant, respectvely. Each forant can be represented by a polynoal usng the allocated poles. The order of the polynoal can be between to 6 dependng the nuber of the allocated poles. Thus, the synthess flter s decoposed as: H ( (6 M A( Q ( a z Q ( s the polynoal, whch represents the th forant, whch represents the th forant gven by: gure. 4: LP synthess flter factorsaton based on the forants and poles locaton classfcaton. 3. Narrowng an forant bandwdth In desgn procedure of the proposed postflter, the hgher energy forant s consdered as the an forant. Although the frst forant has usually ISSN: Issue 5, Volue 4, May 8

5 Hassan ars hgher energy for voced speech, soetes the second or even the thrd forant has ore energy. Ths happens for wea voced and feale speech sgnals. The energy of the forant s coputed usng the LPC spectru and the forant bandwdth as follows: E d c N H ω + π d c (8 ω f ndcates the forant wth axu energy. Snce the an forant s represented by a band pass flter, n DSP pont, ts bandwdth can be narrowed usng the followng technques: Movng the relatve poles of the an forant towards the unt crcle, Changng the phase of the relatve poles of the an forant, Changng the constants of the synthess, nverse and hgh pass flters usng polynoals representng the forants. Where c and c d d are gven by: N δb π N δb + π (9 (a 4 Modfed The bandwdth of the th forant, δb, represents 3 bandwdth of the relatve polynoal, / Q (. In case of presentng th forant by two poles, or equvalently Q ( wth a -order polynoal, and for r close to unty δb s gven by [5]: (b Modfed δ b ( r ( Noralsed requency The sooth varatons of the an forant agntude are perfored usng the prevous, current and next an forant agntudes as follows: G ηg G ( _ prv + λg _ next + ( η λ _ curr locatons New locatons Where G, G _ prv, G and _ next G _ ndcate the curr sooth, prevous, next and current an forant agntudes and η λ. 5. Snce the sooth agntude, G, ay be lower than the G _, the curr optu agntude s truncated to place n regon [ G curr.5g curr ]. or the voced segents, snce the frst forant (or the frst LS paraeters plays the an role n speech qualty [3], the an forant, ω, s coputed based on the frst forant usng the forant energes as follows: (c 8 4 gure 5: The effect of changng the rad of the poles representng the an forant, (a the resultng an forant and (b the LP spectru, (c the new and orgnal pole locatons. 7 3 ( E, ω.e Max, ω ω f Otherwse L, ( 3.. The poles oveent In the frst technque the poles representng the an forant are oved towards the unt crcle through an addtve step szeδ r, gven by Equaton (3, to ISSN: Issue 5, Volue 4, May 8

6 Hassan ars radus of the poles. r δ r (3 S Where r s the radus of the pole P and S ndcates the nuber of steps (S5. gure 5 shows the effect of ovng the pole n the LPC where the radus of the pole s changed fro.86 to.95. In ths technque, three condtons are consdered: I the an forant has to be antaned at the dentcal angle, II stablty of the synthess flter, III preventng undesrable forants. (a (b 6 4 Modfed Modfed Noralsed requency Modfed sze, δ r, and the other poles are then oved as well so that the new an forant, ω, s close enough to the an forant: π ω ω (4 N Stablty of the synthess flter s naturally provded usng the property that the roots of LPC flter are nsde of unt crcle. Although theoretcally ovng the poles towards the unt crcle guarantees stablty of the synthess flter, our experents show that poles too close to the unt crcle, especally n case of hgh-energy resdual, result n a saturated output. Thus, the axu radus of the ovng pole was restrcted to.985, whch was obtaned experentally. In case of ore than two conjugate poles, ovng the poles wth the saller radus ay create an undesrable forant or even ncreases the an forant bandwdth. Ths s shown n g. 6 where ovng the pole P fro.7 to.9 has created an undesrable forant. Ths stuaton can be prevented by checng a local axu exstence at the relatve pole angle and the resultng bandwdth. In order to reduce the coplexty of the desgn procedure, the pole wth bgger radus, r, s oved towards unt crcle and then the other pole radus, r, s ultpled by factor of λ : P P r λ (5 r (c 8 4 gure 6: The effect of naccurate ovng the poles representng the an forant on the forant (a and the LP spectru (b, (c the new and orgnal pole locatons. If two poles represent the an forant, the order of the correspondng polynoal s two and so the an forant s located at the postve angle of the pole. or ths case, the frst condton s satsfed. Whereas for the an forant representng by ore than two poles, the prncpal pole (the pole closer to unt crcle s oved towards the unt crcle wth a step 7 3 In fact, ths causes the rato of the new pole rad to be dentcal to the orgnal one. Note that the prncpal pole plays the an role n the LPC spectru and thus ovng ths pole s perfored wth hgher resoluton. In the desgn procedure, the addtve step sze gven by Eq. (3 s odfed as γδ r, where r s the radus of the prncple pole and γ Changng the angles In the second technque, the angles of the poles are odfed to ae the closer to each other and the rad of the poles are antaned dentcal wth orgnal ones. Obvously, ths technque s appled when ore than two poles represent the an forant. gure 7 shows the effect of ths technque on the frst forant where poles P and P wth angles of.3 and.5 rad presentng the frst forant are odfed to have sae rad wth angles ISSN: Issue 5, Volue 4, May 8

7 Hassan ars of.3 and.45 rad. n ths case, we also consder three condtons: I the an forant has to be antaned at the dentcal angle, II stablty of the synthess flter. (a (b 4 Modfed Modfed Noralsed requency Modfed Where ω s the an forant frequency and L. In our experent, frstly the angle of the prncple pole and then the angle of the other pole are updated so that the Eq. (4 s satsfed. It s entoned that snce the prncple pole plays the an role n the an forant shape, the angle of ths pole s norally closer to ω and therefore t s updated by saller step sze. In addton, the closer the poles are to each other results a hgher resonance for the correspondng forant. Snce ths can result n a saturated output, the odfcaton of the angles contnues untl the dfference between the updated angles s ore than a threshold. Ths threshold was experentally found to be. rad. In the proposed postflter desgn procedure, two descrbed technques are used for enhancng the an forant. The frst s for the case of a par of conjugate poles presentng the an forant whereby only the radus s altered. Both odfcaton technques are used for the case, where ore than two conjugate poles representng the an forant. (c.6 5 P.4. P Changng the shapng constants In the thrd technque the an forant bandwdth decreases usng the constants of the synthess, nverse and hgh pass flters. or nstant, gure 8 shows the effect of two dfferent pars α.7, β.8 and α.5, β. 9 on the an forant and also LPC spectru where these constants are equal to.8 and.7 for the other forants n both cases. 6 4 Modfed # Modfed # gure 7: The effect of changng the angles of the poles representng the an forant, (a the resultng an forant and (b the LP spectru, (c the new pole locatons. (a Assue that θ s the angle of one of the poles representng the an forant whch s updated usng Eq. 6. θ θ + δθ (6 (b Modfed # Modfed # δθ ndcates step-sze angle varaton and gven by: ω θ δθ (7 L Noralsed requency gure 8: The effect of changng the constants on, (a the an forant and (b the LP spectru for two dfferent choces, #: α.7, β. 8, #: α.5, β. 9. ISSN: Issue 5, Volue 4, May 8

8 Hassan ars In fact, the hgher dfference between α and β ore decreases the bandwdth. However, as shown n g. 8.b, ths hgher dfference attenuates other forants and so affects speech qualty. Thus, antanng the other forants nforaton s a factor, whch s used to control α, β. Ths s perfored usng dfferent constants for each forant. Unfortunately, due to the exstng the nteracton between the spectrus of the polynoals representng the forants, t s possble to fnd the optu constants as a close for and thus these are searched usng a weghtng functon descrbed n the followng secton. 3.3 Postflter desgn The polynoals representng the forants are used to desgn the new postflter. The new postflter s gven by: P(. Ω(. hp( D Q ( z / α Q ( z / α (8 Ω( Q ( z / β, Q ( z / β h ( ( µ z h p ( s a frst-order hgh-pass flter ncluded for tlt copensaton [6] and µ s gven by: where p R( µ (9 R( L R( τ p( n. p( n + τ ( n descrbed n sectons 3.. and 3.., whereas Q (. s only a functon of the constants α and β. Movng the poles and changng the constants causes the an forant gan dffers fro G _, a factor D opt s used to satsfy Eq.. D. H ( ω. Ω( ω. hp ( ω ( G _ opt Snce the poles representng the forants are avalable, the agntude spectru of Ω (. and H p (. are coputed usng the pole locatons as follows: Ω( ω P ( ω. Q ( ω P ( ω Q ( ω H ( ω p l l + α r + β r l l + α r + β r α r cos( θ ω β r cos( θ ω α r β r + µ µ cos( ω θ µ cos( θ ω cos( θ ω π ω N,, L, N ( Where l ndcates the nuber of poles for the th forant and θ µ s gven by: f µ θ µ π otherwse (3 and p (. s the pulse response of flter Ω (, L s the length of the pulse response, whch s consdered to be of length.5s, ndcates the nuber of the polynoals (forants, Q (. and Q (. are the polynoals representng the th and the an forants, respectvely and γ. 9. The reason for solaton of Q (. fro the other polynoals s that Q (. s a functon of both constants ( α and β and also the odfed poles resultng fro the frst and second technques Next, we fnd the optu constants so that the other forant nforaton s antaned and the valleys are attenuated. In addton, snce the lowfrequency forants and valleys play a ore portant role on perceptual speech qualty, antanng the forant nforaton and attenuatng the valleys are weghted. Ths s perfored usng the weghtng functon gven n Eq. 4. Ψ( α, β, p γ R( W ( + ( γ U( n W ( n (4 r n r ISSN: Issue 5, Volue 4, May 8

9 Hassan ars The Eq. (4 s splt nto two parts. The frst part, R( Wr (, s related to nsng the resultng error n the forants bandwdth excludng the an forant, whereas the second part, U ( Wr (, s related to axsng the dfferences (whch are negatve for desrable postflter n the valleys regons. These parts are gven by: R( U ( n d c d c N N H eq N N H eq n H n ϕ + ϕ +. W π π ω + H ω +. Ws ( π π (5 ω and ϕ n ndcate th and n th forant and null frequences, respectvely, N s T length and H eq ( H ( P(. A weghted wndow functon W s (., s used to ephasse the forants and nulls such that ore weght s assgned to the forant frequences and less for the nulls. W s (. s based on the band-lted an lobe of the Snc functon. The bandwdth s selected based on the 3 pont, whch corresponds to.77 of the axu apltude. Ths occurs when the arguent of the Snc functon s equal to ± It has to be also entoned that the length of W s (. depends on the forant bandwdth and s coputed by: L s b s ( N δ π. (6 ro above, the coeffcents of W s (. are calculated as:.886 L s Ls Ws ( Snc(, K, (7 Ls Next, the resultng coeffcents are noralsed such that: Ws ( (8 A second weghtng wndow, W r (., s also used to assgn ore weght to the low frequency forants and nulls. The length of ths wndow depends to the nuber of the forants and the nulls. The optu constants and the odfed poles representng the an forant are obtaned by nsaton of the functon Ψ (.. { α, β, µ }, { } P argn Ψ( α, β, P When l,, l K l, K, l.5 α.7, α +. β.95,.4 α.65, α +.3 β.95 r.98 l, L, l l (9 ( Note that ndex ndcates the an forant paraeters, s the nuber of the forants, l s the nuber of the poles, P, representng the an l forant. Ths nsaton results n the optu constants of { α, β } for each polynoal, also the, L, optu pole locatons of the an forant. Ths nforaton s used to construct the new postflter gven n Equaton 8. As an exaple, gure 9(a shows the enhanced LPC spectru n coparson wth the synthessed one along wth the correspondng optu constants for each forant. The odfed poles locaton copared to the orgnal ones has been depcted n g. 9(b. Snce the gan of the enhanced LP flter s not necessarly dentcal to orgnal LP flter, the gan of the enhanced speech sgnal, s pf (n, can dffer fro the orgnal speech, s (n. An adaptve gan control proposed n [7] s used to copensate for gan dfferences between s pf (n and s (n. The gan scalng factor G for the current frae s coputed by: Where N f s( n n G (3 N s ( n f n pf N f s the length of the current frae. The gan-scaled enhanced speech sgnal, sˆ pf ( n s gven by: sˆ ( n g( n s ( n n,, K, N (3 pf pf f ISSN: Issue 5, Volue 4, May 8

10 Hassan ars Where g (n s updated on a saple-by-saple bass and gven by: g( n.85g( n +.5G n,, K, N f (33 (a (b α.65 β.85 α.7 β.9 α.6 β.8 α.65 β.75 New Conventonal Noralsed requency P P Modfed 4. The postflter evaluaton Due to non-exstence of quanttatve easures, the new postflter s evaluated by subjectve lstenng test. The ACELP coder operatng at 8.5 b/s [6], where the speech sgnal s synthessed usng the nterpolated LP coeffcents for four-5s sub-bloc, s used. The eployed postflterng s as follows: P( Ω(.( µ z A( z / α Ω( A( z / β (34 Where α. 7, β. 8and µ s obtaned usng the sae procedure eployed n the new postflter. In order to easure the subjectve perforance between the new postflter and the one eployed n ACELP, two postflters were separately used n the sae bt-rate and an A vs. B test was conducted. In ths test, sentence pars for 6 speaers (3 ale and 3 feale speaers were processed by the two 8.5 b/s ACELP coder. ourteen lsteners (4 traned and untraned perfored ths test. The results are shown n Table. The results obtaned ndcate that the new postflter provdes sgnfcantly better perceptual speech qualty than the conventonal one. As shown n gure 9, the reason s that the new postflter provdes narrower an forant bandwdth and attenuates the valleys ore copared wth the conventonal postflter whle antanng the other forants nforaton. 4 7 gure. 9: (a The resultng LP spectrus usng the new and conventonal postflters n coparson wth the synthessed LP spectru, (b The odfed pole locatons copared to the orgnal ones. 3 Table : A-B test results for the new and conventonal postflters n cobnaton wth ACELP coder. Speech Type Better Slghtly better Sae Slghtly worse Worse ACELP + new postflter vs. ACELP + conventon al postflter The ntal value of g (. s used. Then for next frae, g ( s set equal to g ( N f of the prevous frae. 5. Concluson In ths paper, the new postflter desgn approach was descrbed. The new postflter was desgned based on four features. These features are: sooth evoluton ISSN: Issue 5, Volue 4, May 8

11 Hassan ars of the an forant, narrower an forant bandwdth, valleys attenuaton, v antenance of other forant nforaton. Ths was perfored by LP synthess flter factorsaton and searchng the optu pole locatons representng the an forant and the constants α, β for each forant. The new postflter was evaluated n coparson wth the conventonal pos-flter. or ths purpose, the two postflters were used n ACELP 8.5 b/s speech coder []. The subjectve lstenng tests show that the proposed postflter n cobnaton wth the ACELP provdes sgnfcantly better qualty than the conventonal flter wth ACELP. References: [] J. H. Chen and Allen Gersho, Adaptve postflterng for qualty enhanceent of coded speech, IEEE Transacton on Speech and Audo Processng, Vol. 3, No., January 995. [] C. Srratanaban, A. Kondoz, A ull-rate GSM- AMR canddate, Proceedngs of the 6th European Conference on Speech and Technology, Eurospeech'99, Budapest, Hungary, pp , Septeber 999. [3] K. K. Palwal and B. S. Atal, Effcent vector quantsaton of LPC paraeters at 4 bts/frae, IEEE Transactons on Speech and Audo Processng, pp. 3-7, Jan., 993. [4] Wlla H. Press, Saul A. Teuolsy and Wlla T. Vetterlng. Nuercal Recpes n C. Cabrdge Unversty Press, Cabrdge,. [5] J. G. Proas and D. G. Monalas. Dgtal Sgnal Processng: Prncples, algorths and applcatons. Macllan publshng copany, New Yor, 99. [6] ITU-T, Codng of speech at 8 bt/s usng Conjugate Structure Algebrac Code-Excted Lnear Predcton (CS-ACELP, Mar. 996, ITU- T Recoendaton G.79. [7] Azhar Mustapha and Suat Yeldener, Adaptve post-flterng technque based on the odfed Yule-waler flter, Unted states patents, Patent No. US B, May. ISSN: Issue 5, Volue 4, May 8