[33]. As we have seen there are different algorithms for compressing the speech. The
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- Percival Joseph
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1 49 5. LD-CELP SPEECH CODER 5.1 INTRODUCTION Speech compresson s one of the mportant doman n dgtal communcaton [33]. As we have seen there are dfferent algorthms for compressng the speech. The mportant factor that separates one algorthm from the other algorthm s ts complexty. The coder complexty s a functon of the sgnal processng nvolved. For a complex codng algorthm the processng tme wll be maxmum hence the processng delay wll be maxmum. The dfferent types of delays that can be encountered whle processng the speech are 1. Bufferng delay at the encoder: Ths delay s caused by the number of samples that are to be gathered before the processng begns. 2. Processng delay at the encoder: Ths s the tme requred to processes all the buffered samples. For the complex algorthm the processng delay wll be very hgh. 3. Transmsson delay: Ths s the tme requred to transmt the processed data from source to the destnaton. 4. Bufferng delay: The speech sgnal from the transmtter s transmtted n the form of dfferent parameters lke LPC, ptch, gan and so on. To start the synthess at the recever sde a full knowledge of these parameters s requred. Usually t s assumed that the bufferng delay at the transmtter sde s smlar to the delay at the recever sde.
2 50 5. Processng delay at the recever: The tme requred by the decoder to get back the orgnal nformaton that was transmtted from the transmtter usng the parameters obtaned from the decoder. The total delay can be estmated as 3.5 tmes the codng delay. The algorthm wth least codng delay wll have less total processng delay. Such delay can have mportant ramfcatons n aspects of speech communcatons such as echo control n long dstance communcaton [25]. For any communcaton system the path wth least path delay are chosen to avod the use of echo cancellers. The conventonal CELP has got hgh processng delay as t uses forward adaptve technque over frame sze of 160 (20ms) samples rather than LD-CELP whch uses backward adaptve technque wth the frame sze of fve samples. Hence whle choosng speech compresson algorthm processng delay algorthm plays a vtal role. One such algorthm s Low Delay CELP [LD-CELP]. Ths has processng delay less than ms. The flow of ths chapter: Outlne of LD-CELP algorthm LD-CELP Encoder LD-CELP Decoder Outlne of LD-CELP algorthm In conventonal CELP coder the predctor parameters along wth the exctaton sgnals are transmtted. The predctor coeffcents are updated by performng a LPC analyss on the prevously quantzed speech. In case of LD-CELP t s backward adaptve verson of CELP. The LD-CELP coder works usng the analyss by synthess approach to codebook search. Ths coder uses backward adaptaton of predctors and gan to acheve
3 51 an algorthmc delay less than ms. Here only the ndex to the exctaton codebook s transmtted. The predctor coeffcents are updated through the LPC analyss of prevously quantzed speech. The block sze of the exctaton vector chosen s of fve samples [30]. The long term predctors of the CELP are replaced by the hgh order STP predctor. The coeffcents of STP are updated once every four exctaton vector by performng the LPC analyss on prevously quantzed speech. The exctaton gan s updated once every fve samples or a vector usng 10 th order adaptve lnear predctor n the logarthmc doman. The coeffcents of the log gan predctor are updated once every four exctaton vectors by performng a LPC analyss on prevously quantzed and scaled exctaton vectors. A 10 th order perceptual flter s updated once every four exctaton vectors by performng the LPC [31] analyss on the orgnal speech samples at the encoder. The fve speech samples are quantzed and represented by 10 bts. The exctaton codebook s made up of a 3-bt gan and 7-bt shape codebook [25] Basc LD-CELP Encoder and Decoder: LD-CELP Encoder: The speech sgnals are sampled and are parttoned nto blocks of fve consecutve nput sgnal samples. Each block s called a vector and these vectors are stored n the vector buffer. For each nput block the encoder passes each of 1024 codebook vectors through the gan scalng unt and a synthess flter. From the obtaned resultng 1024 canddate quantzed sgnal vector the encoder dentfes the one whch mnmzes a frequency weghted mean square error when the quantzed sgnal vector s compared wth the nput sgnal vector. The best canddate quantzed sgnal vector s represented by a 10 bt codebook ndex and ths s transmtted to the decoder. The best code vector s passed through the gan scalng unt and the synthess flter to
4 52 establsh the correct flter memory n preparaton for the encodng of the next sgnal vector. The gan coeffcents and the synthess flter coeffcents are up dated perodcally n a backward adaptve manner based on the prevously quantzed sgnal vector. The basc smplfed encoder block dagram s as shown n the fgure 5.1 I/p voced data 64kb/s Convert to unform PCM 64kb/s Vector buffer Exctaton VQ code book Gan Synthess flter + Perceptual weghtng flter Mnmum MSE + VQ ndex 16kb/s output Backward gan adaptaton - Backward predctor adaptaton Fg: 5.1 Basc LD-CELP Encoder Block LD-CELP Decoder: The decoder on recevng the 10 bt ndex performs the table lookup to extract the correspondng codevector from the exctaton codebook. The extracted codevector s then passed through a gan scalng unt and a synthess flter to produce the current decoded sgnal vector. The gan and the synthess flter coeffcents are up dated n the smlar way as n the encoder. The decoded sgnal vector s then passed through an adaptve postflter to enhance the perceptual qualty. The postflter coeffcents are updated perodcally usng the nformaton avalable at the decoder. The fve samples of the postflter sgnal vector are converted nto the PCM output samples. The basc decoder block dagram s as shown n the fgure 5.2
5 53 VQ Index 16kb/s Exctaton VQ code book Gan Synthess flter Post flter Convert to PCM 64kb/s O/P Backward gan adaptaton Backward predctor adaptaton Fg: 5.2 Basc LD-CELP Decoder Block Explanaton of LD-CELP encoder: The man explanatory block dagram of LD-CELP [32] encoder s as shown n the fgure 5.3. The nput voced sgnals or unvoced sgnals are sampled wth dfferent samplng frequency values. The wdely chosen samplng frequency s 8 khz and the samples are taken at the nterval of 125µsec.These samples are grouped nto fve consecutve samples and each group s called a vector.
6 54 64kbt/s 1 Lnear 2 Input A-law or µ-law PCM nput speech Input PCM PCM nput speech speech Vector vector s(n) format buffer S 0 (k) converson S u (k) Smulated decoder 8 3 Exctaton VQ codebook Y(n) 21 e(n) Synthess s q (n) Gan Flter Adapter for perceptual weghtng flter σ(n) Backward vector gan adapter P(z) Backward synthess flter adapter W(z) Perceptual weghtng flter 10 v(n) r(n) 11 6 Synthess flter Perceptual weghtng flter 12 VQ target vector normalzaton X(n) 16 Impulse Code book search module 24 response vector VQ target h(n) calculator 14 vector normalzaton X^(n) 13 Error calculator 17 E j Energy table 15 calculator 18 Best codebook P(n) ndex selector Shape codevector convoluton module Tme-reversed convoluton module
7 55 Best codebook ndex Code book ndex Communcaton channel Fg: 5.3 LD-CELP Encoder block schematc These vectors are stored n the vector buffer. After processng each of the vector the exctaton vector quantzaton [VQ] codebook s the only nformaton transmtted from the transmtter to the recever. The three other parameters..e. the exctaton gan, the synthess flter coeffcents and perceptual weghtng flter coeffcents are perodcally updated. These coeffcents are derved n a backward adaptve manner from the sgnals that occur pror to the current sgnal vector. The exctaton gan s updated once every vector whle the perceptual weghtng flter coeffcents and the synthess flter coeffcents are updated once every four vectors. The basc buffer sze s only one vector. Ths small buffer sze makes t possble to acheve a one-way processng delay less than 2ms [34]. Internal lnear PCM converter: Ths converts the nput voced data or unvoced data nto samples. The nput sgnals are sampled wth varable samplng frequency. The wdely used samplng frequency of 8 khz. Vector Buffer: A group fve consecutve speech samples are grouped nto a vector and these vectors are stored n the vector buffer. Adapter for perceptual weghtng flter: Ths adapter calculates the coeffcents of the perceptual weghtng flter once every four speech vectors based on the lnear predcton analyss of unquantzed speech. The coeffcents are updated once every four vector adaptaton cycle. The updatng of the
8 56 coeffcents occurs only durng the thrd speech vector of every four vector adapton cycle. The perceptual weghtng flter manly conssts of Hybrd wndowng module Levnson-Durbn recurson module Weghtng flter coeffcent calculator The nternal blocks of perceptual weghtng flter are as shown n the fgure 5.4 and ts coeffcents are calculated as follows: Input speech Hybrd wndowng module Levnson-Durbn recurson module Weghtng flter coeffcent calculator Perceptual weghtng flter coeffcent Fg: 5.4 Perceptual weghtng flter adapter The nput speech s passed through the hybrd wndowng module. Ths module places the wndow on the prevous speech vectors and calculates the frst 11 autocorrelaton coeffcents of the wndowed speech as the output. These 11
9 57 autocorrelaton functons are converted nto predctors coeffcents by the Levnson- Durbn recursve module. These are fed to the weghtng flter coeffcent calculator whch derves the desred coeffcents of the weghtng flter. Functonng of hybrd wndowng module: The hybrd wndow s used for backward-adaptve LPC analyss. The analyss s done on all the prevous sgnal samples wth a samplng ndex less than m. If there are N non-recursve samples n the hybrd wndow functon, then the sgnal samples are weghted by the non-recursve porton of the wndow. fm( k) b [ k ( m N 1)] f k m N 1 wm( k) gm( k) sn[ c( k m)] f m N k m 1 0, f k m 5.1 Where g m (k) are the samples of non-recursve porton and f m (k) are the samples for the recursve porton. The values of g m (k)and f m (k) for dfferent hybrd wndow s specfed n the Appendx A. The wndow-weghted sgnal s S m (k) can be wrtten as su ( k) fm( k) su ( k) b [ k ( m N 1)] f k m N 1 sm( k) su ( k) wm ( k) su ( k) gm( k) su ( k)sn[ c( k m)] f m N k m 1 0, f k m 5.2 For an M th order LPC analyss we need to fnd M+1 autocorrelaton coeffcents. Let R m () be the th autocorrelaton coeffcent for the current adaptaton cycle and can be wrtten as
10 58 m1 m1 R ( ) s ( k) s ( k ) r ( ) s ( k) s ( k ) m m m m m m k kmn 5.3 And r m () can be wrtten as mn 1 mn 1 r ( ) s ( k) s ( k ) s ( k) s ( k ) f ( k) f ( k ) m m m u u m m k k 5.4 Where r m () s the recursve component of R m () and the second term n the above equaton represent the non-recursve component. The fnte summaton of all components for one adaptaton cycle gves the non-recursve component. The recursve components are calculated recursvely by calculatng and storng all r m () values for the current adaptaton cycle and then gong for the next adaptaton cycle whch starts at the next sample value s u (m+l). Once the hybrd wndow s shfted to the rght by L samples, a new wndow-weghted sgnal for the next adaptaton cycle can be wrtten as L su ( k) fml ( k) su ( k) fm ( k), f k m L N 1 sm L ( k) su ( k) wm L ( k) su ( k) gml ( k) su ( k)sn[ c( k m L)], f m L N k m L 1 0, f k m L 5.5 The recursve component of r m+l () can be wrtten as mln 1 r ( ) s ( k) s ( k ) ml ml ml k 5.6 mn 1 mln 1 s ( k) s ( k ) s ( k) s ( k ) ml ml ml ml k kmn 5.7
11 59 mn 1 mln 1 L L u m u m ml ml k kmn s ( k) f ( k) s ( k ) f ( k ) s ( k) s ( k ) 5.8 Or after further smplfcaton can be wrtten as mln 1 2L ml( ) m( ) ml( ) ml( ) kmn r r s k s k 5.9 Hence the r m+l () can be calculated recursvely from r m () usng the above equaton. Ths value s stored s the memory for the use for next adaptaton cycle. The autocorrelaton coeffcents are calculated as ml1 R ( ) r ( ) s ( k) s ( k ) ml ml ml ml kmln 5.10 The above procedure explans the general calculaton technque of a hybrd wndow module. The parameter value for the hybrd wndowng module can be wrtten as 1 10, 20, L 1 1 M L N and sothat Once the 11 autocorrelaton coeffcents are calculated by the hybrd wndow procedure usng the above method, a whte nose correcton procedure s appled. Ths s done by ncreasng the energy R(0) by small amount R(0) 257 R(0)
12 60 By fllng the spectral valleys wth whte nose reduces the spectral dynamc range and also allevate ll-condtonng of the subsequent Levnson-Durbn recurson. The whte nose correlaton factor of (257/256) corresponds to a whte nose level at about 24db below the average speech power. By usng the whte nose corrected autocorrelaton coeffcents Levnson-Durbn module recursvely computes the predctor coeffcents between the order 1 to 10. The recursve procedure to fnd j th coeffcent of the th order predctor a j () can be specfed as follows: E(0)=R(0) k 1 ( 1) ( ) j ( ) j1 R a R j E ( 1) 5.13 a = k () 5.14 ( ) ( 1) ( a a k a 1) ; 1 j 1 j j j 5.15 E k E 2 ( ) (1 ) ( 1) 5.16 The equatons 5.13 to 5.16 are evaluated recursvely for =1 to 10 and the fnal soluton s gven by q = a (10),
13 61 If q 0 =1 then the 10 th order predcton error flters or analyss flters transfer functon can be wrtten as Q () z 10 0 q z 5.18 And the 10 th order lnear predctor s defned by the followng transfer functon 10 Q() z qz The weghtng flter coeffcent calculator calculates the perceptual weghtng flter coeffcents accordng to the followng equatons: 10 z Q( ) ( q 1 ) z And 10 z Q( ) ( q 2 ) z The transfer functon of a 10 th order pole-zero perceptual weghtng flter s defned by W(z). The values of γ 1 and γ 2 are chosen as 0.9 and 0.6. The perceptual weghtng flter adapter perodcally updates the coeffcents of W(z) and feed the coeffcents to the mpulse response vector calculator and the perceptual weghtng flters. Perceptual weghtng flter:
14 62 The nput speech sgnal vector S(n) when passed through the perceptual weghtng flter results n the weghted speech vector v(n). Only durng ntalzaton the flter memory s reset to zero. Durng the non-speech sgnals or Modem sgnals t s desrable to dsable the perceptual weghtng flter, whch s done by settng W(z) =1. The value W(z) can be made 1 by settng γ1 and γ2 equal to zero. For the speech mode the nomnal value are 0.9 and 0.6[29]. Synthess Flter: There are two synthess flters n the man block. Both the flters are updated by backward synthess flter adapter. The synthess flter s of 50 th order all pole flter wth 50 th order LPC predctor n the feedback branch. The transfer functon of the synthess flter s 1 Fz () 1 pz ( ) 5.22 Where P(z) s the transfer functon of 50 th order LPC predctor. Once the speech vector v(n) s obtaned, a zero nput response vector r(n) wll be generated usng the synthess flter and perceptual weghtng flter. The zero nput response s obtaned by connectng the swtch node 5 to the node 6, hence makng the sgnal gong from node 7 to the synthess flter [block 9] zero. Then the synthess flter [block 9] and perceptual weghtng flter [block 10] are processed for fve samples..e. we contnue the flterng operaton for fve samples wth a zero sgnal appled at the node 7. The resultng output s obtaned at the perceptual weghtng flter s the zero-nput response vector r(n). The memory of the synthess flter [block9] and the perceptual weghtng flter [block10] s non-zero except at the tme of ntalzaton. Hence the value
15 63 of r(n) wll be non-zero and s the response of the two flters to prevous gan-scaled exctaton vectors. The vector r(n) represents the effect due to the flter memory. VQ target vector computaton: Ths block performs the subtracton of the zero-nput response vector r(n) from the weghted speech vector v(n) to obtan the VQ codebook search target vector x(n). Backward synthess flter adapter: Ths backward synthess flter updates the coeffcents of both the synthess flters [blocks 9 and 22]. Ths takes the quantzed speech as nput and produces a set of synthess flter coeffcents as output. The operaton of ths block s smlar to that of perceptual weghtng flter adapter [block 3] except the followng dfferences: The nput sgnal s quantzed rather than unquantsed speech sgnal The predctor order s 50 rather than 10. Quantzed Speech Hybrd wndowng module Levnson-Durbn recurson module Weghtng flter coeffcent calculator Synthess flter coeffcent Fg: 5.5 Backward synthess flter adapter
16 64 The block dagram of the backward synthess flter adapter s as shown above n fgure 5.5. The early verson of the encoder had 10 th order backward LPC analyss and a backward adaptve 3-tap ptch predctor. The dsadvantage of ths confguraton was ts poor performance under the channel errors. The ncluson of a LTP makes the system very senstve to channel errors. Ths drawback s overcome by replacng the LTP by a hgh order backward STP. The 50 th order s chosen for the backward STP. The advantages of usng hgh order STP are as follows: Hgh order backward LPC s qute robust to channel error. No sde nformaton s needed for hgher order speech. Wth hgher order STP the algorthm becomes less speech specfc, hence gves better performance for both voce sgnal and non-voce sgnals. The man dsadvantage of usng hgh order LPC s due to ts hgh computatonal complexty as t requres to compute large number of correlaton parameters. Intally a 20ms Hammng wndowng was used to compute the 50 LPC coeffcents but resulted n hgh computaton complexty. Hence to overcome ths Barnwell s recursve wndowng technque was used. Barnwell has shown that f the mpulse response of a 2-pole flter s used as the wndow functon, then the correspondng autocorrelaton functon can be calculated recursvely. The flter response of a 2-pole flter used as a wndow functon s gven by H( z) 1 2z z The use of the above equaton results n numercal and precson problem wth the hgher order LPC flter. Hence ths problem s overcome by replacng the drect order
17 65 flter by a three frst order flters n cascade. The transfer functon of the modfed flter s gven by m ( m 1) ( m 1) z H() z 1 ( m2) z 5.24 In the above equaton α s the parameter that controls the shape of wndow and m s the samplng ndex. Ths method reduced the computatonal complexty but created a new problem wth the fxed pont processor. The product of two 16 bt values requres 32- bt dynamc range. The fxed pont processor requres double precson arthmetc and ths nturn ncreases the computaton complexty. To avod ths drawback hybrd wndow was used whch reduces the computaton complexty by spreadng the computaton load over four speech frames as coeffcents are updated only after four speech frames [25]. These coeffcents are fed to the both the synthess flters [block 9 & 22] and also to the mpulse response vector calculator [block 12]. The perceptual weghtng flter along wth the synthess flter are updated once every four vectors. The updatng s done durng every thrd speech vector of every four adaptaton cycle. A delay of two vectors s ntroduced as the updates are based on the prevously quantzed speech. Even though the autocorrelaton coeffcents of prevously quantzed speech s avalable at the frst vector of each four vector cycle, computatons may requre more than one vector worth of tme. Therefore, to mantan a basc buffer sze of one vector (so as to keep the codng delay low), and to mantan real-tme operaton, a 2-vector delay n flter updates s ntroduced norder to facltate real-tme mplementaton [30]. Backward vector gan adapter: Ths adapter updates the exctaton gan σ(n) for every vector tme ndex n. The exctaton gan s a scalng factor used to scale the selected exctaton vector y(n). The
18 66 backward vector gan adapter takes the gan scaled exctaton vector e(n) as ts nput and produces an exctaton gan σ(n) as ts output. Ths block bascally tres to predct the gan e(n) based on the gans of prevous vectors usng adaptve lnear predcton n the logarthmc gan doman. The block dagram of the backward vector gan adapter s as shown n the fgure 5.6. Gan scaled Exctaton gan exctaton vector Log -gan predctor + Log gan lmter Inverse logarthmc calculator Bandwdth expanson module Log-gan off set value holder One vector delay Levnson- Durbn recurson Hybrd wndowng module + Logarthm Calculator Root-mean square calculator Fg: 5.6 Backward vector gan adapter The backward gan adapter operates as follows. The one-vector delay unt makes the prevous gan scaled vector avalable. The root-mean-square calculator calculates the RMS value of the vector farwarded by the one vector delay unt. Ths output s further gven to the logarthm calculator whch converts the RMS values nto ts db equvalent values. The log-gan offset value s stored n the log-gan offset value holder. The loggan offset s meant to be roughly equal to the average exctaton level durng the voced speech. The adder subtracts ths log-gan offset value from the logarthmc gan produced
19 67 by the logarthmc calculator. The resultng offset removed logarthmc gan s used by the logarthmc gan module and Levnson-Durbn recurson module. The analyss performed s smlar to the perceptual weghtng flter module except the parameters of the hybrd wndow are dfferent and the sgnal under analyss s offset removed logarthmc gan rather than the nput speech. The logarthmc gan produced s the gan value for every fve speech sgnal samples. The hybrd wndow parameters are 1 8 M 3 10, N 20, L 4, The output of the Levnson-Durbn recurson module s the coeffcent of a 10 th order lnear predctor wth a transfer functon of 10 Rˆ () z ˆ z The bandwdth expanson module moves the roots of the polynomal towards the z-plane resultng n expanded bandwdth. The transfer functon R(z) of the bandwdth expanded gan predctor s gven by 10 R() z z Where the coeffcents of α are computed as 29, ˆ ˆ
20 68 The bandwdth expanson makes the gan adapter more robust to the channel errors. Ths drawback s over come by choosng the α whch s used as coeffcents of the log-gan lnear predctor. Ths predctor s updated once every four speech vectors. The predctor attempts to predct δ(n) based on a lnear combnaton of prevous values. The predcted value of δ(n) s denoted by ˆ( n) and s gven by 10 ˆ( n ) ( n ) Once the log-gan predctor fnds the value of ˆ( n), to ths we add log-gan offset value stored n the Log-gan offset value holder. Ths added up value s passed through the log-gan lmter, whch n turn lmts the value between 0db and 60 db. The obtaned value s fed to the nverse logarthmc calculator whch converts the log values back to the lnear values. The gan lmter ensures that the gan values are lyng n the range 1 to The Appendx C gves the nteger values for the pole control, zero control and bandwdth broadenng vectors. Codebook search module: Ths module search through the 1024 canddate code vectors n the exctaton VQ codebook and dentfes the ndex of the best code vector whch corresponds to the quantzed speech that s closest to the nput speech vector. To reduce the search tme the codebook s decomposed nto two smaller codebooks, a 7-bt shape codebook whch contans 128 ndependent code vectors and a 3-bt gan codebook contanng eght scalar values. The fnal output code vector s the product of the best shape code vector and best gan level.
21 69 Prncple of codebook search: The codebook search module scales each of the 1024 canddate code vectors by the current exctaton gan σ(n) and then passes the resultng 1024 vectors one at a tme through the cascaded flters consstng of the synthess flter F(z) and a perceptual weghtng flter W(z). The flter memory s ntalzed to zero each tme when a new codevector s fed to the cascaded flter. The transfer functon of the cascaded flter s H(z)=F(z)*w(z) 5.30 The flterng of VQ codevector can be expressed n terms of matrx-vector multplcaton. Let v j be the j th codevector Let g be the th level n the gan codebook Let h(n) represent the mpulse response of the cascaded flter. When the ndces and j are fed to the cascaded flter H(z) the flter output can be expressed as x H ( n) g y j 5.31 Where H can be expressed as h(0) h(1) h(0) H h(2) h(1) h(0) 0 0 h(3) h(2) h(1) h(0) 0 h(4) h(3) h(2) h(1) h(0)
22 70 The code book search module searches for the best combnaton of the ndces and j whch mnmzes the mean square error ˆ j yj D x( n) x ( n) x( n) g H 5.32 Where xn ˆ( ) s the gan normalzed VQ target vector. Expandng the terms xn ( ) ( n) gves us ( ) ˆ( ) 2 ˆ T ( ) yj y D n x n g x n H g H Snce the terms xn ˆ( ) 2 and the value of σ 2 (n) are fxed durng the codebook search. Mnmzng D s equvalent of mnmzng ˆD Dˆ 2 g p ( n) y g E T 2 j j 5.34 Where p( n) H T xˆ ( n) 5.35 and Ej H y The value E j s the energy of the j th fltered shape codevector and does not depend on the VQ target vector xn ˆ( ). Note that the shape codevector v j and the matrx H only depends on the synthess flter and the weghtng flter and H s fxed over a perod of four speech vectors. Hence E j s also fxed over a perod of four speech vectors. When
23 71 these two flters are updated E j store the 128 possble energy terms and 128 correspond to the 128 shape codevectors. Ths arrangement reduces the codebook search complexty. To further reduce the computaton complexty the values can be per computed and stored n the two arrays. 2 b =2g and c =g for =0,1,2,..7.These two arrays are fxed snce g s fxed. Hence we can express ˆD as Dˆ b p c E j j 5.37 Where P j =P T (n)y j Note that once E j, b and c j tables are precomputed and stored. The value of the nner product term P j manly depends on j. Once these values are computed then ˆD can be easly determned as t s dependent on the prevous computed values of E j, b, c j and P j. Thus the codebook search procedure steps through the shape codebook and dentfes the best gan ndex for each shape codevector y j. There are several ways of fndng the best gan ndex for a gven shape codevector y j as mentoned below The easest way s to fnd eght dfferent values of ˆD correspondng to the eght possble values of and pck the ndex wth smallest ˆD. But ths method requres two multplcatons for each value of. A second way s to compute the optmal gan ĝ =P j /E j and then quantze the obtaned gan nto one of the eght dfferent levels n the 3-bt gan codebook. The best ndex s selected where the dfference between the computed gan ĝ and
24 72 gan level g s mnmal. But ths operaton requres dvson and s not preferred for DSP mplementaton. Ths approach s the modfed verson of the second approach and s effcent n DSP mplementaton. The optmal quantzaton gan ĝ s found by testng f P j < d E j where d s the mdpont adjacent gan between the gan levels g and g +1.Ths method avods the dvson operaton. Once the best code book ndces ' and j are found they are concatenated to form the output of the codebook search module. The Appendx B gves the 7-bt exctaton VQ shape codebook table. Operaton code book search module: Once the synthess flter and the perceptual weghtng flter are updated, the mpulse response vector calculator computes the mpulse response of the cascaded flter. To compute the mpulse response the memory of the cascaded flter s set to zero. The mpulse response vector that s computed wll be used n the codebook search for the followng four speech vectors untl the synthess flter and the perceptual flter are updated agan. Then the shape codevector convoluton module computes 128 vectors by convolvng the shape codevector wth the mpulse response. The convoluton s only performed for the frst fve samples. The energes of the resultng 128 vectors are computed and stored by the energy table calculator. The energy of vector s defned as the sum of the squared value of the each vector component. The computaton n the mpulse response vector calculator, shape codevector convoluton module and the energy table calculator block s done only once for every four speech vector and computaton n the
25 73 other blocks of codebook search module s done for each speech vector. The VQ target vector normalzaton module calculates the gan-normalzed VQ target vector xn ˆ( ), where xn ˆ( ) = x(n)/σ(n). The tme reversed convoluton module computes vector by reversng the order of the components of xn ˆ( ) and then convolvng the resultant vector wth the mpulse response vector. The convolved resultant vector component order s reversed to get the desred vector. The error calculator and the best codebook ndex selector work together to perform the effcent codebook search. Once the best codebook vector s transmtted by the encoder, the other addtonal task performed by the encoder s to prepare the encoder for the next followng speech vector. The preparaton s done n the followng steps 1. The best codebook s fed to the exctaton VQ codebook to extract the correspondng best codevector y(n). 2. The best codevector s scaled by the current exctaton gan σ(n) n the gan block. Ths results n the gan scaled vector e(n). 3. The e(n) s then passed through the synthess flter to obtan the current quantzed speech vector S q (n). 4. The quantzed speech vector S q (n) s fed to the backward synthess flter adapter, whch nturn updates the synthess flter coeffcents and perceptual weghtng flter coeffcents. 5. The backward vector gan adapter needs gan-scaled exctaton vector e(n) to update the coeffcents of the log-gan lnear predctor. 6. Before processng the next speech vector the memory updates of the synthess flter and perceptual weghtng flter s done. The memory update s done by
26 74 performng the zero-nput response computaton. Then the gan-scaled exctaton vector e(n) s passed through the zero memory synthess and perceptual weghtng flters. Snce e(n) s only fve samples long and hence the computaton tme requred s fve sample perod long. 7. The saved flter memory s added back to the zero nput response to get the zero state response of the synthess flter and perceptual weghtng flter. Ths resultant wll be used to compute the zero-nput response durng the encodng of the next speech vector. The encodng of the entre speech waveform s acheved by repeatng the above operatons. Practcally extra bts for synchronzng the transmtter and the recever are added along wth the 16kb of data. Sometme the synchronzng bts are added along wth the message bts by nsertng the synchronzng bts after every N speech vectors. By robbng one bt out of every N th transmtted codebook ndex a synchronzaton bt s nserted Explanaton of LD-CELP decoder: The block dagram of the LD-CELP post flter block dagram s as shown n the fgure 5.7 and ts functonal descrpton s as gven below Exctaton VQ codebook: The exctaton VQ codebook manly contans the shape and gan codebook dentcal to the LD-CELP encoder. It uses the best codebook ndex to extract the best code vector y(n) selected n the LD-CELP encoder. Gan scalng unt: Ths computes the scaled exctaton vector e(n) by multplyng each component of y(n) by the gan σ(n).
27 75 Backward vector gan adapter and Backward synthess flter adapter: The functonalty performed by these blocks s exactly smlar to that of encoder. Postflter: Ths flters the decoded speech to enhance the perceptual qualty of the speech. The postflter manly conssts of long -term postflter Short-term postflter Output gan scalng unt Sum of absolute value calculator A Scalng factor Calculator B Sum of absolute value Frst order low pass Decoded speech I/P Long -term postflter Short- term postflter Output gan scalng unt Post fltered speech Long-term post flter update nformaton short-term post flter update nformaton From post flter adapter Fg: 5.7 Post flter block dagram Long-term post flter: The long-term postflter s also called as ptch postflter. Ths s a comb flter wth the spectral peaks located at multples of the fundamental frequency of the speech to be
28 76 post fltered. The nverse of the fundamental frequency s called ptch perod. The ptch perod can be extracted from the decoded speech usng the ptch detector. If P s the fundamental ptch perod obtaned by the ptch detector, then t s the transfer functon can be wrtten as H1 z g1 bz p ( ) (1 ) 5.38 The coeffcents g l, b and ptch perod p are updated for every four speech vectors or one adaptaton cycle. One adaptaton cycle s also called as a frame. Synthess flter: The transfer functon of ths block s smlar to the synthess flter n the LD- CELP encoder for errorless transmsson. Ths block flters the scaled exctaton vector e(n) to produce the decoded speech vector S d (n). To avod the roundng off error t s preferable to duplcate the procedure done at the transmtter sde. The S d (n) s the sum of zero nput response and the zero-state response of the synthess flter. Short term post flter: Ths manly conssts of 10 th order pole-zero flter cascaded to the frst order all zero flter. The 10 th order pole zero flter attenuates the frequency component between formant peaks and the frst order all zero flter compensates for the spectral tlt n the frequency response of 10 th order pole-zero flter. Let a be the coeffcent of the 10 th order LPC predctor obtaned by the backward LPC analyss of the decoded speech and let k 1 be frst reflecton coeffcent obtaned by the LPC analyss. Both of these coeffcents can be obtaned as by-product of the 50 th order backward LPC analyss. The transfer functon of the short-term flter can be wrtten as
29 bz 1 Hs ( z) az 1 z Where b a (0.65) : 1,2,...,10 a a (0.75) : 1,2,...,10 µ = (0.15) k 1 The coeffcents a, b and µ are updated once a frame and updatng takes place at the frst vector of each frame. Once the decoded speech s passed through the long term and short-term flter the power level of the speech reduces hence t s necessary to mantan automatcally the same power level at the output of the post flter as that of ts nput. The sum of absolute value calculator operates vector by vector. Ths block takes the current decoded speech S d (n) as ts nput and calculates the sum of the absolute values of ts fve vector components. The next block s the absolute value calculator whch performs the same calculaton but on the output vector S f (n) of the short-term post flter. The scalng factor calculator dvdes the output of the absolute value calculator [block A] by the output of the absolute value calculator [block B]. Ths scalng factor s then fltered by the frst order low pass flter to get separate scalng factor for each of the fve components of S f (n). The output of the low pass flter s used by the output gan scalng unt to perform sample by sample scalng of the short-term post flter output. The scalng factor calculator generates one scalng factor for every vector hence has a star case effect on the sample by sample operaton. The low pass flters present n turn smoothens ths star case effect. The 1 khz lowpass flter used n the ptch lag extracton and encodng
30 78 module s a thrd-order pole-zero flter wth the coeffcents a and b and these coeffcent values are gven n the Appendx D To long-term postflter to short-term postflter Long-term post flter coeffcent calculator Ptch predctor tap calculator Short-term post flter coeffcent calculator Decoded speech 10 th order LPC nverse flter Ptch perod extracton module 10 th order LPC Frst reflecton Predctor coeffcents Coeffcent Fg: 5.8 Post flter adapter block schematc Post flter adapter Ths calculates and updates the coeffcents of the postflter once every frame. The explanatory block of postflter adapter s as shown n the fgure 5.8. Both 10 th order LPC nverse flter and the ptch predctor extracton module work together to extract the
31 79 ptch perod from the decoded speech. Let 10 th order LPC nverse flter has a transfer functon Az () and can be expressed as A ( z) a z 5.40 The coeffcents a are suppled by the Levnson-Durbn recurson module and these coeffcents are updated at the frst of each vector frame. Ths LPC nverse flter takes the decoded speech as nput and produces the LPC predcton resdual sequence d(k) as ts output. The sze of the ptch analyss wndow chosen s 100 samples and the range of the ptch perod may vary between 20 to 140 samples of the LPC predcton resdual. The ptch extracton module extracts the ptch perod once every frame hence the LPC nverse flter output vectors must be stored nto LPC resdual buffer. Once the values are stored n the resdual buffer the ptch extracton module works as follows: The last 20 samples of the LPC resdual buffer are low pass fltered at 1 khz and then down sampled by a factor of 4. Ths results n fve lowpass fltered and decmated LPC resdual samples. These are stored as last fve samples n the LPC resdual buffer. Besde these fve samples the other 55 samples are obtaned by shftng prevous frame of decmated LPC. The th correlaton of the decmated LPC resdual samples are computed usng the equaton below 25 ( ) d( n) d( n ) n In the above equaton can take any value n between 5 to 35 and the value of corresponds to ptch perod from 20 to 140 samples. Let p be the ptch perod of the pervous frame whch s extracted by the ptch perod extracton module. The ptch predctor tap calculates the optmal weght of the sngle-tap ptch predctor for the
32 80 decoded speech. Both the ptch predctor and the long-term postflter share a long buffer of decoded speech samples. Ths buffer contans the decoded speech samples of the current decoded speech. The long-term postflter uses ths buffer as a delay unt and the ptch predctor tap calculator uses ths as buffer to calculate ptch predctor tap β once the ptch perod extracton module extracts the ptch perod p. 0 k 99 0 k 99 s ( k) s ( k p) d d s ( k p) s ( k p) d d 5.42 Once the p and β are calculated the long-term postflter calculates the coeffcents b and g 1 usng the followng equatons 0 f 0.6 b 0.15 f f g b 5.44 As β value becomes closer to unty the speech waveform obtaned wll be more perodc. If β<0.6 corresponds to unvoced or transton regon of speech then the values of b=0, g 1 =1 and the transfer functon of a long-term post flter H 1 (z) wll be one..e. flterng operaton of the long-term postflter wll be dsabled. If the β les n the range of 0.6 to 1 then the long-term postflter wll be enabled and the degree of comb flterng wll be determned by the value of β. If the value β>1 then b s lmted to 0.15 to avod too much of comb flterng. The coeffcent g 1 whch s the scalng factor of long-term postflter ensures that voced regon gets amplfed over that of unvoced regon. Ths corresponds n makng some consonants sound unclear or too soft. The short-term
33 81 postflter coeffcent calculator calculates the short-term post flter coeffcents [34]. The updatng of dfferent adapters s shown n Appendx D. Output PCM format converson: Ths block converts the fve components of the decoded speech vector nto fve correspondng PCM samples. If the PCM sgnal s scaled at the transmtter sde then at the recever sde nverse scalng must be performed. 5.2 SUMMARY Ths chapter clearly explans about the LD-CELP speech coder. The functonalty of all the blocks n the LD-CELP encoder and decoder are clearly explaned. Ths chapter also explans how the processng delay s reduced n LD-CELP compared to CELP. In ths chapter the advantage of usng the hybrd wndow over the hammng wndow or recursve wndow s clearly explaned. Ths also gves the scope to further reduce the computaton load by reducng the order of the hybrd wndow.
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