Linear predictive coding

Transcription

1 Linear predictive coding Thi method combine linear proceing with calar quantization. The main idea of the method i to predict the value of the current ample by a linear combination of previou already recontructed ample and then to quantize the difference between the actual value and the predicted value. Linear prediction coefficient are weighting coefficient ued in linear combination. A imple predictive quantizer or differential pule-coded modulator i hown in Fig If the predictor i imply the lat ample and the quantizer ha only one bit, the ytem become a delta-modulator. It i hown in Fig. 5..

2 Differential pule-coded modulator x( nt ) e( nt ) QUANTIZER q( nt ) xˆ ( nt ) d( nt x ( nt R ) ) DEQUANTIZER LINEAR PREDICTOR

3 Delta-modulator x ( nt ) x ( nt ) xˆ ( nt ) COMPARATOR x ( nt ) xˆ ( nt ) 1 0 Staircae function former

4 Linear predictive coding The main feature of the quantizer hown in Fig 5.1, 5. i that they exploit not all advantage of predictive coding. Prediction coefficient ued in thee cheme are not optimal Prediction i baed on pat recontructed ample and not true ample Uually coefficient of prediction are choen by uing ome empirical rule and are not tranmitted For example quantizer in Fig.5.1 intead of actual value of error e ue recontructed value d and intead of true ample value x their etimate x obtained via d. R

5 Linear predictive coding The mot advanced quantizer of linear predictive type repreent a bai of the o-called Code Excited Linear Predictive (CELP) coder. It ue the optimal et of coefficient or in other word linear prediction coefficient of thi quantizer are determined by minimizing the MSE between the current ample and it predicted value. It i baed on the original pat ample Uing the true ample for prediction require the looking-ahead procedure in the coder. The predictor coefficient are tranmitted

6 Linear predictive coding Aume that quantizer coefficient are optimized for each ample and that the original pat ample are ued for prediction. Let x( T ), x(t ),... be a equence of ample at the quantizer input. Then each ample x( nt ) i predicted by the previou ample according to the formula ˆ xˆ( nt ) m k 1 a k x( nt kt where x( nt ) i the predicted value, k are prediction coefficient, m denote the order of prediction. The prediction error i a e( nt ) x( nt ) xˆ( nt ). ), (5.1)

7 Linear predictive coding Prediction coefficient are determined by minimizing the um of quared error over a given interval n E e ( nt ) (5.) 1 nn Inerting (5.1) into (5.) we obtain 0 n 1 E ( x( nt ) a1 x( nt T )... a x( nt mt )) nn0 n m n1 x( nt ) nn j1 nn 1 0 a j 0 x( nt m ) x( nt jt ) m m j1 k1 a j a k n 1 nn 0 x( nt jt ) x( nt kt ). (5.3)

8 Linear predictive coding Differentiating (5.3) over ak, k 1,,..., m yield E / a k n 1 nn 0 x( nt ) x( nt kt Thu we obtain a ytem of unknown quantitie ) m a a,..., 1, m a j j1 a n 1 nn 0 x( nt kt ) x( nt linear equation with m m jt ) 0 m j1 a j c jk c ok, k 1,,..., m (5.4) where c jk c kj n 1 nn 0 x( nt jt ) x( nt kt ). (5.5) The ytem (5.4) i called the Yule-Walker equation.

9 If a,..., Linear predictive coding 1, a am are olution of (5.4) then we can find the minimal achievable prediction error. Inert (5.5) into (5.3). We obtain that m m m E c a c a a c. (5.6) Uing (5.3) we reduce (5.6) to 00 k 0k k k1 k 1 j1 m E c 00 k 1 a k c 0k j jk

10 Interpretation of the Yule-Walker equation like a digital filter Eq. (5.1) decribe the th order predictor with tranfer function equal to m ) ( ) ( ˆ ) ( z X z X z P m k k a k z 1. z-tranform for the prediction error i m k k k z z X a z X z E 1. ) ( ) ( ) ( The prediction error i an output ignal of the dicrete-time filter with tranfer function m k k a k z z X z E z A 1. 1 ) ( ) ( ) ( The problem of finding the optimal et of prediction coefficient = problem of contructing th order FIR filter. m

11 Interpretation of the Yule-Walker equation like a digital filter Another name of the linear prediction (5.1) i the autoregreive model of ignal x( nt ). It i aumed that the ignal x( nt ) can be obtained a the output of the autoregreive filter with tranfer function 1 H ( z), m 1 a z k k k 1 that i can be obtained a the output of the filter which i invere with repect to the prediction filter. Thi filter i a dicrete-time IIR filter.

12 Method of finding coefficient c, i 0,1,..., m, j 1,,..., m ij In order to olve the Yule-Walker eq. (5.4) it i neceary firt to evaluate value c, i 0,1,..., m, j 1,,..., m There are two approache to etimating thee value: ij The autocorrelation method and The complexity of olving (5.4) i proportional to m the covariance method. The complexity of olving (5.4) i proportional to 3 m

13 c ij The value c We et ij c c ij ji Autocorrelation method are computed a i 1 ni 0 x( nt it ) x( nt jt ). (5.7) i0,i1 and x( nt ) 0 if n 0, n N, where N i called the interval of analyi. In thi cae we can implify (5.7) N 1 n0 x( nt it ) x( nt jt ) N 1 i j n0 x( nt ) x( nt i Normalized by N they coincide with etimate of entrie of covariance matrix for x nt ) Rˆ( i j ) c ij ( / N 1/ N N 1 i j n0 x( nt ) x( nt i jt jt ). ). (5.8)

14 Autocorrelation method

15 Autocorrelation method The Yule-Walker equation for autocorrelation method have the form m a Rˆ ( i j ) Rˆ( j), j 1,,..., m. (5.9) i1 i Eq.(5.9) can be given by matrix equation a R where a a, a,..., a ), ( 1 m b, b ( Rˆ(1), Rˆ(),..., Rˆ( m)), Rˆ(0) Rˆ(1)... Rˆ( m 1) Rˆ(1) Rˆ(0)... Rˆ( m ) R R ˆ( m 1) Rˆ( m )... Rˆ(0)

16 Autocorrelation method It i aid that (5.9) relate the parameter of the autoregreive model of m th order with the autocorrelation equence. R Matrix propertie. of the autocorrelation method ha two important It i ymmetric, that i Rˆ ( i, j) Rˆ( j, i) It ha Toeplitz property, that i Rˆ ( i, j) Rˆ( i j ). The Toeplitz property of R make it poible to reduce the computational complexity of olving (5.4). The fat Levinon-Durbin recurive algorithm require only operation. m

17 We chooe 0 0 Covariance method i i1 N1 and and ignal i not contrained in time. In thi cae we have Set c ij c k ij N i 1 k i N 1 n0 n i x( kt x( nt it ) x( nt jt x( nt ) ). (5.10) then (5.10) can be rewritten a ) x( kt ( i j) T ), i 1,..., m, j 0,... m. (5.11) (5.11) reemble (5.8) but it ha other range of definition for k. It ue ignal value out of range 0 k N 1, The method lead to the cro-correlation function between two imilar but not exactly the ame finite egment of x ( kt ).

18 Rˆ( i, j) c Covariance method ij / N 1/ N N 1 n0 x(( n i) T ) x(( n j) T The Yule-Walker equation for the covariation method are m a Rˆ( i, j) Rˆ(0, j), j 1,,..., m. (5.1) i1 i Eq. (5.1) can be given by the matrix equation a P where a a, a,..., a ), c ( 1 m. c, Rˆ(1,1) Rˆ(1,)... Rˆ(1, m) Rˆ(,1) Rˆ(,)... Rˆ(, m) P R ˆ( m,1) Rˆ( m,)... Rˆ( m, m) ( Rˆ(0,1), Rˆ(0,),..., Rˆ(0, m)), ).

19 Covariance method R Unlike the matrix of autocorrelation method the matrix P i ymmetric ( Rˆ ( i, j) Rˆ( j, i) ) but it i not Toeplitz. Since computational complexity of olving an arbitrary ytem of linear equation of order m i equal to m 3 then in thi cae to olve (5.1) it i neceary m operation. 3

20 Algorithm for the olution of the Yule-Walker equation The computational complexity of olving the Yule- Walker equation depend on the method of evaluating value c ij. Aume that cij are found by the autocorrelation method. In thi cae the Yule-Walker equation ha the form (5.9) and the matrix R i ymmetric and the Toeplitz matrix. Thee propertie make it poible to find the olution of (5.9) by fat method requiring operation. There are a few method of thi type: the Levinon- Durbin algorithm, the Euclidean algorithm and the Berlekamp-Maey algorithm. m

21 The Levinon-Durbin algorithm It wa uggeted by Levinon in 1948 and then wa improved by Durbin in Notice that thi algorithm work efficiently if matrix of coefficient R i imultaneouly ymmetric and Toeplitz. The Berlekamp- Maey and the Euclidean algorithm do not require the matrix of coefficient to be ymmetric. We equentially olve equation (5.9) of order l 1,..., m. ( l) ( l) ( l) ( l) Let a ( a1, a,..., al ) denote the olution for the (l ) ytem of the l th order. Given a we find the olution for the ( l 1) th order. At each tep of the algorithm we evaluate the prediction error E of the l th order ytem. l

22 The Levinon-Durbin algorithm (0) Initialization: l 0, E Rˆ(0), a 0. 0 Recurrent procedure: For l 1,..., a ( l) l m compute ( Rˆ( l) l 1 i1 a ( l1) i Rˆ( l i)) / E l1, ( l) ( l1) ( l) ( l1) a a a a, 1 j l 1, j j l l j E l E l 1 (1 ( a ( l) l ) ). When l m we obtain the olution a ( a, a,..., a ) a, E E ( m) 1 m m.

23 (1) m 1 R(0) a 1 R(1), (1) a R(1) / 1 R (0), Example k1 R(1) / R(0), (1) a1 R(1) / R(0), E R(0) a (1) 1 1 R (1) E ( R (0) R (1)) / () 1 R (0). m R(0) a R(1) a1 () 1 () R(1) a R(0) a () () R(1) R(), a R(1) (1 a R(0) () () 1 ) a (1) 1 a () a (1) 1 a () R() R(0) R(1) a a (1) 1 (1) 1 R(1) R() R(1) a E 1 (1) 1

24 Example () a1 ( R(1) R(0) R(1) R()) /( R (0) R () a ( R(0) R() R(1) ) /( R (0) R () (1)) (1)). E E1(1 ( a () ) ) E R(0) a R(1) a R() ( R(0) a R(1))(1 ( () () (1) () 1 1 a ) ) E (1 ( () 1 a ) ).

25 Linear prediction analyi-by-ynthei (LPAS) coder The mot popular cla of peech coder for bit rate between 4.8 and 16 kb/ are model-baed coder that ue an LPAS method. A linear prediction model of peech production (adaptive linear prediction filter) i excited by an appropriate excitation ignal in order to model the ignal over time. The parameter of both the filter and the excitation are etimated and updated at regular time interval (frame). The compreed peech file contain thee model parameter etimated for each frame. Each ound correpond to a et of filter coefficient. Rather often thi filter i alo repreented by the pole of it frequency repone called formant frequencie or formant.

26 Model of peech generation Pitch period Generator of periodical impule train Random noie generator Tone/noie u(n) g Original peech Adaptive linear prediction filter Syntheized peech

27 LPAS coder The filter excitation depend on the type of the ound: voiced, unvoiced, vowel, hiing or naal. The voiced ound are generated by ocillation of vocal cord and repreent a quaiperiodical impule train. The unvoiced ignal are generated by noie-like ignal. The period of vocal cord ocillation i called pitch period. CELP coder i Code Excited Linear Predictive coder. It i a bai of all LPAS coder (G.79, G.73.1, G.78, IS-54, IS- 96, RPE-LTP(GSM), FS-1016(CELP)).

28 CELP Standard 51 Stochatic codebook i g Linear Prediction analyi Input peech (8kHz ampling) LSP E 56 i a g a Interpolate by 4 LP filter - PW filter Minimize PE i g i a g a N C O D E Adaptive codebook updating Sync. bit R

29 Main idea: CELP Standard A 10 th order LP filter i ued to model the peech ignal hort term pectrum, or formant tructure. Long-term ignal periodicity or pitch i modeled by an adaptive codebook VQ. The reidual from the hort-term LP and pitch VQ i vector quantized uing a fixed tochatic codebook. The optimal caled excitation vector from the adaptive and tochatic codebook are elected by minimizing a timevarying, perceptually weighted ditorted meaure that improve ubjective peech quality by exploiting making propertie of human hearing.

30 CELP Standard CELP ue input ignal at ampling rate 8 khz and 30 m (40 ample) frame ize with 4 ubframe of ize 7.5 m(60 ample.) Short-term prediction It i performed once per frame by open-loop analyi. We contruct 10 th order prediction filter uing the autocorrelation method and the Levinon-Durbin procedure. The LP filter i repreented by it linear pectral pair (LPS) which are function of the filter formant. The 10 LSP are coded uing 34-bit nonuniform calar quantization. Becaue the LSP are tranmitted once per frame, but are needed for each ubframe, they are linearly interpolated to form an intermediate et for each of the four ubframe.

31 CELP

32 CELP

33 For the firt frame we obtain : CELP Coefficient of the Yule-Walker equation (m=10) are: 1.0, 0.75, 0.17, -0.38, -0.65, -0.59, -0.35,-0.08, 0.17, 0.39, R( 0) The prediction filter coefficient are: 1.989, 1.734, 0.41, 0.096, 0.18, , , 0.303, 0.131, The prediction error i :

34 CELP x

35 Linear pectral parameter Let H (z) be the tranfer function of the invere filter, that i H ( z) 1/ A( z), where A(z) i the prediction filter. Then the frequencie i, i 1,..., m which correpond to the pole of function H (z) or zero of A(z), are called formant frequencie or formant. LSP are function of formant frequencie. They can be found uing the algorithm hown in Fig.10.1

36 A() 6 Amplitude function of the prediction filter

37 Amplitude function of the invere filter H()

38 Contruct auxiliary polynomial P( z), Q( z) Contruct polynomial P * Reducing degree of by 1 ( z), Q * ( z) of degree m/ P( z), Q( z) LSP A( z) m A() z P( z) 1 ( A() A(1)) z (z) 1 ( A(1) A()) z 1 A(1) z 1 1 ( A() A(1)) z 1 ( A(1) A()) z z z Q 3 PL( z) P( z) /( z QL( z) Q( z) /( z 1 1 1) 1 ( A(1) A() 1) z 1) 1 ( A(1) A() 1) z * P ( z) ( A() A(1) 1) / z * Q ( z) ( A(1) A() 1) / z z z 3 Solve the equation * * P ( z) 0, Q ( z) 0 1 z p ( A() A(1) 1) / 1 ( A(1) A() 1) / z q Find pi arcco( zpi ) qi arcco( zqi ), i 1,... m / p arcco( z q arcco( z 1 p 1 q ) )

39 LSP LSP Bit Output Level (Hz) ,170,5,50,80,340,40, ,35,65,95,35,360,400,440, 480,50,560,610,670,740,810, ,460,500,540,585,640,705,775,850,950, 1050,1150,150,1350,1450, ,660,70,795,880,970,1080,1170, 170,1370,1470,1570,1670,1770, 1870, ,1050,1130,110,185,1350,1430,1510,1590, 1670, 1750, 1850, 1950, 050, 150, , 1570, 1690, 1830, 000, 00, 400, , 1880, 1960, 100,300, 480, 700, , 370, 3350, 340, 3490, 3590, 3710, 3830

40 CELP Long-term ignal periodicity i modeled by an adaptive codebook VQ. The adaptive codebook earch i performed by cloed-loop analyi uing a modified minimum quared prediction error (MPSE) criterion of the perceptually weighted error ignal. The adaptive codebook contain 56 codeword. Each codeword i contructed by the previou excitation ignal of length 60 ample delayed by 0 M 147 ample. For delay le than the ubframe length (60 ample) the codeword contain the initial M ample of the previou excitation vector. To complete the codeword to 60 element, the hort vector i replicated by periodic extenion.

41 Adaptive codebook Index Delay Adaptive CB ample number , -146, -145,, - 89, , -145, -144,, - 88, , -144, -143,, - 87, , -60, -59,, -, ,,-,-1,,-,- 1,, ,, -1, -0, -1, - 0,, -1

42 Adaptive codebook

43 Adaptive codebook To find the bet excitation in the adaptive codebook the 1t order linear prediction i ued. Let be the original peech vector and ai be a filtered codeword ci from the adaptive codebook then we earch for min i g a g a a i min i g (, a ) g a, where i a prediction coefficient or the adaptive codebook gain. By taking derivative with repect to g a and etting it to zero we find the optimal gain: (, ai) g a a (10.) a i i a i (10.1) Inerting (10.) into (10.1) we obtain (, ai) (, ai) (, ai mini g a ai mini min i a a a ) i i (10.3) i

44 Adaptive codebook Minimizing (10.3) over i i equivalent to maximizing the lat term in (10.3) ince the firt term i independent of the codeword a i. Thu the adaptive codebook earch procedure find codeword c i which maximize the o-called match function m i m i (, a a The adaptive codebook index ia and gain a are tranmitted four time per frame (every 7.5 m). The gain i coded between 1 and + uing nonuniform, calar, 5 bit quantization. i ) i g

45 Adaptive codebook Gain encoding level

46 Stochatic codebook The tochatic codebook (SC) contain 51 codeword. The pecial form of SC repreent ternary quantized (-1,0,+1) Gauian equence of length 60. The tochatic codebook earch target i the original peech vector minu the filtered adaptive codebook excitation, that i, u g a The SC earch i performed by cloed-loop analyi uing conventional MSPE criterion. We find uch a codeword x i which maximize the following match function ( u, y i ), y where i a opt y i the filtered codeword. i x i

47 Stochatic codebook The tochatic codebook index and gain are tranmitted four time per frame. The gain (poitive and negative) i coded uing 5-bit nonuniform calar quantization. The weighted um of the found optimal codeword from the adaptive codebook and the optimal codeword from the tochatic codebook are ued to update the adaptive codebook. It mean that 60 the mot ditant pat ample are removed from the adaptive codebook, all codeword are hifted and the following new 60 ample are placed a the firt c i a g a x i g

48 Stochatic codebook Stochatic codebook gain encoding level

49 CELP The total number of bit per frame can be computed a 4( b b b b ) b 4( ) 34 14, g i b g, g a b b, i a LSP where i and g are number of bit for index a ia and gain of the tochatic and adaptive codebook, repectively, b LSP i the number of bit for linear pectral pair. Taking into account that a frame duration i 30 m we obtain that the bit rate of the CELP coder i equal to R b b/. Adding bit for ynchronization and correcting error we get that bit rate i equal to 4800 b/.

50 CELP The critical point of the tandard i computational complexity of two codebook earche. The number of multiplication for adaptive codebook earch can be etimated a ( ) The tochatic codebook earch require multiplication. ( )

51 Speech coding for multimedia application The mot important attribute of peech coding are: Bit rate. From.4 kb/ for ecure telephony to 64 kb/ for network application. Delay. For network application delay below 150m i required. For multimedia torage application the coder can have unlimited delay. Complexity. Coder can be implemented on PC or on DSP chip. Meaure of complexity for a DSP or a CPU are different. Alo complexity depend on DSP architecture. It i uually expreed in MIPS. Quality. For ecure telephony quality i ynonymou with intelligibility. For network application the goal i to preerve naturalne and ubjective quality.

52 Standardization International Telecommunication Union (ITU) International Standard Organization (ISO) Telecommunication Indutry Aociation(TIA),NA R&D Center for Radio ytem (RCR),Japan

53 Standard Bit rate Frame ize / look-ahead Complexity ITU tandard G.711 PCM 64 kb/ 0/ MIPS G.76, G.77 ADPCM 16, 4, 3, 40 kb/ 0.15 m/0 MIPS G.7 Wideband coder 48, 56, 64 kb/ 0.15/1.5 m 5 MIPS G.78 LD-CELP 16 kb/ 0.65 m/0 30 MIPS G.79 CS-ACELP 8 kb/ 10/5 m 0 MIPS G.73.1 MPC-MLQ 5.3 & 6.4 kb/ 30/7.5 m 16 MIPS G.79 CS-ACELP annex A 8 kb/ 10/5 m 11 MIPS Cellular tandard RPE-LTP(GSM) 13 kb/ 0 m/0 5 MIPS (TIA) IS-54 VSELP 7.95 kb/ 0/5 m 15 MIPS PDC VSELP( RCR) 6.7 kb/ 0/5 m 15 MIPS IS-96 QCELP (TIA) 8.5/4//0.8 kb/ 0/5 m 15 MIPS PDC PSI-CELP (RCR) 3.45 kb/ 40/10 m 40 MIPS U.S. ecure telephony tandard FS-1015 LPC-10E.4 kb/.5/90 m 0 MIPS FS-1016 CELP 4.8 kb/ 30/30 m 0 MIPS MELP.4 kb/.5/0 m 40 MIPS

54 Hitory of peech coding 40 PCM wa invented and intenively developed in delta modulation and differential PCM were propoed 1957 law encoding wa propoed (tandardied for telephone network in 197 (G.711)) 1974 ADPCM wa developed (1976 tandard G.76 and G.77) 1984 CELP coder wa propoed (majority of coding tandard for peech coding today ue a variation of CELP) 1995 MELP coder wa invented

55 Subjective quality of peech coder

56 Speech coder. Demo. Original file 8kHz, 16 bit, file ize i byte A-law 8 khz, 8 bit, file ize i 3684 byte ADPCM, 8 khz, 4 bit, file ize i byte GSM, file ize i 7540 byte CELP-like coder, file ize i 4896 byte MELP-like coder, file ize 90 byte MELP-like coder, file ize 690 byte MELP-like coder, file ize 460 byte

57 Direct ample-by-ample quantization: Standard G.711 The G.711 PCM coder i deigned for telephone bandwidth peech ignal. The input ignal i peech ignal ampled with rate 8 khz. The coder doe direct ample-by-ample quantization. Intead of uniform quantization one form of nonuniform quantization known a companding i ued. The name of the method i derived from the word compreing-expanding. Firt the original ignal i compreed uing a memoryle nonlinear device. The compreed ignal i then uniformly quantized. The decoded waveform mut be expanded uing a nonlinear function which i the invere of that ued in compreion.

58 Compreion amplifier F(x) Standard G.711 Uniform quantizer Uniform dequantizer Expanion amplifier F 1 ( x)

59 Standard G.711 Companding i equivalent to quantizing with tep that tart out mall and get larger for higher ignal level. There are different tandard for companding. North America and Japan have adopted a tandard compreion curve known a a -law companding. Europe ha adopted a different, but imilar, tandard known a A-law companding. The -law compreion formula i F( ) F max ln 1 / gn( ) ln 1 max, where i the input ample value. G.711 ue 55.

60 Implementation of G.711

61 55 Implementation of G.711 The curve i approximated by a piecewie linear curve. When uing thi law in network the uppreion of the all zero character ignal i required. The poitive portion of the curve i approximated by 8 traight line element. We divide the poitive output region into 8 equal egment. The input region i divided into 8 correponding nonequal egment. To identify which egment the ample lie we pend 3 bit. The value of ample in each egment i quantized to 4 bit number. 1 bit how the polarity of the ample. In total we pend bit for each ample.

62 Example In order to quantize the value 66 we pend 1 bit for ign, The number of the egment i 010, The quantization level i 0000 (value 65,66,67,68 are quantized to 33). At the decoder uing the codeword we recontruct the approximating value (64+68)/=66. The ame approximating value will be recontructed intead of value 65,66,67,68. Each egment of the input axi i twice a wide a the egment to it left. The value 19,130,131,13,133,134,135,136 are quantized to the value 49. The reolution of each next egment i twice a bad a of the previou one.

63 ADPCM coder: Standard G.76, G.77 Coder of thi type are baed on linear prediction method. The main feature of thee coder i that they ue nonoptimal prediction coefficient and prediction i baed on pat recontructed ample. Thee coder provide rather low delay and have low computational complexity a well. Delta-modulation i a imple technique for reducing the dynamic range of the number to be coded. Intead of ending each ample value, we end the difference between ample and a value of a taircae approximation function. The taircae approximation can only either increae or decreae by tep at each ample point.

64 Delta-modulation

65 Granular noie

66 Slope overload

67 The choice of tep ize Delta-modulation and ampling rate i important. If tep are too mall we obtain a lope overload condition where the taircae cannot trace fat change in the input ignal. If the tep are too large, coniderable overhoot will occur during period when the ignal i changing lowly. In that cae we have ignificant quantization noie, known a granular noie. Adaptive delta-modulation i a cheme which permit adjutment of the tep ize depending upon the characteritic of the input ignal.

68 Adaptive delta-modulation The idea of tep ize adaptation i the following: If output bit tream contain almot equal number of 1 and 0 we aume that the taircae i ocillating about lowly varying analog ignal and reduce the tep ize. An exce of either 1 or 0 within an output bit tream indicate that taircae i trying to catch up with the function. In uch cae we increae the tep ize. Uually delta-modulator require ampling rate greater than the Nyquit rate. They provide compreion ratio -3 time.

69 G.76, G.77 The peech coder G.76 and G.77 are adaptive differential pule-coded modulation (ADPCM) coder for telephone bandwidth peech. The input ignal i 64 kb/ PCM peech ignal (ampling rate 8 khz and each ample i 8 bit integer number). The format converion block convert the input ignal from A-law or -law PCM to a uniform PCM ignal The difference d( n) xu ( n) x p ( n), here x p (n) i the predicted ignal, i quantized. A 3-, 16-, 8- or 4 level nonuniform quantizer i ued for operating at 40, 3, 4 or 16 kb/, repectively. Prior to quantization d(n) i converted and caled l( n) log d( n) y( n), where y(n) computed by the cale factor adaptation block. x(n) (n). x u i

70 G76,G77 x(n) Input PCM format converion x u (n) d(n) Adaptive quantizer q(n) y(n) x p (n) x p (n) Adaptive predictor d q (n) Invere adaptive quantizer Quantizer cale factor adaptation x r (n)

71 l(n) G.76, G77 The value i then calar quantized with a given quantization rate. For bit rate 16 kb/ l(n) i quantized with R 1 bit/ample and one more bit i ued to pecify the ign. Two quantization interval are: (,.04) and (.04, ). They contain the approximating value 0.91 and.85, repectively. A linear prediction i baed on the two previou ample of the recontructed ignal x and the ix r ( n) xp( n) dq( n) previou ample of the recontructed difference (n) : x p ( n) i1 e( n) a i 6 i1 ( n b i 1) x ( n r ( n 1) d q i) ( n e( n), i). d q

72 G.76, G.77 The predictor coefficient a well a the cale factor are updated on ample-by-ample bai in a backward adaptive fahion. For the econd order predictor : a ( n) (1 ) a ( n 1) (3 )gn( p( n))gn( p( n gn( p( n))gn( p( n )) f a ( n 1) gn( p( n))gn( p( n 1)), 7 7 a( n) (1 ) a( n 1) 1 For the ixth order predictor : p( n) dq( n) e( n) 1)) b i ( n) (1 8 ) b i ( n 1) 7 gn( d q ( n))gn( d q ( n i)), i 1,,...,6.