ECE 4371, Fall, 2009PCMSlide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Coded Excited Linear Prediction (CELP)Time-Division MultiplexingDS1/T1/E1SynchronizationSlide 22T Carrier SystemFiber CommunicationSlide 25Slide 26Slide 27Slide 28Slide 29Slide 30ECE 4371, Fall, 2009Zhu HanDepartment of Electrical and Computer EngineeringClass 10Sep. 24th, 20090000111111101101110010111010100100010010001101000101011001110000 0110 0111 0011 1100 1001 1011Numbers passed from ADC to computer to represent analogue voltageResolution=1 part in 2nPCMPCM(Channel noise, quantization noise) Noise consideration in PCM systemsNoise consideration in PCM systemsEncode information in terms of signal transition; a transition is used to designate Symbol 0 Regeneration (reamplification, retiming, reshaping ) 3dB performance loss, easier decoderDifferential EncodingConsider a finite-duration impulse response (FIR) discrete-time filter which consists of three blocks :1. Set of p ( p: prediction order) unit-delay elements (z-1) 2. Set of multipliers with coefficients w1,w2,…wp3. Set of adders (  ) Linear Prediction Coding (LPC)                  (3.62) 2have we(3.61) and (3.60) (3.59) From minimize to,,, Find(3.61) error) square (mean be eperformanc ofindex Let the(3.60) ˆ iserror prediction The (3.59) )(ˆ is )input theof preditionlinear (Theoutput filter The1 1122121  pjpkkjpkkppkkknxjnxEwwknxnxEwnx EJJwwwneEJ nxnxneknxwnx                       equations Hopf-Wiener called are (3.64)(3.64) 21 , 022 (3.63) 2 as simplify may We)( ationautocorrel The )( 0)]][[( mean zero withprocess stationary is )( Assume111 1122222,p,,kkRkRjkRwjkRwkRwJjkRwwkRwJJknxnxEkRkTRnxEnxEnxEnxEtXpjXXXjpjXjXkpjpkXkjpkXkXXsXX                          2min1 120212112min210 101 than less always is 0, (3.67) 2yields (3.63) into (3.64) ngSubstituti,..., 1, 0 0...21..2...011...10 ]][],...,2[ ],1[[ ,...,, where (3.66) exists if , asXXXTXXXTXXTXXpkXkXpkXkpkXkXXXXXXXXXXXXXXTXXXXTpXXXJkRwkRwkRwJpRRRRpRpRpRRRpRRRpRRRwwwrRrrRrwrRrwrRwRQMFor convenience, we may rewrite the Wiener-Hopf equationsThe filter coefficients are uniquely determined by       on.presentati of econveniencfor is 21 andparameter size-step a is where(3.69) 21 ,211 1 updateThen .n iteration at value thedenotes (3.68) ...21 , ectorgradient v theDefinedescentsteepest of method theusingiteration Do 2. valuesinitialany starting ,,...,2,1 , Compute 1. sense follow in the adaptive ispredictor The ,p,,kgnwnwnwnw,p,,kwJgpkwkkkkkkkkK  kRXLinear adaptive prediction (If for varying k is not available)                                                 algorithm square-mean-lease called are equations above The(3.73) (3.60)(3.59)by ˆ where )72.3( ,...,2,1 , ˆ ˆˆ1ˆ)71.3( ,...,2,1 , 22ˆn)expectatio the(ignorek]]-E[x[n]x[nfor use wecomputing hesimplify t To(3.70) ,...,2,1 , 22 22 11111jnxnwnxnepkneknxnwjnxnwnxknxnwnwpkknxjnxnwknxnxngknxnxpkknxjnxEwknxnxEjkRwkRwJgpjjkpjjkkpjjpjjPjXjXkkkSubstituting (3.71) into (3.69)Differentiating (3.63), we haveBlock diagram illustrating the linear adaptive prediction process.Reduce the sampling rateDifferential Pulse-Code Modulation (DPCM)Usually PCM has the sampling rate higher than the Nyquist rate.The encode signal contains redundant information. DPCM can efficiently remove this redundancy. 32 Kbps for PCM QualityInput signal to the quantizer is defined by:                          (3.78) (3.77) ˆisinput filter prediction Theerror. onquantizati is where(3.75) isoutput quantizer The value.predictiona is ˆ(3.74) ˆnqnmnmnmnqnenmnmnqnqnenenmnmnmneqqqFrom (3.74)Differential Pulse-Code Modulation (DPCM)    ) (minimize G maximize filter to prediction aDesign G Gain, Processing )SNR( is ratio noiseon quantizati-to-signal theanderror sprediction theof variance theis where)SNR( ))(((SNR) and 0)]][[( of variancesare and where (SNR) is system DPCM theof (SNR) The222222 2222o2222ooEpEMpQEQEQpQEEMQMQMG nqnmEnmProcessing GainNeed for coding speech at low bit rates , we have two aims in mind: 1. Remove redundancies from the speech signal as far as possible. 2. Assign the available bits in a perceptually efficient manner. Adaptive quantization with backward estimation (AQB).Adaptive Differential Pulse-Code Modulation (ADPCM)ADPCM Adaptive prediction with backward estimation (APB).8-16 kbps with the same quality of PCMCoded Excited Linear Prediction (CELP)Coded Excited Linear Prediction (CELP)Currently the most widely used speech coding algorithmCode booksVector