PCM DM 1 PulseCode Modulation PCM n In

PCM & DM 1

Pulse-Code Modulation (PCM: ( n In PCM each sample of the signal is quantized to one of the amplitude levels, where B is the number of bits used to represent each sample. ¨ The n rate from the source is bps. The quantized waveform is modeled as : n q(n) represent the quantization error, Which we treat as an additive noise. 2

Pulse-Code Modulation (PCM: ( ¨ The quantization noise is characterize as a realization of a stationary random process q in which each of the random variables q(n) has uniform pdf. n Where the step size of the quantizer is 3

Pulse-Code Modulation (PCM: ( ¨ If : maximum amplitude of signal, ¨ The mean square value of the quantization error is : ¨ Measure in d. B, The mean square value of the noise is : 4

Pulse-Code Modulation (PCM: ( ¨ The quantization noise decreases by 6 d. B/bit. ¨ If the headroom factor is h, then The signal to noise (S/N) ratio is given by (Amax=1) n ¨ In d. B, this is 5

Pulse-Code Modulation (PCM: ( n Example : ¨ We require an S/N ratio of 60 d. B and that a headroom factor of 4 is acceptable. Then the required word length is : ¨ 60=10. 8 + 6 B – 20 ¨ If we sample at 8 KHZ, then PCM require 6

Pulse-Code Modulation (PCM: ( n A nonuniform quantizer characteristic is usually obtained by passing the signal through a nonlinear device that compress the signal amplitude, follow by a uniform quantizer. Compressor A/D D/A Expander Compander (Compressor-Expander) Compressor-Expande 7

Pulse-Code Modulation (PCM: ( n A logarithmic compressor employed in North American telecommunications systems has input-output magnitude characteristic of the form n is a parameter that is selected to give the desired compression characteristic. 8

Pulse-Code Modulation (PCM: ( n The logarithmic compressor used in European telecommunications system is called A-law and is defined as 9

DPCM: n A Sampled sequence u(m), m=0 to m=n-1. n Let be the value of the reproduced (decoded) sequence. 10

DPCM: n At m=n, when u(n) arrives, a quantify , an estimate of u(n), is predicted from the previously decoded samples i. e. , ¨ n ”prediction rule” Prediction error: 11

DPCM: n If is the quantized value of e(n), then the reproduced value of u(n) is: n Note: 12

DPCM CODEC: Σ Communication Channel Quantizer Predictor Coder Σ Σ Predictor Decoder 13

DPCM: n Remarks: ¨ The pointwise coding error in the input sequence is exactly equal to q(n), the quantization error in e(n). ¨ With a reasonable predictor the mean sequare value of the differential signal e(n) is much smaller than that of u(n). 14

DPCM: n Conclusion: ¨ For the same mean square quantization error, e(n) requires fewer quantization bits than u(n). ¨ The number of bits required for transmission has been reduced while the quantization error is kept the same. 15

Delta Modulation : (DM( n Predictor : one-step delay function n Quantizer : 1 -bit quantizer 16

Delta Modulation : (DM( n Primary Limitation of DM ¨ Slope overload : large jump region n Max. slope = (step size)X)sampling freq(. ¨ Granularity ¨ Instability Noise : almost constant region to channel noise 17

DM: Unit Delay Integrator Coder Unit Delay Decoder 18

DM: Step size effect: Step Size (i) slope overload )sampling frequency) ( ii) granular Noise 19

Adaptive DM: Adaptive Function Unit Delay q. This adaptive approach simultaneously minimizes the effects of both slope overload and granular noise 20

Vector Quantization (VQ) 21

Vector Quantization: n Quantization is the process of approximating continuous amplitude signals by discrete symbols. Partitioning of two-dimensional Space into 16 cells. n 22

Vector Quantization: The LBG algorithm first computes a 1 vector codebook, then uses a splitting algorithm on the codeword to obtain the initial 2 -vector codebook, and continue the splitting process until the desired M-vector codebook is obtained. n This algorithm is known as the LBG algorithm proposed by Linde, Buzo and Gray. n 23

Vector Quantization: n The LBG Algorithm : ¨ Step 1: Set M (number of partitions or cells)=1. Find the centroid of all the training data. ¨ Step 2: Split M into 2 M partitions by splitting each current codeword by finding two points that are far apart in each partition using a heuristic method, and use these two points as the new centroids for the new 2 M codebook. Now set M=2 M. ¨ Step 3: Now use a iterative algorithm to reach the best set of centroids for the new codebook. ¨ Step 4: if M equals the VQ codebook size require, STOP; otherwise go to Step 2. 24