Differential PCM Systems

Matched differential PCM systems are analyzed for stationary first order Gauss Markov process inputs. The computational procedure yields convergent solutions for the variance and the probability density function of the point-wise error for all sampling intervals. Time average error between the input signalX(t)and a time continuous estimateX≈̂(t)is computed and it is used as the basis for finding the optimum number of quantizer levels and hence, the optimum sampling interval for a given bit rate. For time average error values of practical interest, 4 level DPCM is superior; the time average error exceeds the appropriate rate-distortion bound by only 2.5 dB. A comparison with a good PCM system shows that 4 level DPCM is superior for large bit rates and the difference increases with bit rate. The same DPCM systems are analyzed under the assumption that the prediction error is Gaussian and the results are within 10% of the exactly computed results for the region of optimum performance.