OPTIMUM QUANTIZATION OF RANDOM SEQUENCES.
HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS
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Whenever information is to undergo digital processing it must be given a quantized representation. The quantizers investigated are those which are optimum with respect to a mean square error criterion for stationary input sequences. They are permitted to have memory and it is shown that they belong to the class of quantized feedback systems which includes delta-modulators and predictive quantization systems differential pulse-code modulation. Emphasized are the application of quantization to digital communication and considered are the analog to digital and digital to analog operations of the quantizer to be performed respectively by a transmitter and receiver. The analysis of the quantization system with a linear receiver is considered in depth. The results for random sequences are made applicable to the transmission of time continuous information by considering the random sequence to have been obtained by sampling a time continuous process, and by using an interpolator to reconstruct the continuous process from the quantized samples. Several examples are presented for the transmission of a Gauss-Markov process. The effect of bandlimiting the continuous process before sampling is also investigated. Comparisons are made with PCM and the rate distortion function.