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Differential pulse-code modulation (DPCM) has been proposed as a practical encoding scheme for speech, television, and telemetry signals. In this paper, the mean-square error for DPCM systems is derived, and its minimization by proper choice of system variables is examined. A simple analytical method is then presented for optimizing the system bandwidth , the number of quantization bits , and the parameters of the DPCM feedback network when the input is a speech signal and channel noise is negligible. A method is then developed for measuring the subjective quality of voice communication systems as a function of an arbitrary number of system parameters. The method was used to measure the quality of PCM speech and DPCM speech as a function of and . Quantization was logarithmic, the sampling rate , and channel noise was assumed negligible. Optimum and were found for every bit rate . For both PCM and DPCM, the equations relating the optimum and are of the form , where and are constants independent of . The maximum speech quality obtainable for PCM and DPCM was found as a function of , and the reduction in bit rate resulting when optimum DPCM rather than optimum PCM is used was determined as a function of and as a function of the speech quality. Included in the paper is a brief description of the realtime DPCM systems used in the research.