Quantization error is one of the important measures that determine the performance of the differential PCM. This paper investigates the DPCM quantization error characteristic and the exact determination of the stationary error density. The input signal considered is a time‐discrete increment process which is similar to the Wiener sequence, but with Laplacian increments.
A system of equations satisfied by the characteristic function of the prediction error is derived first and the exact formulas are derived for error probability distributions. Using these distributions the meansquared error, the entropy of the quantized outputs, and the probability of granular error are determined. For the obtained optimum quantization step size, it is shown that the granular error exceeds the slope overload error, that the distribution of quantized outputs is nearly geometrical, that the quantization error is almost equal to that of increments for a large number of quantization levels, and that the results agree with rate distortion theory.
The present analysis will be useful to performance analysis of DPCM with stationary non‐Gaussian autoregressive inputs.