Optimum quantization of laplace density signal and its characteristics
Hirohisa Yamaguchi · Electronics and Communications in Japan (Part I Communications) · 1984
Abstract The distribution of prediction error at DPCM coding of audio or video signals can be approximated closely by Laplace distribution which, therefore, has been used widely for the determination of the quantization characteristics. The procedure for the practical determination of the quantizing characteristics for a given number of quantization levels, however, relies basically on the approximation methods chosen. Thus, considerable inconvenience is experienced during the theoretical analysis of the various characteristics corresponding to the different coding systems. In this paper, the optimum (Lloyd‐Max) quantization of Laplace density signals is considered and a recursive formula for the determination of the optimum quantization interval has been derived to show that the optimum quantization noise power is given as smin2/4 (smin is the minimum quantization interval length) when the number of the quantization levels is sufficiently large. Furthermore, the optimum quantization intervals (steps) have been determined by a digital computer with an accuracy of 8 digits and compared with the results of known approximations.