Effects of quantization on feedback systems with stochastic inputs

An approximate analysis of the effects of quantization in a feedback system is made. The system input is a Gaussian random signal. The error autocorrelation as a function of the quantizer box size is the goal of the analysis. The approximation lies in the assumption that certain error joint distributions are Gaussian. In the limit as the quantizer box size approaches zero, these distributions do become Gaussian. On the basis of the approximation, a nonlinear integral equation relating the error autocorrelation to the system parameters is developed. An iteration procedure for successive approximations to the solution is outlined, and several examples are presented. Finally, experimental results obtained on a digital computer are shown.