On the Wigner distribution of discrete-time noisy signals with application to the study of quantization effects

The influence of noise on the Wigner distribution (WD) of discrete-time signals is analyzed. Signals contaminated by white noise are considered. The expressions for the mean and variance of the WD estimator are derived. It is then shown that the application of only one window is sufficient to make the variance of the estimator finite. This is a significant difference from the analog case, where two windows are needed. The expression for the optimal window width is derived. The results are illustrated by several numerical examples. Using the derived expressions, the effects of finite register length on the WD are analyzed. Fixed and floating point arithmetic are considered.