Linear System Description Using Wigner Distribution Functions

The Wigner Distribution Function (WDF) is a time-frequency descriptor capable of tracking the time-varying second order statistics in a signal. In this paper, we characterize linear systems in terms of the WDFs of the inputs and outputs. These input/output relations are provided for both continuous-time and discrete-time systems. An application of these results for the identification of a random, time-varying system is suggested.