Time-frequency analysis of random signals

A conjoint time-frequency representation of harmonizable random signals is defined as a generalization of the Wigner distribution of finite energy signals. It is shown that this conjoint time-frequency representation possesses properties analogous to those of finite energy signals. Furthermore, we state a necessary and sufficient condition for the existence of a random Wigner distribution as a stochastic integral in quadratic mean. Then, we can define a random instantaneous frequency and a random group delay, and give expressions of their expectation and variance. This is done without assuming narrow band conditions or stationarity of the random signal.