Abstract: We study the instantaneous frequency (IF) of continuous-time, complex-valued, zero-mean, proper, mean-square differentiable, nonstationary Gaussian stochastic processes. We compute the probability density function for the IF for fixed time, which generalizes a result known for wide-sense stationary processes to nonstationary processes. For a fixed point in time, the IF has either zero or infinite variance. For harmonizable processes, we obtain as a consequence the result that the mean of the IF, for fixed time, is the normalized first-order frequency moment of the Wigner spectrum.

2000 AMS Mathematics Subject Classification: Primary: 60G15, 62M15; Secondary: 60G35, 94A12.

Keywords and phrases: Continuous-time Gaussian stochastic processes, instantaneous frequency, probability density function, Wigner spectrum.