On the instantaneous frequency of Gaussian stochastic processes

Patrik Wahlberg; Peter J. Schreier

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arXiv · 1007.1069

On the instantaneous frequency of Gaussian stochastic processes

Patrik Wahlberg·Peter J. Schreier

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Abstract

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

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Patrik Wahlberg, Peter J. Schreier. 2010-07-07. On the instantaneous frequency of Gaussian stochastic processes. https://arxiv.org/abs/1007.1069

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