On the instantaneous frequency of Gaussian stochastic processes

2010/07/07 by Patrik Wahlberg, Wahlberg, Patrik, Peter J. Schreier +1
Computer Science · Mathematics · #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Mathematics #Image and Signal Denoising Methods #Information Theory (cs.IT) #Probability (math.PR) #Target Tracking and Data Fusion in Sensor Networks #cs.IT #math.IT #math.PR

paper · pdf · doi:10.48550/arxiv.1007.1069

22 pages

arxiv created 2010/07/07 · openalex publication_date 2010/07/07 · arxiv updated 2010/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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