The Wigner distribution of Gaussian tempered generalized stochastic processes

Patrik Wahlberg

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arXiv · 2504.03493

The Wigner distribution of Gaussian tempered generalized stochastic processes

Patrik Wahlberg

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Abstract

We define the Wigner distribution of a tempered generalized stochastic process that is complex-valued symmetric Gaussian. This gives a time-frequency generalized stochastic process defined on the phase space. We study its covariance and our main result is a formula for the Weyl symbol of the covariance operator, expressed in terms of the Weyl symbol of the covariance operator of the original generalized stochastic process.

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Patrik Wahlberg. 2025-04-04. The Wigner distribution of Gaussian tempered generalized stochastic processes. https://arxiv.org/abs/2504.03493

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