The random Wigner distribution of Gaussian stochastic processes with covariance in \(S_0(\mathbb R^{2d})\). (English) Zbl 1082.60031
The paper deals with the time-frequency analysis of a Gaussian random process on \(\mathbb{R}^d\) (random fields). It is proved that if the covariance function belongs to the Feichtinger algebra \(S_0(\mathbb{R}^{2d})\), then the Wigner distribution (Wigner spectrum) of the process exists as finite stochastic integral and the Cohen’s class (i.e. convolution of the Wigner process by a deterministic function) gives a finite variance process.
Reviewer: Nikolai N. Leonenko (Cardiff)
MSC:
60G15 | Gaussian processes |
60G35 | Signal detection and filtering (aspects of stochastic processes) |
62M15 | Inference from stochastic processes and spectral analysis |
94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
60G60 | Random fields |
42B35 | Function spaces arising in harmonic analysis |