%0 Journal Article
%T The random Wigner distribution of Gaussian stochastic processes with covariance in
%A Patrik Wahlberg
%J Journal of Function Spaces and Applications
%D 2005
%I Hindawi Publishing Corporation
%R 10.1155/2005/252415
%X The paper treats time-frequency analysis of scalar-valued zero mean Gaussian stochastic processes on ℝd. We prove that if the covariance function belongs to the Feichtinger algebra S0(ℝ2d) then: (i) the Wigner distribution and the ambiguity function of the process exist as finite variance stochastic Riemann integrals, each of which defines a stochastic process on ℝ2d, (ii) these stochastic processes on ℝ2d are Fourier transform pairs in a certain sense, and (iii) Cohen's class, ie convolution of the Wigner process by a deterministic function Φ∈C(ℝ2d), gives a finite variance process, and if Φ∈S0(ℝ2d) then W∗Φ can be expressed multiplicatively in the Fourier domain.
%U http://www.hindawi.com/journals/jfsa/2005/252415/abs/