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The random Wigner distribution of Gaussian stochastic processes with covariance in S0(R2d)
Lund University.
2005 (English)In: Journal of Function Spaces and Applications, ISSN 0972-6802, E-ISSN 1758-4965, Vol. 3, no 2, p. 163-181Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
New York: Hindawi Publishing Corporation, 2005. Vol. 3, no 2, p. 163-181
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-27590DOI: 10.1155/2005/252415OAI: oai:DiVA.org:lnu-27590DiVA, id: diva2:637391
Available from: 2013-07-17 Created: 2013-07-17 Last updated: 2017-12-06Bibliographically approved

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