The random Wigner distribution of Gaussian stochastic processes with covariance in S0(ℝ2d)
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...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2005/252415 |
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| _version_ | 1832566999525359616 |
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| author | Patrik Wahlberg |
| author_facet | Patrik Wahlberg |
| author_sort | Patrik Wahlberg |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e9cc0276a53e4c26848145f13f0fa4c0 |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-e9cc0276a53e4c26848145f13f0fa4c02025-02-03T01:02:41ZengWileyJournal of Function Spaces and Applications0972-68022005-01-013216318110.1155/2005/252415The random Wigner distribution of Gaussian stochastic processes with covariance in S0(ℝ2d)Patrik Wahlberg0Department of Electroscience, Lund University, Box 118, SE-22100 Lund, SwedenThe 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.http://dx.doi.org/10.1155/2005/252415 |
| spellingShingle | Patrik Wahlberg The random Wigner distribution of Gaussian stochastic processes with covariance in S0(ℝ2d) Journal of Function Spaces and Applications |
| title | The random Wigner distribution of Gaussian stochastic processes with covariance in S0(ℝ2d) |
| title_full | The random Wigner distribution of Gaussian stochastic processes with covariance in S0(ℝ2d) |
| title_fullStr | The random Wigner distribution of Gaussian stochastic processes with covariance in S0(ℝ2d) |
| title_full_unstemmed | The random Wigner distribution of Gaussian stochastic processes with covariance in S0(ℝ2d) |
| title_short | The random Wigner distribution of Gaussian stochastic processes with covariance in S0(ℝ2d) |
| title_sort | random wigner distribution of gaussian stochastic processes with covariance in s0 r2d |
| url | http://dx.doi.org/10.1155/2005/252415 |
| work_keys_str_mv | AT patrikwahlberg therandomwignerdistributionofgaussianstochasticprocesseswithcovarianceins0r2d AT patrikwahlberg randomwignerdistributionofgaussianstochasticprocesseswithcovarianceins0r2d |