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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0972-6802 |