Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/806726

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Title
Gabor discretization of the Weyl product for modulation spaces and filtering of nonstationary stochastic processes
Author/Creator
Wahlberg, Patrik;  Schreier, Peter J.
Institution
The University of Newcastle. Faculty of Engineering & Built Environment, School of Electrical Engineering and Computer Science
Description
We discretize the Weyl product acting on symbols of modulation spaces, using a Gabor frame defined by a Gaussian function. With one factor fixed, the Weyl product is equivalent to a matrix multiplication on the Gabor coefficient level. If the fixed factor belongs to the weighted Sjöstrand space M ω∞,¹ then the matrix has polynomial or exponential off-diagonal decay, depending on the weight ω.Moreover, if its operator is invertible on L², the inverse matrix has similar decay properties. The results are applied to the equation for the linear minimum mean square error filter for estimation of a nonstationary second-order stochastic process from a noisy observation. The resulting formula for the Gabor coefficients of the Weyl symbol for the optimal filter may be interpreted as a time–frequency version of the filter for wide-sense stationary processes, known as the noncausal Wiener filter.
Relation
Applied and Computational Harmonic Analysis Vol. 26, Issue 1, p. 97-120
Publisher Link
http://dx.doi.org/10.1016/j.acha.2008.02.005
Date
2009
Publisher
Academic Press
Keyword(s)
pseudodifferential calculus;  Weyl calculus;  modulation spaces;  Gabor frames;  nonstationary stochastic processes;  optimal filtering
Resource Type
journal article
Identifier
http://hdl.handle.net/1959.13/806726
Identifier
ISSN:1063-5203
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Subject
"Applied and Computational Harmonic Analysis"
 
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