Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/806726
- Gabor discretization of the Weyl product for modulation spaces and filtering of nonstationary stochastic processes
Schreier, Peter J.
- The University of Newcastle. Faculty of Engineering & Built Environment, School of Electrical Engineering and Computer Science
- 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.
- Applied and Computational Harmonic Analysis Vol. 26, Issue 1, p. 97-120
- Publisher Link
- Academic Press
nonstationary stochastic processes;
- Resource Type
- journal article