On Wiener filtering of certain locally stationary stochastic processes

Authors:
Patrik Wahlberg;Peter J. Schreier
Affiliations:
Dipartimento di Matematica, Universití di Torino, Via Carlo Alberto 10, 10123 Torino, Italy;School of Electrical Engineering & Computer Science, The University of Newcastle, Callaghan, NSW 2308, Australia
Venue:
Signal Processing
Year:
2010

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Abstract

We study linear minimum mean squared error filters for continuous-time second-order stochastic processes that are locally stationary in Silverman's sense. We show that the optimal filter is rarely locally stationary even when the covariance functions have Gaussian shape. Using Mehler's formula we derive series expansions of the filter kernel for locally stationary covariances that are determined by Gaussians.