Title :
A time-frequency formula for LMMSE filters for nonstationary underspread continuous-time stochastic processes
Author :
Wahlberg, Patrik ; Schreier, Peter J.
Author_Institution :
Sch. of Electr. Eng. & Comput. Sci., Univ. of Newcastle, Callaghan, NSW, Australia
Abstract :
We study linear minimum mean square error (LMMSE) filters for estimating a nonstationary second-order continuous-time stochastic process from a noisy observation. The equation for the optimal filter is treated in the Weyl symbol domain, and the involved Weyl symbols are assumed to belong to certain modulation spaces. By discretizing this equation using a Gabor frame we transform it into a matrix equation and obtain a formula for the filter by matrix inversion. The inverse matrix has off-diagonal decay at a rate that increases the more underspread the process is.
Keywords :
Gabor filters; continuous time filters; least mean squares methods; matrix inversion; stochastic processes; time-frequency analysis; Gabor frame; LMMSE filters; linear minimum mean square error filters; matrix equation; matrix inversion; noisy observation; nonstationary second-order continuous-time stochastic process; nonstationary underspread continuous-time stochastic processes; optimal filter; time-frequency formula; Equations; Europe; Kernel; Modulation; Stochastic processes; Time-frequency analysis;
Conference_Titel :
Signal Processing Conference, 2008 16th European
Conference_Location :
Lausanne