{"abstract":[{"text":"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.","lang":"eng"}],"user_id":"43497","citation":{"apa":"Wahlberg, P., &#38; Schreier, P. J. (2008). A time-frequency formula for LMMSE filters for nonstationary underspread continuous-time stochastic processes. <i>Proc. 16th\\ European Signal Process.\\ Conf.</i>","ama":"Wahlberg P, Schreier PJ. A time-frequency formula for LMMSE filters for nonstationary underspread continuous-time stochastic processes. In: <i>Proc. 16th\\ European Signal Process.\\ Conf.</i> ; 2008.","chicago":"Wahlberg, Patrik, and Peter J. Schreier. “A Time-Frequency Formula for LMMSE Filters for Nonstationary Underspread Continuous-Time Stochastic Processes.” In <i>Proc. 16th\\ European Signal Process.\\ Conf.</i>, 2008.","bibtex":"@inproceedings{Wahlberg_Schreier_2008, title={A time-frequency formula for LMMSE filters for nonstationary underspread continuous-time stochastic processes}, booktitle={Proc. 16th\\ European Signal Process.\\ Conf.}, author={Wahlberg, Patrik and Schreier, Peter J.}, year={2008} }","ieee":"P. Wahlberg and P. J. Schreier, “A time-frequency formula for LMMSE filters for nonstationary underspread continuous-time stochastic processes,” 2008.","mla":"Wahlberg, Patrik, and Peter J. Schreier. “A Time-Frequency Formula for LMMSE Filters for Nonstationary Underspread Continuous-Time Stochastic Processes.” <i>Proc. 16th\\ European Signal Process.\\ Conf.</i>, 2008.","short":"P. Wahlberg, P.J. Schreier, in: Proc. 16th\\ European Signal Process.\\ Conf., 2008."},"department":[{"_id":"263"}],"date_created":"2023-01-30T11:52:04Z","title":"A time-frequency formula for LMMSE filters for nonstationary underspread continuous-time stochastic processes","publication":"Proc. 16th\\ European Signal Process.\\ Conf.","type":"conference","year":"2008","_id":"40867","date_updated":"2023-01-30T11:56:10Z","author":[{"first_name":"Patrik","last_name":"Wahlberg","full_name":"Wahlberg, Patrik"},{"first_name":"Peter J.","last_name":"Schreier","full_name":"Schreier, Peter J."}],"status":"public"}