Abstract
An important application of linear time-invariant filtering of WSS random processes is for the design of optimum estimation filters. In this problem, given some observations Y (t) related to a process X(t) of interest, one seeks to design a filter which is optimal in the sense that if Y (t) is the filter input, the estimate \(\hat {X} (t)\) produced at the filter output minimizes the mean-square estimation error with the desired process X(t). The level of difficulty of this problem depends on whether the estimation filter is required to be causal or not. The first complete solution of this problem for both the noncausal and causal cases was proposed by Wiener, and optimal estimation filters are therefore often referred to as Wiener filters.
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Levy, B.C. (2020). Wiener Filtering. In: Random Processes with Applications to Circuits and Communications. Springer, Cham. https://doi.org/10.1007/978-3-030-22297-0_11
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DOI: https://doi.org/10.1007/978-3-030-22297-0_11
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