Detail of publication

Abstract

The paper studies connections between the Kalman-Bucy and classical frequency domain filters. A non-stochastic but not necessarily deterministic (possibly non-linear) alternative approach to signal filtering based mainly on concepts of signal power, signal energy and an equivalence relation plays a dominant role in the presentation. Causality, error invariance and especially error convergence properties are the most important features of resulting filters. Therefore, it is natural to call them asymptotic filters. Although error convergence aspects are emphasized in the approach, it is shown that introducing the signal power as the quantitative measure of signal energy dissipation makes it possible to achieve reasonable results from the optimality point of view as well. It is shown in the paper that the notion of the asymptotic filter can be used as a proper tool for unifying stochastic and non-stochastic, linear and non-linear approaches to signal filtering.