On Some New Facts in Comparing Frequency Domain, Optimal and Asymptotic Filtering

V. Černý and J. Hrušák (Czech Republic)


Optimization, Invariance, Structure, Convergence, Power, Energy, Equivalence


The paper studies some connections between the main results of the well known Wiener-Kalman-Bucy stochas tic approach to filtering problems based mainly on linear stochastic estimation theory and emphasizing the optimal ity aspects of the achieved results and the classical deter ministic frequency domain linear filters (such as Cheby shev, Butterworth, Bessel, etc.). A new non-stochastic but not necessarily deterministic (possibly non-linear) alterna tive approach to signal filtering based mainly on the con cepts of signal power, signal energy and a system equiv alence relation plays a dominant role in the presentation. 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. Causality, error invariance and espe cially error convergence properties are the most important and fundamental features of resulting filters. Therefore, it is natural to call them the asymptotic filters. It is shown in the paper that the notion of the asymptotic filter can be a proper tool for unifying stochastic and non-stochastic, lin ear and non-linear approaches to signal filtering.

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