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Černý, V. and Hrušák, J. : Comparing frequency domain, optimal, and asymptotic filtering: a tutorial . Control and Intelligent Systems, 34, vol. 2, p. 136-142, 2006.


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.

Detail of publication

Title: Comparing frequency domain, optimal, and asymptotic filtering: a tutorial
Author: Černý, V. ; Hrušák, J.
Language: English
Date of publication: 1 Jan 2006
Year: 2006
Type of publication: Papers in journals
Title of journal or book: Control and Intelligent Systems
Series: 34
Číslo vydání: 2
Page: 136 - 142
ISBN: 1480-1752
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filter, invariance, convergence, signal power, signal energy, equivalence


 author = {\v{C}ern\'{y}, V. and Hru\v{s}\'{a}k, J.},
 title = {Comparing frequency  domain, optimal, and asymptotic filtering: a tutorial},
 year = {2006},
 journal = {Control and Intelligent Systems},
 volume = {2},
 pages = {136-142},
 series = {34},
 ISBN = {1480-1752},
 url = {},