On the time-frequency analysis based filtering

Efficient processing of nonstationary signals requires time-varying approac h. An interesting research area within this approach is time-varying filter ing. Since there is a certain amount of freedom in the definition of time-v arying spectra, several definitions and solutions for the time-varying filt ering have been proposed so far. Here were will consider the Wigner distrib ution based time-varying filtering form defined by using the Weyl correspon dence. Its slight modification will be proposed and justified in the proces sing of noisy frequency modulated signals based on a single signal realizat ion. An algorithm for the efficient determination of the filters' region of support in the time-frequency plane, in the case of noisy signals, will be presented. In the second part of the paper, the theory is applied on the f iltering of multicomponent noisy signals. The S-method is used as a tool fo r the filters' region of support estimation in this case. This method, comb ined with the presented algorithm, enables very efficient time-varying filt ering of the multicomponent noisy signals based on a single realization of the signal and noise. Theory is illustrated by examples.