WAVELET-BASED LINEAR-SYSTEM MODELING AND ADAPTIVE FILTERING

It is shown how linear time-varying systems can be modeled in several different ways by discrete-time wavelets or, more generally, by some s et of functions. Interpretation of physical meanings, possible efficie ncy, and other characteristics of the modeling are considered. System identification minimizing the mean square output error is studied, Opt imal coefficients and the corresponding minimum mean square error are found, and they are, in general, time varying. Least-mean-square adapt ive filtering algorithms are derived for on-line filtering and system identification. Theoretically and by simulations, the advantages of us ing wavelet-based filtering are shown: separation of adaptation effect s from unknown time-varying system behavior and fast convergence. Adap tive coefficients estimated by a recursive-least-square algorithm can tend toward constants, even in the case of time-varying systems. Time- invariant system identification and adaptive filtering is given as a s pecial case of the general time-varying setting.