Wavelet based time-varying linear system modeling and adaptive filtering

It is shown how time-varying systems can be modeled in several different ways by discrete-time wavelets. Interpretation of physical meanings, possible efficiency and other characteristics of the modeling are considered. System identification minimizing the mean square output error is studied. Optimal coefficients and the corresponding minimum MS error are found and they are time-varying. A least-mean-square adaptive filtering algorithm is derived for on-line filtering and system identification. Theoretically and by simulations the advantages of using wavelet-based filtering are shown: separation of adaptation effects from unknown time-varying system behavior and fast convergence. Adaptive coefficients estimated by a recursive-least-square algorithm can tend towards constants