Wavelet-based adaptive filtering

Theoretical and experimental analysis and description of wavelet-based filtering are given in the case of a stationary desired signal. The impulse responses of the adaptive filter and the unknown system producing the desired signal are represented by discrete-time wavelet series. The authors have found the coefficients that minimize the mean square error and pointed out the time-frequency localized structure of the modeling error. An LMS (least mean square) adaptive filtering algorithm is derived. Its transform domain interpretation is shown, as are possibilities for faster convergence and better numerical properties. The authors have observed better modeling of desired signals in the time-frequency plane, faster convergence, and smaller error than in the case of FIR (finite impulse response) filters.<>