Ten lectures on wavelets
Adaptive filter theory (2nd ed.)
Adaptive filter theory (2nd ed.)
Modeling and estimation of multiscale stochastic processes
ICASSP '91 Proceedings of the Acoustics, Speech, and Signal Processing, 1991. ICASSP-91., 1991 International Conference
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Theoretical and experimental analysis and description of wavelet-based filtering are given in the case of stationary desired signal. The impulse responses of adaptive filter and unknown system producing the desired signal are represented by discrete-time wavelet series. We have found the coefficients that minimize the mean square error and pointed out the time-frequency localized structure of modeling error. An LMS adaptive filtering algorithm is derived. Its transform domain interpretation is shown, as well as possibilities for faster convergence and better numerical properties. We have noticed the better modeling of desired signals in the time-frequency plane, faster convergence, and smaller error than in the case of FIR filters.