Adaptive filters based on the best matched wavelet tree

In applications where some prior information exists about the physical system that gives rise to the signals under consideration, simplification is to be expected in search of representational optimality. Often the purpose of processing is to separate signals from uncorrelated and correlated noise, the latter being certifiably difficult to do without the knowledge of features that enables one to distinguish the signal from noise. Under such circumstances, a priori information about the signal can be used to chose a fixed wavelet basis so that a fixed best wavelet tree can be found in which at least one scale level contains the statistical majority of the input signal energy. Such a wavelet basis is said to match the signal. It is shown that adaptive filtering using matched wavelet filter banks results in improved convergence speed as compared to adaptive filtering with no consideration of matching. The adaptation is done with the LMS algorithm. A fast algorithm is also provided to further reduce the computation complexity. Finally, an application of the method to interference and noise cancellation is presented.