Performance analysis of adaptive filter structure employing wavelet and sparse subfilters

A new structure for adaptive filtering which employs a wavelet transform and sparse filters is presented. A description of the algorithm, including particularities such as the delay introduced in the output signal and the minimum number of adaptive coefficients required, is provided. A theoretical analysis of the convergence speed of the adaptation algorithm is developed, which allows one to choose the adequate wavelet transform according to the input signal statistics. Simulations with coloured input signals are presented to illustrate the convergence behaviour of the proposed structure with different wavelets and to verify the theoretical analysis.