Performance analysis of an adaptive filter structure employing wavelets and sparse subfilters

The properties of an adaptive filter structure which employs a wavelet to decompose the input signal and sparse adaptive filters in the subbands are investigated in this paper. The necessary conditions on the structure parameters for the exact modeling of an arbitrary linear system with finite impulse response (FIR) are derived. An analysis of the convergence speed of the adaptation algorithm is presented, showing that a significant improvement in the convergence rate can be obtained using very simple wavelets. Computer simulations are presented to illustrate the convergence behavior of the adaptive structure investigated in the paper.