A fast wavelet transform-domain LMS algorithm

This paper presents a fast wavelet transform-domain LMS (FWTDLMS) algorithm whose computational complexity is very low as compared to what has been reported so far, because it is completely independent from the adaptive filter order. In our method, the reduction in the computational load has been achieved by exploiting the redundancy in the computation of the wavelet coefficients as the data window slides on by one sample at each new iteration. As a result, the complexity of the wavelet transform is reduced from O(mN) where m is the wavelet filter length and N is the adaptive filter order to O(m(m+M)/2) where M (M<m) is the number of subbands in the maximally decimated filter bank. In addition, we have introduced a recursion in the estimation of the energy of the wavelet coefficients. This complexity then becomes O(2N+m(m+M)/2+m+4M), which is comparable to time-domain LMS complexity when short wavelet filters (m≪N) are used