On the convergence enhancment of the wavelet transform based LMS

The wavelet transform least mean squares algorithm (WTLMS) has been recently proposed as an alternative to the simple and transform based (DCT) LMS algorithms, because of its faster convergence. In this paper, we first show the influence of the regularity of the wavelet low-pass filter on the convergence behavior of the normalized WTLMS algorithm (NWTLMS). Then, we show that the subband decomposition of the input signal along a regular subband tree, which splits the signal frequency band uniformly, gives better results, i.e., a faster convergence rate than the dyadic subband tree, which splits the signal frequency band dyadically. Finally, we show that perfect reconstruction quadrature mirror filters (PR-QMFs), which are less regular, can lead to as good results while the multiplier-free PR-QMFs offer, furthermore, a very reduced computational complexity, and hence can be used as an alternative to the wavelet filters for accelerating the convergence rate of the NWTLMS algorithm.