Wavelet transform domain LMS algorithm

A novel normalized wavelet domain least-mean-square (LMS) algorithm is described. The faster convergence rate of this algorithm as compared with time-domain LMS is established. The wavelet domain LMS algorithm requires only real arithmetic. In its most basic form it has a computational complexity that is higher than that of the traditional LMS technique by a factor of cN, where N is the length of the transformed vector (or sliding analysis window) and c is the length of the analysis wavelet. Other preconditioning strategies that yield a faster convergence rate for a given fixed excess mean squared error are discussed. The authors also describe low-complexity implementations of the wavelet domain LMS algorithm. These implementations exploit the structure of the wavelet transform of the underlying stochastic process.<<ETX>>