Wavelet transform domain RLS algorithm

This paper describes a new wavelet domain RLS algorithm. The algorithm exploits the special sparse structure of the wavelet transform of wide classes of correlation matrices and that of the Cholesky factors of these matrices. Specifically, the algorithm updates a sparse QR factorization of the wavelet domain input data matrix. It then uses these factors to obtain the least-squares (LS) filter coefficients. The computational complexity of the proposed method is O(M log(M)) flops even when the input signal is not a time-series. Its convergence performance is similar to the traditional RLS algorithm. The new algorithm provides a method for trading error performance for lower computational complexity. Simulation results validate the performance of the algorithm