New adaptive algorithms based on multi-band decomposition of the error signal

New adaptive algorithms based on multi-band decomposition of the error signal and application of a different convergence factor for each band are derived. With this approach, tracking ability and performance in steady state can be traded off along the frequency domain giving rise to estimates of the adaptive filter coefficients closer to the ideal response as compared to those obtained with conventional least-mean-square (LMS) and recursive least-squares (RLS) algorithms, particularly when the statistical properties of the analyzed signal vary along the frequency spectrum. A new adaptation technique for the forgetting factor depending exclusively on the autocorrelation values of the input signal is also introduced and a multi-band RLS algorithm, with an independent variable forgetting factor for each band, suitable for the analysis of nonstationary signals is described. Computer experiments comparing the performance of multi-band and conventional LMS and RLS algorithms are shown.