Adaptive noise cancellation with a multirate normalized least mean squares filter

Multirate adaptive filtering is related to the problem of reconstructing a high-resolution signal from two or more observations that are sampled at different rates. A popular existing method for solving this problem uses the multirate adaptive filter structure that is based on the least mean squares (LMS) approach. However, its low convergence rate restricts the use of this method. In this study, a multirate normalized LMS (NLMS) filter is proposed as an alternative to that of LMS based filter, for the reconstruction of the high-resolution signal from several low-resolution noisy observations. In the simulation example performed on an audio signal, it is observed that the proposed method leads to the better results than the existing method especially in the convergence rate.