Analysis of the FXLMS algorithm with norm-constant time-varying primary path

Abstract

We analyze the behaviors of active noise control with a time-varying primary path using a statistical-mechanical method. The principal assumption used in the analysis is that the impulse responses of the primary path and adaptive filter are sufficiently long. We analyze a novel model in which the reference signal is not necessarily white and the primary path is timevarying while its norm is kept constant in the mean sense. We show the existence of macroscopic steady states and the optimal step size.