Improved adaptive recursive even mirror Fourier nonlinear filter for nonlinear active noise control

Abstract

In this paper, we analyze the theoretical mechanism for the effectiveness of recursive filters including both linear and nonlinear feedforward and feedback subsections to accurately approximate nonlinear distributions in the active noise control (ANC) system. As a result, we improve the recursive even mirror Fourier nonlinear (REMFN) filter by adding an additional linear section termed REMFNL filter together with its channel reduced form (CRREMFNL) to explore better control performance. As for the linear feedback section introduced, we have studied the bound-input bound-output (BIBO) stability condition for the REMFNL filter and designed a stable control scheme to guarantee the filter satisfying the stability criteria. The performance of the proposed filters equipped with a filtered-x least mean square (FXLMS) algorithm is validated through analyses of computational complexity and simulations of various nonlinearities for nonlinear ANC (NANC) systems. Simulation results demonstrate that the proposed REMFNL and CRREMFNL filters can achieve better performance over the bilinear, recursive second-order Volterra (RSOV), recursive functional link artificial neural network (RFLANN) and standard REMFN filters based on the FXLMS algorithm, which often outperform the conventional Volterra FXLMS (VFXLMS) and filtered-s least mean square (FSLMS) algorithms.