Adaptive even mirror Fourier filtered error LMS algorithm for multichannel nonlinear active noise control

In this paper, the multichannel even mirror Fourier nonlinear (EMFN) filter based filtered-x least mean square (FFLMS) algorithm and filtered-error least mean square (FFELMS) algorithm are proposed for nonlinear active noise control (NANC) applications. The FFLMS algorithm is extended from a single-channel NANC system to a multi-channel NANC system, and the efficient filtered-error structure with the EMFN filter is explored in the developed FFELMS algorithm to reduce the computational complexity without sacrificing its control performance. The computational complexity analyses in comparison with the second-order Volterra filtered-x LMS (VFXLMS), first-order filtered-s LMS (FSLMS) and second-order Legendre filtered-x LMS (LFXLMS) algorithms are provided. The performance of the both FFLMS and FFELMS algorithms are validated through computer simulations. The computer simulations demonstrate that the developed multichannel FFLMS and FFELMS algorithms not only outperform the VFXLMS, FSLMS and LFXLMS algorithms in terms of the noise control performance but also converge faster than the second-order VFXLMS and the second-order LFXLMS algorithms.