A novel FELMS-based narrowband active noise control system and its convergence analysis

Abstract

The computational efficiency of the filtered-x least mean square-based narrowband active noise control (FX-NANC) system is heavily dependent on the number of targeted frequencies and the length of the estimated secondary path, so that its performance may be limited in the case of multi-frequency noise. In order to address this limitation, filtered-error least mean square (FELMS) algorithm is first considered in narrowband active noise control (NANC) system in this paper. Compared to the FX-NANC system, the FELMS-based NANC (FE-NANC) system requires only one error signal filtering block regardless of the number of targeted frequencies. As the increase of the number of targeted frequencies and/or the length of the estimated secondary path, the FE-NANC becomes much more cost-saving. The closed-form convergence analysis of mean and mean-square of the FE-NANC system for discrete Fourier coefficients (DFC) and error signal are derived along with the stability condition on step size. Numerical simulations comparing FE-NANC with other NANC systems and the real-time implementations of FE-NANC demonstrate the effectiveness of FE-NANC system. Furthermore, we show that the numerical results of FE-NANC system agree with theoretical predictions.