Low-Complexity Hermite Nonlinear Filter for Active Noise Control

Abstract

In this article, a class of low-complexity Hermite nonlinear (HN) filters is proposed for nonlinear active noise control (NLANC). The HN filters belong to linear-in-the-parameter (LIP) nonlinear filters, which also have the orthogonal property for white input signals. Based on the HN filters, the fast affine projection algorithm (FAPA) and the dichotomous coordinate descent (DCD) method are introduced, generating DCD-filtered-h FAPA (DCD-FhFAPA). Benefiting from fast recursive filtering and DCD strategies, the computational complexity of the algorithm can be reduced. To further alleviate computational complexity, two methods of discarding redundant data are proposed based on the Mahalanobis distance, leading to the DCD-low-complexity filtered-h FAPA-I (DCD-LFhFAPA-I) and DCD-LFhFAPA-II algorithms. At the price of slightly slow convergence, two new algorithms significantly reduce the computational load for NLANC. Simulation results exhibit the effectiveness of the DCD-FhFAPA, DCD-LFhFAPA-I, and DCD-LFhFAPA-II algorithms.