Cascaded Random Fourier Filter for Robust Nonlinear Active Noise Control

The random Fourier filter-based filtered-x least mean square (RF-FxLMS) algorithm has been proposed for the nonlinear active noise control (NANC) system to reduce the computational burden of the kernel filter. However, the RF-FxLMS algorithm markedly fluctuates when dealing with impulsive noise. In addition, the computing cost for the RF-FxLMS algorithm is still pricey in practice. In this work, a random Fourier filter based filtered-x generalized hyperbolic secant function (RF-FxGHSF) algorithm is presented to deal with impulsive noise. In virtue of the bilinear scheme, a cascaded random Fourier filter model is designed for concise computations, and the cascaded RF-FxGHSF (CRF-FxGHSF) algorithm is derived. Moreover, the steady-state convergence conditions are analyzed. The calculation complexity of the proposed algorithms is compared, and experiments emphatically analyze the principle for the presented model. Numerical simulations with α-stable noise and real noise carried out in different nonlinear path scenarios verify the convergence ability of proposed algorithms.