Active noise control (ANC) has been widely studied to eliminate low-frequency noise. However, efficiently controlling higher-order distortions of nonlinear primary and secondary path is still a major challenge. To address this, this paper proposes a novel nonlinear ANC algorithm based on the fast empirical wavelet transform and recursive Chebyshev nonlinear filter. In this method, the fast empirical wavelet transform based on order-statistic filtering is first applied to decompose non-stationary noise into empirical mode functions (EMFs) which are more stationary and easy to control. Furthermore, a novel third-order Chebyshev nonlinear filter including the non-recursive subsection and recursive one is proposed to individually expand EMFs for compensating higher-order nonlinear distortions from primary path and secondary path. Moreover, the strategy of channel-reduced diagonal structure is designed to optimise the number of expanded channels, and the computational complexity of proposed algorithm is also investigated. Experimental results demonstrate that proposed method performs the highest noise reduction over the conventional algorithms but also has a fast convergence rate.

有源噪声控制 (ANC) 已被广泛研究以消除低频噪声。然而，有效控制非线性初级和次级路径的高阶失真仍然是一个重大挑战。为了解决这个问题，本文提出了一种基于快速经验小波变换和递归切比雪夫非线性滤波器的新型非线性ANC算法。在该方法中，首先应用基于阶统计滤波的快速经验小波变换将非平稳噪声分解为更平稳且易于控制的经验模式函数（EMF）。此外，提出了一种包括非递归子部分和递归子部分的新型三阶切比雪夫非线性滤波器，以单独扩展 EMF，以补偿主路径和次路径的高阶非线性失真。而且，设计了信道减少对角结构的策略来优化扩展信道的数量，并研究了所提出算法的计算复杂度。实验结果表明，与传统算法相比，所提出的方法具有最高的降噪效果，但收敛速度也很快。