The acoustic feedback is widely seen in the active noise control (ANC) system for short acoustic duct such as the intake system of an automobile engine, which severely destabilizes the stability of the original ANC system. The conventional acoustic feedback compensation methods based on IIR filter can only be applied to the linear acoustic path and is not suitable for a nonlinear ANC (NANC) system. To solve this problem, this paper proposes a Volterra recursive even mirror Fourier nonlinear (VREMFN) filter, which can effectively suppress both linear acoustic feedback and nonlinear acoustic feedback in the NANC system. In this paper, we show the solutions for the linear acoustic feedback and nonlinear acoustic feedback of VREMFN and discuss its stability condition. Moreover, a new leaky normalized LMS algorithm is also developed to further improve the performance of NANC system based on VREMFN. Simulated results comparing IIR, Volterra and VREMFN based on parameter adaptive algorithm (PAA), FXLMS and FULMS show that the proposed VREMFN dramatically improves the noise reduction performance of NANC system both in linear acoustic feedback path and nonlinear acoustic feedback path. Furthermore, two experiments with different acoustic feedback paths also demonstrate the effectiveness of the proposed VREMFN.

在用于短声导管的有源噪声控制（ANC）系统（例如汽车发动机的进气系统）中，声反馈得到了广泛的应用，这严重破坏了原始ANC系统的稳定性。基于IIR滤波器的常规声反馈补偿方法只能应用于线性声路径，不适用于非线性ANC（NANC）系统。为了解决这个问题，本文提出了一种Volterra递归均匀镜傅立叶非线性（VREMFN）滤波器，该滤波器可以有效抑制NANC系统中的线性声反馈和非线性声反馈。在本文中，我们展示了VREMFN的线性声反馈和非线性声反馈的解决方案，并讨论了其稳定性条件。而且，还开发了一种新的泄漏归一化LMS算法，以进一步提高基于VREMFN的NANC系统的性能。通过基于参数自适应算法（PAA），FXLMS和FULMS对IIR，Volterra和VREMFN进行比较的仿真结果表明，所提出的VREMFN大大提高了NANC系统在线性声反馈路径和非线性声反馈路径中的降噪性能。此外，两个具有不同声反馈路径的实验也证明了所提出的VREMFN的有效性。FXLMS和FULMS表明，所提出的VREMFN在线性声反馈路径和非线性声反馈路径中均显着提高了NANC系统的降噪性能。此外，两个具有不同声反馈路径的实验也证明了所提出的VREMFN的有效性。FXLMS和FULMS表明，所提出的VREMFN在线性声反馈路径和非线性声反馈路径中均显着提高了NANC系统的降噪性能。此外，两个具有不同声反馈路径的实验也证明了所提出的VREMFN的有效性。