This paper introduces a new class of nonlinear filters for nonlinear acoustic echo cancellation (NLAEC) based on Hermite nonlinear filters (HNFs), which is a sub-class of linear-in-the-parameters nonlinear filters (LIPNFs). Specifically, the basis functions of HNFs include cross-terms of the expanded inputs at different time instants, and are mutually orthogonal for white normally distributed input signals. Although HNFs yield good performance for NLAEC, they suffer from high computational complexity. To tackle this problem, a computationally efficient pipelined variant of HNFs is introduced. The pipelined HNFs (PHNFs) include a nonlinear part followed by a linear one such that the input space is first expanded nonlinearly and then cast by a linear mapping to the output space. Experimental results using both synthesized and real data, and involving several nonlinear scenarios show the effectiveness of the proposed approach.

中文翻译：

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基于管道Hermite滤波器的非线性声学回声消除

本文介绍了一种基于 Hermite 非线性滤波器 (HNF) 的新型非线性声学回声消除 (NLAEC) 非线性滤波器，它是参数线性非线性滤波器 (LIPNF) 的子类。具体来说，HNF的基函数包括不同时刻的扩展输入的交叉项，并且对于白色正态分布输入信号是相互正交的。尽管 HNF 为 NLAEC 带来了良好的性能，但它们的计算复杂度很高。为了解决这个问题，引入了一种计算高效的 HNF 流水线变体。流水线 HNF (PHNF) 包括一个非线性部分和一个线性部分，这样输入空间首先非线性扩展，然后通过线性映射投射到输出空间。使用合成数据和真实数据以及涉及多个非线性场景的实验结果表明了所提出方法的有效性。