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Active Impulsive Noise Control Algorithm Based on Adjustable Hyperbolic Tangent Function

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Abstract

To solve the noise reduction failure of the filter-x least mean squares (FxLMS) algorithm in the impulsive noise environment, the filter-x tanh LMS (FXtanhLMS) algorithm is proposed in this paper. The algorithm enhances the robustness by introducing an adjustable nonlinear hyperbolic tangent function. The hyperbolic tangent function is used to compress the residual signal. It can solve the problem that the impulsive noise does not have a bounded second-order moment. Compared to the fixed compression function, the automatically adjustable compression function can balance the convergence speed and the robustness of the algorithm under different intensities of impulsive noises. It allows the algorithm to have a slow change in the adaptive steady stage. In addition, the normalized filtered-x tanh LMS (NFXtanhLMS) algorithm is proposed to improve the performance in heavy spike impulsive noise by combining the FXtanhLMS algorithm with the normalized step-size. The proposed algorithms do not require complex threshold estimation compared to existing algorithms. Simulation results show that faster convergence, minor residual errors, and better system tracking can be achieved in both SaS synthesis noise and punching noise.

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All data, models and code generated or used during the study are available from the corresponding author on reasonable request.

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Authors and Affiliations

  1. School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai, 201600, China

    Chunyang Li, Guangcan Jin & Jin Li

  2. Shanghai Li Auto Technology Co., Ltd, Shanghai, 201800, China

    Hao Liu

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  1. Chunyang Li
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  2. Guangcan Jin
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  4. Jin Li
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Correspondence to Guangcan Jin.

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Li, C., Jin, G., Liu, H. et al. Active Impulsive Noise Control Algorithm Based on Adjustable Hyperbolic Tangent Function. Circuits Syst Signal Process 42, 5559–5578 (2023). https://doi.org/10.1007/s00034-023-02374-7

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