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<p>Thanks to the decorrelation capability of the discrete cosine transform (DCT), the DCT-based filtered-x normalized least mean square (DCT-FxNLMS) algorithm has been implemented in feedforward active noise control (ANC) systems. However, its effectiveness is severely degraded in the presence of impulsive noises and constrained by the limitations of the fixed step-size. To address these issues, we first propose a generalized framework of the robust DCT-FxNLMS (R-DCT-FxNLMS) algorithm by introducing the robust correntropy criterion to enhance performance under impulsive noises. We then consider a mean square deviation (MSD) recursion model that characterizes the algorithms behavior and reveals the aforementioned trade-off. Based on the derived MSD recursion, we design a switched step-size (SSS) strategy and propose the SSS-R-DCT-FxNLMS algorithm, which dynamically selects the optimal step-size at each iteration by evaluating the predicted MSD values associated with a predefined set of step-sizes. This SSS-based algorithm enables both fast convergence and low steady-state residual error simultaneously. Simulation results under various noise scenarios validate the superior performance of the proposed algorithms as compared to existing counterparts.</p>

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Transform-Domain Filtered-x Least Mean Square Algorithms with Switched Step-Size Mechanism for Feedforward ANC Systems

  • 期刊论文

  • 发表日期：

    2026年2月20日

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  • Zhiyuan Li,
  • Yi Yu,
  • Yuyu Zhu,
  • Hongsen He,
  • Rodrigo C. de Lamare

摘要

Thanks to the decorrelation capability of the discrete cosine transform (DCT), the DCT-based filtered-x normalized least mean square (DCT-FxNLMS) algorithm has been implemented in feedforward active noise control (ANC) systems. However, its effectiveness is severely degraded in the presence of impulsive noises and constrained by the limitations of the fixed step-size. To address these issues, we first propose a generalized framework of the robust DCT-FxNLMS (R-DCT-FxNLMS) algorithm by introducing the robust correntropy criterion to enhance performance under impulsive noises. We then consider a mean square deviation (MSD) recursion model that characterizes the algorithms behavior and reveals the aforementioned trade-off. Based on the derived MSD recursion, we design a switched step-size (SSS) strategy and propose the SSS-R-DCT-FxNLMS algorithm, which dynamically selects the optimal step-size at each iteration by evaluating the predicted MSD values associated with a predefined set of step-sizes. This SSS-based algorithm enables both fast convergence and low steady-state residual error simultaneously. Simulation results under various noise scenarios validate the superior performance of the proposed algorithms as compared to existing counterparts.