A Frequency-Domain Output-Constrained Active Noise Control Algorithm Based on an Intuitive Circulant Convolutional Penalty Factor

Abstract

Due to their computational efficiency, least mean square (LMS)–based algorithms are still widely utilized to achieve optimal control in active noise control (ANC) applications. Real-world implementation of advanced ANC functionalities, such as selective cancellation of frequencies, is nonetheless hampered by complexity trade-offs, especially with computationally-expensive frequency-domain approaches. Prevailing time-domain adaptive algorithms – proposed to alleviate complexities from transformation – continue to incur increased complexities while constraining the magnitude of frequency bins in the time-domain filters. To address existing complexities in time-domain approaches, this paper proposes a circulant convolutional penalty factor that assists the extended leaky filtered-reference LMS (FxLMS) algorithm in achieving frequency constraint without any frequency-domain transform. This circulant convolutional penalty factor is readily determined by methods for designing finite response filters, such as frequency sampling. Additionally, the coordinate descent method is adopted to further reduce the proposed algorithm's computations, significantly increasing its feasibility for implementation on conventional real-time processors. Finally, the numerical simulations performed on the measured primary and secondary paths demonstrate the effectiveness of the proposed algorithm.