A study of active impulsive noise control based on an adjustable fractional cost function

Active noise control (ANC) systems using the classic filtered-x least mean square (FxLMS) algorithm are ineffective in the control of impulsive noise. Alternative algorithms were proposed to serve this purpose, which mainly consider impulsive noise having instantly decayed impulses. Nevertheless, impulsive noise from real-life applications typically has a finite decaying time. The effectiveness of existing algorithms on the control of such impulsive noise is largely untested. To this end, this paper proposes an enhanced FxLMS algorithm by replacing the cost function with an adjustable fractional function to perform nonlinear compression transform of the error signal to resolve the challenge of the non-Gaussian distribution of impulsive noise on an ANC algorithm. An adjustable compression factor is also introduced to vary the compression shape of the error function to suit impulsive noise of different intensities. A time-varying normalized function is introduced to adaptively adjust the step-size in the filter iteration to further speed up the system convergence. Simulation results show that the proposed algorithm not only has a better performance than existing ANC algorithms on the control of impulsive noise with finite decaying time, it also outperforms the existing algorithms in the control of instantly decayed impulsive noise and broadband Gaussian noise.