A simplified variable step-size gradient algorithm for IIR notch filtering: Properties and application

In this paper, first of all, a simplified variable step-size (VSS) plain gradient (SVSS-PG) algorithm is proposed for a second-order IIR notch filter with constrained poles and zeros. It makes the filter converge significantly faster than its original version (PG algorithm) with a fixed step size, at the expense of a small amount of computational cost increase. Secondly, the performance of the proposed SVSS-PG algorithm is analyzed in some detail. Difference equations are derived to reveal the dynamics of the proposed algorithm. Thirdly, the SVSS-PG based IIR notch filter is applied to active noise control (ANC) of sinusoidal noises generated by rotating machines. Finally, extensive simulations are provided to show the effectiveness of the proposed algorithm, the validity of the analytical results, and the improved capability of the ANC system using the proposed VSS-type algorithm.