Convergence of the Filtered-x LMS Algorithm for Canceling Multiple Sinusoidal Acoustic Noise

Application of the filtered-x LMS adaptive filter to active noise cancellation requires to estimate the transfer charactersitics between the output and the error signal of the adaptive canceler. In this paper, we derive the filtered-x adaptive noise cancellation algorithm and analyze its convergence behavior when the acoustic noise consists of multiple sinusoids. The results of the convergence analysis of the filtered-x LMS algorithm indicate that the effects of the parameter estimation inaccuracy on the convergence behavior of the algorithm are characterized by two distinct components : Phase estimation error and estimated gain. In particular, the convergence is shown to strongly affected by the accuracy of the phase response estimate. Simulation results are presented to support the theoretical convergence analysis.