Convergence Behavior of the filtered-x LMS Algorithm for Active Noise Caneller

Application of the Filtered-X LMS adaptive filter to active noise cancellation requires to estimate the transfer characteristics between the output and the error signal of the adaptive canceler. In this paper, we derive an adaptive cancellation algorithm and analyze is convergence behavior when the acoustic noise is assumed to consist of multiple sinusoids. The results of the convergence analysis of the Filtered-X LMS algorithm indicate that the effects of parameter estimation inaccuracy on the convergence behavior of the algorithm are characterize by two distinct components : Phase estimation error and estimated magnitude. In particular, the convergence of the Filtered-X LMS algorithm is show to be strongly affected by the accuracy of the phase response estimate. Simulation results of the algorithm are presented which support the theoretical convergence analysis.