Stochastic Analysis of FxLMS Algorithm for Feedback Active Noise Control

Feedback active noise control (ANC) systems are effective in reducing predictable noise, e.g. periodic, narrowband and colored noise. There are still few studies on the theoretical analysis of feedback ANC systems, and are limited to idealized signals such as sinusoidal or Gaussian signals. This paper presents the stochastic analysis of a feedback ANC system based on the filtered-x least mean square (FxLMS) algorithm, which is not relying on a specific noise model and perfect secondary path. The equations for the mean and mean-square convergence behavior are derived. Extensive simulations of sinusoidal, band-limited white noise, and hybrid signals illustrate the accuracy of the analysis.