Convergence analysis of FxLMS-based active noise control for repetitive impulses

This paper presents the performance of applying the filtered-x least mean squares (FxLMS) algorithm to attenuate repetitive impact acoustic noise. The FxLMS algorithm has been widely adopted in active noise control (ANC) system for various relatively stationary disturbances. However, its convergence behavior for transient impulse has not received as much attention. Directly applying this algorithm to individual transient event exhibit difficulties since it requires certain adaptation time to converge satisfactorily. But for transient noise with certain repeatability, the FxLMS algorithm may be capable of learning. A theoretical convergence analysis of the FxLMS algorithm for repetitive impact noise is conducted. To simplify the derivation, the secondary path is assumed to be a pure delay model. Through this analysis, a step size bound condition is derived, and an optimal step size that leads to the fastest convergence rate is determined. Then, numerical simulations are performed considering various pure delay secondary path models to validate the theoretical analysis. Furthermore, a laboratory test is developed to demonstrate the capability of FxLMS algorithm for active control of repetitive impact noise. The analysis shows promising results of applying active noise control system with the FxLMS algorithm to repetitive transient noise typically seen in industrial facilities.