Properties of FXLMS-Based Narrowband Active Noise Control With Online Secondary-Path Modeling

Rotating machines such as diesel engines, cutting machines, fans, motors, etc., generate sinusoidal noise signals that may be effectively reduced by narrowband active noise control (ANC) systems. In this paper, a typical filtered-X LMS (FXLMS) based narrowband ANC system equipped with an online secondary-path modeling subsystem is analyzed in detail. First, difference equations governing the dynamics of the FXLMS algorithm for secondary source synthesis and the LMS algorithm for secondary-path estimation are derived in terms of convergence in both mean and mean square. Steady-state expressions for mean-square error (MSE) as well as the residual noise power are then developed in closed form. Extensive simulations are performed to demonstrate the validity of the analytical results.