Statistical properties of the FXLMS-based narrowband active noise control system

Noise signals generated by rotating machines such as diesel engines, cutting machines, fans, etc. may be modeled as noisy sinusoidal signals which can be successfully suppressed by narrowband active noise control (ANC) systems. In this paper, the statistical performance of such a conventional filtered-X LMS (FXLMS) based narrowband ANC system is investigated in detail. First, difference equations governing the dynamics of the system are derived in terms of convergence of the mean and mean square estimation errors for the discrete Fourier coefficients (DFC) of the secondary source. Steady-state expressions for DFC estimation mean square error (MSE) as well as the remaining noise power are then developed in closed forms. A stability bound for the FXLMS in the mean sense is also derived. Extensive simulations are performed to demonstrate the validity of the analytical findings.