Analysis of Frequency Mismatch in Narrowband Active Noise Control

This paper analyzes the effects of frequency mismatch between the actual frequency of the primary noise and the frequency of the synthesized reference signal in narrowband active noise control (ANC) systems using the filtered-X least-mean-square (FXLMS) algorithm. Two stability conditions are derived in terms of the frequency mismatch and the phase error of the estimated secondary-path model. Conditions to guarantee that ANC systems can achieve noise reduction are also developed by considering the overall effect of frequency mismatch and phase error. The optimum step-size to reach the minimum excess mean-square error is obtained and analyzed. Theoretical analysis shows that the noise reduction and convergence rate are functions of frequency mismatch, step size, and phase error in the secondary-path model for the FXLMS algorithm. Computer simulations are conducted to verify the analysis results presented in the paper.