The Filtered-X Least-Mean-Square (FXLMS) algorithm is widely used in active noise control due to its robustness, simplicity, and ability to be implemented in real time. In a feedforward implementation of the FXLMS algorithm, a reference signal that is highly correlated with the noise to be controlled is filtered with an estimate of the transfer function of the secondary path. The convergence characteristics of the FXLMS algorithm have been well studied. A convergence parameter is used to optimize the convergence of the algorithm. However, the optimal value for the convergence parameter is frequency dependent. Thus for noise containing multiple tones at different frequencies the convergence parameter can only be optimized for one of those tones. Other tones will have slower convergence rates and in general less attenuation than they would have if they were treated singly and parameters could be optimized for those frequencies separately. A method is developed to modify the magnitude response of the secondary path estimate while maintaining the original phase response, which equalizes the convergence characteristics over multiple frequencies, giving more uniform convergence and attenuation for all tones being controlled. Stability of the algorithm is not compromised. The modification to the FXLMS algorithm is relatively simple to implement and has been shown to increase overall attenuation of a signal containing multiple tones by an additional 6-9 dB.



College and Department

Physical and Mathematical Sciences; Physics and Astronomy



Date Submitted


Document Type





Active Noise Control, Eigenvalues, Algorithm, Noise, Filtered-X, LMS