A variable step-size filtered-x least mean square algorithm for continuously varying noise

The filtered-x least mean square algorithm (FxLMS) is a widely used technique in active noise control. In a conventional FxLMS algorithm, the value of convergence coefficient is kept constant which may not yield optimum performance if frequency of the primary noise changes. For some frequencies, this may result into a slower convergence and for some other frequencies, it may lead to instability. To deal with this situation, a normalized FxLMS algorithm, in which the convergence coefficient is normalized with the power of the filtered reference signal, is proposed. In the eigenvalue equalization method, the magnitude of secondary path transfer function is equalized such that the power of filtered reference signal remains equal at all the frequencies. The method proposed in this paper attempts to optimally adapt the convergence coefficient of the FxLMS algorithm for continuously varying noise. It is based on estimating how frequency of noise is varying using fast Fourier transforms of the reference signal and then, using this information to optimally adapt the convergence coefficient. The optimum value of the convergence coefficient is decided based upon the power and delay of the filtered reference signal and sampling frequency. A numerical study in a 3D acoustic cavity is presented to test the effectiveness of the proposed method and the results are also compared with the conventional FxLMS and the frequency-domain FxLMS algorithm. It is found that the proposed method leads to a faster convergence which results in higher noise reduction especially when the frequency of noise varies continuously. Simulation results show that the noise reduction obtained depends upon the rate at which the frequency of the primary noise varies. The higher the rate of variation and the duration for which the variation exist, the better the performance of the proposed method is over the conventional FxLMS algorithm in terms of noise reduction. The frequency-domain FxLMS algorithm is not found to be effective if the frequency of primary noise varies continuously.