An adaptive algorithm, based on modified tanh non-linearity and fractional processing, for impulsive active noise control systems

This paper presents an adaptive algorithm for active control of noise sources that are of impulsive nature. The impulsive type sources can be better modeled as a stable distribution than the Gaussian. However, for stable distributions, the variance (second order moment) is infinite. The standard adaptive filtering algorithms, which are based on minimizing variance and assuming Gaussian distribution, converge slowly or become even unstable for stable (impulsive) processes. In order to improve the performance of the standard filtered-x least mean square (FxLMS)-based impulsive active noise control (IANC) systems, we propose two enhancements in this paper. First, we propose employing modified tanh function-based nonlinear process in the reference and error paths of the standard FxLMS algorithm. The main idea is to automatically give an appropriate weight to the various samples in the process, i.e. appropriately threshold the very large values so that system remains stable, and give more weight to samples below threshold limit so that the convergence speed can be improved. A second proposal is to incorporate the fractional-gradient computation in the update vector of IANC adaptive filter. Computer simulations have been carried out using experimental data for the acoustic paths. The simulation results demonstrate that the proposed algorithm is very effective for IANC systems.