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

Abstract

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.

Review of Advances in Active Impulsive Noise Control with Focus on Adaptive Algorithms

“…Wu and Qiu utilized the Fair function to transform the error signal, facilitating the setting of thresholds for error signals [33]. Akhter introduced a hyperbolic tangent threshold transformation for both the reference and error signals, replacing the manual threshold-setting approach [34]. Sun improved the FLMM's performance by substituting a more precise method for estimating the proportion of the distribution in the reference noise with a higher degree of accuracy [35].…”

Delayless Block Individual-Weighting-Factors Sign Subband Adaptive Filters With an Improved Band-Dependent Variable Step-Size

“…5 since the conventional AINC algorithms exhibited unstable convergence performance. In the simulations, two existing AINC algorithms, i.e., modified normalized filtered-x least mean p-power (MNFxLMP) [23] and fractional FxLMS algorithm with a modified tanh threshold function (MTanh-Th-FrLMS) [25], were considered. In the MNFxLMP, the parameter p was set to α − 0.01 as recommended.…”

“…Here, α controls the impulsive nature. Second, the peaky reference/error signals are truncated with a threshold value because the weight can be largely fluctuated by the peaky samples during the weight update due to the modelling error, which finally degrades the convergence performance [25]. However, the aforementioned two approaches should estimate the value of α or the reference/error signal statistic to determine the threshold value, which may not be available in practice.…”

“…FIGURE 5. ANR performance obtained by the MNFxLMP[23] and the MTanh-Th-FrLMS[25] when (a) α = 1 and (b) α = 0.8.…”