A Study Of Adaptive Filtering Algorithms And Their Applications In α-Stable Impulsive Noise Environments

distribution has been the focus of intensive research in signal processing fields. This thesis mainly studies the adaptive filtering algorithms and their applications inα-stable impulsive noise. The main works can be summarized as follows.1. We start our discussion with the introduction of two important definitions: fractional lower-order moments and minimum dispersion criterion, which are the foundation of signal processing inα-stable noise environments. Then the commonly used least mean l p-norm (LMP) and recursive least l p-norm (RLP) algorithms are studied in detail. The performance of the algorithms is evaluated via simulations .2. A robust adaptive algorithm for FIR filters based on the quasi-Newton class of optimization methods is derived, which can be regarded as the improvement of RLP algorithm on the problem of stability. Moreover, a weighted least l p-norm of the output error is selected as the cost function. The proposed algorithm has a tracking ability comparable to that of RLP algorithm, while being stable numerically.3. A modified NLMP (MNLMP) algorithm for adaptive noise cancellation inα-stable environments is proposed. In the algorithm, the l p-norm of the output error is calculated to adjust the step size. During convergence, a decrease in the l p-norm of the output error results in a step size decrease. Computer simulations are presented to compare the relative performance of LMP , NLMP and MNLMP algorithms. Results show that MNLMP algorithm has a higher output SNR than that of LMP and NLMP algorithms for each input SNR.