Combating impulse noise in adaptive filters with signed regressor adaptive threshold nonlinear algorithm

In this paper, we first present mathematical models for two types of impulse noise in adaptive filtering systems; one in additive observation noise and another at filter input. To combat such impulse noise, a new algorithm named signed regressor adaptive threshold nonlinear algorithm (SR-ATNA) is proposed. Through analysis and experiment, we demonstrate effectiveness of the SR-ATNA in making adaptive filters highly robust in the presence of both types of impulse noise while realizing fast convergence. Good agreement between simulated and theoretical convergence behavior in transient phase, and in steady state as well, proves the validity of the analysis.