One Dimensional Nonlinear Adaptive Filters for Impulse Noise Suppression

An adaptive filter is essentially a digital filter with self-adjusting characteristic. It adapts, automatically, to changes in its input signals. The contamination of a signal of interest by other unwanted, often lager, signals or noise is a problem often encountered in many applications. Typical applications where adaptive filters are appropriate are the following: Digital communication using a spread spectrum, where a large jamming signal, possibly intended to disrupt communication, could interfere with the desired signal. The interference often occupies a narrow but unknown band within the wideband spectrum, and can only be effectively dealt with adaptively. Digital data communication over the telephone channel at the high data rate. Adaptive algorithms are used to adjust the coefficients of the digital filter such that error signal is minimized according to some criterion, for example in the least squares sense. The Nonlinear Normalized Mean Square algorithm is applicable to a wide variety of nonlinear filters. In this paper, algorithms are developed for an optimal time-varying step-size for FIR, Volterra, weighted median and weighted myriad filters. Key-Words: Adaptive filters, nonlinear filters, weighted median filter, weighted myriad filter, impulse noise.