Robust Frequency - Selective Filtering usingWeighted Myriad Filters

Weighted Myriad Smoothers have recently been proposed as a class of nonlinear l-ters for robust non-Gaussian signal processing in impulsive noise environments. However , weighted myriad smoothers are severely limited, since their weights are restricted to be non-negative. This constraint makes them unusable in bandpass or highpass ltering applications which require negative lter weights. Further, they are incapable of amplifying selected frequency components of an input signal, since the output of a weighted myriad smoother always lies within the dynamic range of its input samples. In this paper, we generalize the weighted myriad smoother to a richer structure, a weighted myriad lter admitting real-valued weights. This involves assigning a pair of lter weights, one positive and the other negative, to each of the input samples. Equivalently, the lter can be described as a weighted myriad smoother applied to a transformed set of samples that includes the original input samples as well as their negatives. The weighted myriad lter is analogous to a normalized linear FIR lter with real-valued weights whose absolute values sum to unity. By suitably scaling the output of the weighted myriad lter, we extend it to yield the so-called scaled weighted myriad lter, which includes (but is more powerful than) the traditional unconstrained linear FIR lter. Finally, we derive stochastic gradient-based nonlinear adaptive algorithms for the optimization of these novel myriad lters under the mean square error criterion.