FUZZY PREDICTION AND FILTERING IN IMPULSIVE NOISE

Additive fuzzy systems can filter impulsive noise from signals. Alpha- stable statistics model the impulsiveness as a parametrized family of probability density functions or unit-area bell curves. The bell-curve parameter alpha ranges through the interval (0,2] and gives the Gauss ian bell curve when alpha = 2 and gives the Cauchy bell curve when alp ha = 1. The impulsiveness grows as alpha falls and the bell curves hav e thicker tails. Only the Gaussian statistics have finite variances or finite higher moments. An additive fuzzy system can learn ellipsoidal fuzzy rule patches from a new pseudo-covariation matrix or measure of alpha-stable covariation. Mahalanobis distance gives a joint set func tion for the learned if-part fuzzy sets of the if-then rules, The join t set function preserves input correlations that factored set function s ignore, Competitive learning tunes the local means and pseudo-covari ations of the alpha-stable statistics and thus tunes the fuzzy rules. Then the covariation rules can both predict nonlinear signals in impul sive noise and filter the impulsive noise in time-series data, The fuz zy system filtered such noise better than did a benchmark radial basis neural network.