A new algorithm of realizing arbitrary nonlinear filters-adaptive neural filters

We propose a novel class of nonlinear adaptive filters-adaptive neural filters based on a family of nonlinear functions f(·) used in neural network, and we introduce several concepts of mapping pairs [X _i,y_i (i=1,...,N)]. An important idea is to approximate adaptive filters by iteratively searching f_i(·): Rⁿ→R (i=1,...,K) in N-dimensional topological space, where the f_i(·) is a member of the family of nonlinear functions. Another new approach suggested in this paper is to use nonlinear distribution chart, in which the characteristics of nonlinearity in a given approximation (f_i (·):Rⁿ→R i=1,...,K) can be clearly found, based on the nonlinear distribution charts. There are three steps in the new algorithm: (a) using the least mean-square algorithm to adapt linear approximation with the given approximation pairs [X_i,y_i ]: (b) drawing nonlinear distribution chart and using the new algorithm to choose the exact nonlinear function f_i(·); (c) adding the hidden nodes with the algorithm. If the established nodes cannot reach the desired precision, until the desired accuracy achieves