A new algorithm of realizing arbitrary nonlinear filters-adaptive neural filters
J. Zhan, F. Li · 2002
We propose a novel class of nonlinear adaptive filters-adaptive neural filters based on a family of nonlinear functions f(/spl middot/) used in neural network, and we introduce several concepts of mapping pairs [X/sub i/,y/sub i/ (i=1,...,N)]. An important idea is to approximate adaptive filters by iteratively searching f/sub i/(/spl middot/): R/sup n//spl rarr/R (i=1,...,K) in N-dimensional topological space, where the f/sub i/(/spl middot/) 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/sub i/(/spl middot/):R/sup n//spl rarr/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/sub i/,y/sub i/]: (b) drawing nonlinear distribution chart and using the new algorithm to choose the exact nonlinear function f/sub i/(/spl middot/); (c) adding the hidden nodes with the algorithm. If the established nodes cannot reach the desired precision, until the desired accuracy achieves.>