Abstract: An application of Beta wavelet networks to
synthesize pass-high and pass-low wavelet filters is investigated in
this work. A Beta wavelet network is constructed using a parametric
function called Beta function in order to resolve some nonlinear
approximation problem. We combine the filter design theory with
wavelet network approximation to synthesize perfect filter
reconstruction. The order filter is given by the number of neurons in
the hidden layer of the neural network. In this paper we use only the
first derivative of Beta function to illustrate the proposed design
procedures and exhibit its performance.
Abstract: This paper proposes a comparison between wavelet neural networks (WNN), RBF neural network and polynomial approximation in term of 1-D and 2-D functions approximation. We present a novel wavelet neural network, based on Beta wavelets, for 1-D and 2-D functions approximation. Our purpose is to approximate an unknown function f: Rn - R from scattered samples (xi; y = f(xi)) i=1....n, where first, we have little a priori knowledge on the unknown function f: it lives in some infinite dimensional smooth function space and second the function approximation process is performed iteratively: each new measure on the function (xi; f(xi)) is used to compute a new estimate f as an approximation of the function f. Simulation results are demonstrated to validate the generalization ability and efficiency of the proposed Beta wavelet network.