Abstract: In this paper, we use a new type of network, wavelet network, to approximate a nonlinear function. The wavelet network is studied with the combination of the traditional neural network theory with the most advanced math tool of analysis and it contains wavelons whose activation function is wavelet constructed with sigmoid function. This paper illuminates the approximation theory of the wavelet network and constructs a practical wavelet network. We also discuss the choice of the mother wavelet and the algorithm of decreasing the number of wavelons. The experimental results show that the wavelet network has achieved a high accuracy for approximating nonlinear function, and the scale of the network is small.

Key words: neural network, function approximation, wavelet