Wavelet Neural Network And Its Application

Wavelet analysis and neural network have been researched.Based on BP neural network,analysing the features of the BP neural network's activation function and the structure of the BP neural network,wavelets neural network is constructed with wavelet function.Fourier transform has a important role on signal processing,so the Fourier transform is introduced.A function'Fourier transform is analysed.After introducing the concept of the wavelet analysis,a serval wavelet functions is given out,so the knowledge of wavelet analysis is better understood.The multiresolution analysis has a important role on constructing wavelet function and understanding the wavelet transform. Wavelet function can discriminate function'multiresolution approximation and space and frequency'localizing.A function'wavelet transform is analysed.The function is reconstructed using low frequency coefficient and high frequency coefficient and the reconstructing error is analysed.If the number of the BP neural network'hidden layer nodes is decided according to needing,a neural network hasing three layers can approximate a continuous function with any precision.The relations of the BP neural network'output and input is a mapping relation.The BP neural network hasing n dimensional input and m dimensional output is a continuous mapping from n dimensional space to m dimensional space in a finity area.The mapping is high nonlinear.The features of the wavelet function appoximating nonlinear continuous function in compactly supported set makes wavelet neural network learn better local nonlinear continuous and fast changing function.The wavelet neural network is constucted by using neural network'weights replace the coefficient of the wavelet transform according to wavelet transform.The preprocessing layer of the wavelet neural network is wavelet transform and activation function consists of the hidden layer of the wavelet neural network.If the hidden layer of the wavelet neural network is wavelet function,a new wavelet neural network is constructed.The wavelet neural network has better ability of approximation allowing error and beacause of the better features of the wavelet transform and the ability of the neural network'learning itself.Based on BP neural network,a Legendre wavelets neural network is constructed with Legendre wavelets. The Legendre wavelets defined on the interval has the features of piecewise expression and being polynomials,so the Legendre wavelets neural network has the advantange of simple structure and fast convengencespeed.Trained by BP algorithm,the Legendre wavelets neural network with six wavelet basis functions is used to learn a function and better approximate result is obtained.