Research And Application Of Dynamical Neural Network And Fractional Fourier Transform

The Fractional Fourier Transform is a generalization of the Fourier Transform. It is a time-frequency analysis algorithm in essence. The Fractional Fourier Transform has many excellent properties. It is widely used in nonstationary signal analysis and processing.In this thesis, the Fractional Fourier Transform is used to extract appropriate spike features from scalp EEG signals, based on spikes having the property of Gauss function. Because spikes and background signals have different properties in Fractional Fourier region, first the wavelet transform is used to the scalp EEG signals to reduce affect of background noise; then in proper Fractional Fourier region, the Gauss function is used to simulate the spikes; the good extracting features can be acquired.The Fractional Fourier Transform is sensitive to secondary phasic of linear chirplet. The Fractional Fourier Transform is applied to parameter estimate of Gauss linear chirplet's adaptive decompose algorithm. Because Gauss linear chirplet's model has different width and high in different Fractional Fourier region, a Gauss linear chirplet component that stands out background noise can be acquired to accurately estimate parameter in proper Fractional Fourier region.Basic Elman network is one of the dynamically recurrent neural networks. Its structure is relatively simple; its operation is relatively small; but its dynamical property is sufficient. So it is widely used. Traditionarily, BP algorithm based on grads descending and extended Kalman filter algorithm are used to Basic Elman network's training. But these algorithms have respective merits and lacks. Extended Kalman filter algorithm can quickly converge to convergence. But result is not adequately accurate. BP algorithm based on grads descending can adequately accurately realize nonlinear mapping of in-out systems. But its lacks rest with convergence slowly in polar and the "bad" property of track.Considered respective merits and lacks of BP algorithm and extended Kalman filter algorithm, a new extended Kalman filter algorithm is advanced. This new algorithm consider output of hidden layer as states of nonlinear system, realize states quickly track through Extended Kalman filter algorithm and modified weights of network through grads descending. During network training, precision of convergence is improved through updating training samples.Transient chaotic neural network is a classic network that has the property of transient chaotic kinetic action. When this network is applied to optimization of function, when to exit chaotic action and how to control chaotic action become the biggest difficulty of effectively using this network. The new transient chaotic neural network algorithm selectively carefully searchs some states to clarify distribution of small and convergence region during chaotic search. According to this transcendental information, chaotic kinetic action can be controlled in reason. Another, the training of Basic Elman network is considered as search proper network weights to minify error energy function, and this problem can be regard as a complicated nonlinear function optimization, so it can be deal with transient chaotic neural network algorithm.