Volterra Kernel Identification by Wavelet Networks and its Applications to Nonlinear Nonstationary Time Series
Minu.K.K. and Jessy John.C.
Volterra series representation is the earliest method for the description of a nonlinear system. Volterra kernels completely characterize the Volterra series. Volterra series has been extended to incorporate the non stationarity. Even though Volterra series modeling was suggested much earlier, no canonical method for the identification of the Volterra kernel was available due to the exponential growth of parameters in the kernel with the order of expansion. Developments in the theories of Artificial Neural Networks and Wavelets gave rise to the concept of Wavelet Networks which are found to be effective in modeling the nonlinear nonstationary structures. In this paper a method for identifying the Volterra kernels is developed by applying Wavelet Network. Thereby the Volterra series is applied for the analysis of nonlinear nonstationary time series providing a powerful method in the analysis of nonlinear nonstationary time series, which appear quite often in various fields of study.
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