Novel Approaches In Stochastic Signal Processing

Higher-Order Spectra (HOS) and artificial neural netwroks have been received considerable attention in recent years. Much progress has been made in theoretical analysis and practical applications of higher-order spectra. There are three reasons for using higher-order spectra analysis in signal processing: 1) to extract the information due to deviation from Gaussianity, 2) to recover the correct phase information of the signal, 3) to detect and quantify nonlinearities in time series. The main reason for using neural network in time series analysis and system identification is that a trained neural network has the capability to approximate a arbitrary bounded continuous function.In this thesis, the author uses higher-order spectra and neural networks to systematically study the stochastic signal. The following achievements have been made in this thesis:we first propose a Sigma-Pi-linked neural network model, then derive the learning rules, and successfully apply to linear as well nonlinear system modeling and weather forecasting.we propose the novel approach for the testing for linearity of a time series or unknown model using the higher-order spectra in chapter 3.A new technique of faults identification and condition monitoring of three-phase induction machine using bispectrum has been presented.A generalized moment-space-feature (GMFS) has been proposed, and has been applied to the faults classification and condition monitoring to three phase induction machine. This GMFS can provide much more information than that of MFS. Very promising results have been obtained.A new algorithm based on the bicepstrum for the non-minimum phase system identification are proposed. This algorithm reconstruct the minimum phase component and maximum phase component separately, no phase unwrapping is needed.A cumulant-based recursive least square (CRLS) algorithm has been presented for the nonminimum phase system identification. This algorithm is flexible enough to be applied on AR, MA, ARMA model.Finally, a novel order-recursive algorithm for order determination of nonminimum phase system is proposed. This algorithm is based on the second- and third-order cumulant of the analysed signal. The order and the associated coefficients of the model are obtained simutaneously.