Study on autoregressive trispectrum and its slices

This paper is concerned with the development of techniques to detect and analyse no-Gaussian and non-linear signals. The methods developed are based on the concepts of higher-order cumulants, in particular the fourth-order cumulants for trispectrum. The study has been dominated by work on the trispectrum and its slices. Modeling and analyzing have been done when a zero mean and non-Gaussian white noise interferes with a vibrant system. For certain condition, short data and weak signals, a new method of parameter modelling of the autoregressive (AR) bispectra and trispectra models based on time series are presented. Approaches are described that enable the estimation and display of power spectrum, bispectra and trispectra, especially the slices of high-order spectra (HOS). After theory analysis, experiments have been done to show the characteristic of HOS in processing the sampled data. A series of contrast have been carried on to assess the estimation of HOS. The experimental and theoretical results show that the auturegressive trispectrum and its slices are more accurate to analyze the non-linear and non-Gaussian signals.