Content area
Full text
Keywords Autoregressive modelling, Bispectrum, Estimation
Abstract In this paper we present a new autoregressive (AR) method for bispectrum estimation defined in terms of its third-moment sequence. The method is based on the segmentation of data into coupled records, and can be considered to be a modification of the "third order recursion method"(TOR). Its foundation resides in considering the data of the process at the left and the right of each record (needed for the calculation of third moment sequence) as not null and taking them as the data corresponding to the preceding and succeeding record respectively. Several simulated examples show that this method allows model parameters to be obtained with greater precision, most of all when only few data are available per record. The influence of factors such as number of data and records, model order, and added white and coloured Gaussian noise on the parameters' estimation is also considered.
1. Introduction
Power spectrum has been the fundamental tool for digital-signal processing over the last 40 years, and many techniques for estimating it have been developed[l]. This analysis provides a full description only if the data set of the signal to be analyzed corresponds to a Gaussian process of known mean value. This is due to the fact that the information contained in the power spectrum is essentially the same as that in the autocorrelation sequence, which at the same time describes its second-order statistics[2]. Nevertheless, in many real situations the process is not a Gaussian one and, therefore, a total description requires information of the polyspectra defined in terms of the higher-order cumulants of the process to be obtained[3]. Bispectrum is the polyspectrum that has been most extensively analyzed and used in practical problems[4-6]. This is defined as the 2-D Fourier Transform of...