Bispectrum estimation via autoregressive modeling: a group delay approach

A new method of bispectrum estimation by an AR (autoregressive) model has been proposed for a signal which is the output of a mixed-phase system driven by a non-Gaussian noise. This is achieved by relating the bispectrum phase and magnitude to the system group delay functions. The maximum and minimum phase property of the group delay functions makes AR bispectrum estimation possible, since there exists a direct relation between the cepstral and AR coefficients. The proposed method uses only the bispectrum information and is applicable for moving average (MA) or AR or ARMA system with either mixed-phase poles or mixed-phase zeros or both. Unlike some of the existing methods, it uses all the bispectral information and does not involve any solution of a system of equations. The method has been illustrated for MA and ARMA systems using sample root mean square error as the performance index