LINEAR PREDICTION, MAXIMUM FLATNESS, MAXIMUM-ENTROPY, AND AR POLYSPECTRAL ESTIMATION

It is well known in second-order statistics based autoregressive (AR) spectral estimation that the linear prediction spectral estimator is equivalent to the maximum entropy spectral estimator and they are also equivalent to the maximum spectral flatness spectral estimator for AR processes of known order. In this paper, we present a new theoretical background for the polyspectral estimation and modeling of non-Gaussian AR processes which includes a new higher order statistics (HOS) based linear prediction error filter and associated linear prediction polyspectral estimator, a maximum polyspectral flatness polyspectral estimator, a maximum higher order entropy polyspectral estimator, as well as the equivalencies among these polyspectral estimators.