All-pass identification with modulated cumulant sequences
Thomas Kaiser · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1996
Since a nonminimum-phase system can be divided into a minimum-phase system and into an allpass system, the parameters of the minimum-phase part can be estimated with well known algorithms based on second-order statistics, while for the allpass part higher-order statistics are useful. In this article we present a new algorithm for allpass identification, which processes the third-order cumulant (moment) sequence in contrast to known methods in a linear manner. Thus the inherent problems of nonlinear methods--the not-guaranteed global convergence and the high computational costs--can be avoided. The proposed method reduces the allpass parameter estimation problem to the estimation of MA (Moving Average)-parameters by use of the modulated third-order moment sequence. Some simulation results are provided to show that the algorithm works well. In addition we will compare this algorithm to the well known extended Yule-Walker equations based on third-order cumulant (moment) sequences.