ARMA bispectrum approach to nonminimum phase system identification

An identification procedure is proposed for a nonGaussian white-noise-driven, linear, time-invariant, nonminimum-phase FIR (finite-impulse response) system. The method is based on parametric modeling of the third moments of the output sequence and uses causal and anticausal autoregressive moving-average (ARMA) models. The magnitude and phase response of the system are expressed in terms of the AR parameters of the ARMA models. In particular, the AR part of the causal ARMA model captures the minimum-phase component of the system, and the AR part of the anticausal ARMA captures the maximum-phase component. Both sets of parameters are obtained by solving overdetermined linear systems of equations. A model-order-selection criterion based on third-order moments is proposed. The ARMA bispectrum approach is compared to more conventional approaches for magnitude and phase reconstruction. It is demonstrated that the proposed identification procedure exhibits improved modeling performance. The method does not require knowledge of the non-Gaussian noise distribution