Abstract
Yang and Chi proposed a family of 1-D criteria for estimating the phase of a 1-D nonminimum phase linear time-invariant (LTI) system with only non-Gaussian measurements corrupted by additive Gaussian noise. The phase of the LTI system is obtained through an iterative algorithm which processes the given measurements by an ARMA allpass model such that a single absolute Mth-order (M≥3) cumulant of the all-pass model output is maximum. In this paper, a family of 1-D and 2-D criteria, in which Yang and Chi's 1-D criteria are included, is proposed for phase estimation using a Fourier series based allpass model. The optimum allpass models for 1-D and 2-D LTI systems are obtained by a 1-D and a 2-D iterative algorithms, respectively. The paper concludes with some simulation results followed by some conclusions.