FIR modeling using log-bispectra: Weighted least-squares algorithms and performance analysis

Identification of non-minimum-phase systems with finite impulse response (FIR) is addressed in the bispectrum domain. A phase retrieval algorithm, based on the log-bispectrum, is extended to log-magnitude reconstruction. Both linear-equation-based estimators are then combined to form an integrated, nonparametric system identification method. Weighted forms of these estimators are developed, which are asymptotically minimum-variance in the class of weighted least-squares estimators. Asymptotic variance expressions are derived for both the weighted and the unweighted forms. Theory and simulations illustrate that the approaches can identify non-minimum-phase MA (moving-average) models using output data which may be corrupted by additive Gaussian noise of unknown covariance.