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 bispectrum-based phase retrieval algorithm is modified to handle the phase wrapping problem and is extended to log-magnitude reconstruction. Both linear-equation-based estimators (the phase and the log-magnitude) are then combined to form an integrated, nonparametric system identification method. Weighted forms of the estimators that are asymptotically minimum-variance in the class of weighted least-squares estimators are developed. Asymptotic variance expressions are derived for both the weighted and the unweighted forms. Theory and simulations illustrate that these approaches can identify non-minimum-phase moving-average models, using output data that may be corrupted by additive Gaussian noise of unknown covariance. Due to their nonparametric nature, the proposed algorithms outperform existing linear equation cumulant-based modeling methods in the case of model order mismatch.<>