/spl alpha/-weighted cumulant projections: a novel tool for system identification

Abstract

We propose a new tool, the /spl alpha/-weighted cumulant projection (/spl alpha/-WCP), which is an one-dimensional projection of the exponentially weighted n/sup th/ order cumulants of a process. We show that a real, stable and generally nonminimum phase LTI system can be identified from a single projection, whereas a complex system requires two projections corresponding to two different values of the weight /spl alpha/. We develop two methods for system identification, one based on the complex cepstrum of /spl alpha/-WCP and the other based on the Fourier-phase of /spl alpha/-WCP. The proposed methods exhibit comparable statistical performance and substantially lower computational complexity compared to existing higher-order spectra based techniques.