System identification and modeling of non-stationary signals using the Wold-Cramer representation

In this paper we present an application of the Wold-Cramer representation of non-stationary signals to system identification and modeling. According to the Wold-Cramer representation, a non-stationary signal can be expressed as an infinite sum of sinusoids with time-varying random magnitudes and phases. For the identification of linear time-invariant (LTI) systems, we relate the Wold-Cramer representations of the system´s input and output to obtain estimates of the magnitude and phase frequency responses of the system. Our procedure permits the identification of non-minimum phase systems. Furthermore, we show that when the system output is noisy, and the noise is stationary it is possible to avoid the effects of the noise in the identification. If the noise is non-stationary and Gaussian, one needs to consider the evolutionary bispectrum, recently introduced by Priestley, to get rid of the noise. The analysis also provides a model for a non-stationary signal, as the output of a cascade of a linear time-varying and a linear time-invariant systems with stationary white noise as input. To illustrate our procedure, we present a simulation of the identification of a non-minimum phase system