Identification of second-order Volterra filters driven by non-Gaussian stationary processes

摘要

Abstract: Some recent results relating to system identification are described and illustrated in this contribution. The system considered is nonlinear and time- invariant, being represented by a Volterra series up to second order. Closed- form expressions for the transfer functions of first and second order are derived for a class of non-Gaussian stationary input processes. It is shown that the obtained parameters are optimum in the mean square sense. Once the system is identified, we derive a closed-form expression for the quadratic coherence that is a measure of the goodness of fit of the quadratic model. It is shown that this expression simplifies to well known results when the system is linear or its input is Gaussian. Furthermore, we develop estimates for the transfer functions and the quadratic coherence from spectral and bispectral estimates, based on averaged periodograms and biperiodograms of data stretches of the observed input and output of the system. This method is tested and validated by using simulated input-output data of a known quadratically nonlinear system, with known input signal statistic, Finally, we discuss the problem of testing a specified value of the quadratic coherence. !15