Identification of quadratic Volterra systems driven by non-Gaussian processes

A nonlinear and time-invariant system representable by a Volterra series up to second order is considered. Closed-form expressions for the generalized transfer functions of first and second order are derived for non-Gaussian stationary input processes whose trispectrum vanishes. It is shown that the parameters obtained are optimum in the mean square sense. Once the system is identified, a closed-form expression for the quadratic coherence is derived. This expression simplifies to well-known results when the system is linear or its input is Gaussian. The quadratic coherence is validated using simulated data as input to a known second-order Volterra filter with known statistic