Volterra Systems with Random Inputs: A Formalized Approach

The object of this work is to investigate the problem of Volterra systems driven by random inputs. General expressions for the second-order output statistics of a Volterra system are obtained and formalized. The input-output crosscorrelation and output autocorrelation functions are expressed in terms of higher order input autocorrelation functions. In the frequency domain, the cross-power and output power spectral densities are expressed in terms of higher order input power spectral densities. These expressions are used to obtain closed-form equations for the cross-power and output power spectral densities of a Volterra system driven by a real, stationary, zero-mean Gaussian input.