Second-order Volterra system identification (Q2734437)

The paper deals with second-order Volterra system identification. The system is described as NEWLINE\[NEWLINEy(n)= h_0+ \sum^\infty_{i=0} h_1(i) u(n- i)+ \sum^\infty_{i= 0} \sum^\infty_{j=0} h_2(i,j) u(n-i) u(n- j)+ \eta(n)NEWLINE\]NEWLINE with input \(u\), output \(y\) and disturbance \(\eta\). The input is assumed to be a zero mean \(k\)th-order stationary stochastic process with a positive power spectral density. Closed-form expressions for the Volterra kernels and for general random inputs are derived. The formulas are rather long and complicated. Input-output crosscumulant expressions are formulated as Fredholm integral equations. They are approximately solved by the determinant method. Exact expressions of the Volterra kernels are obtained for special filtered signals.