Exploitation of cyclostationarity for identifying the Volterra kernels of nonlinear systems

A class of random time-series inputs for nonlinear time-invariant systems that permit the analytical specification of a set of operators on the input that are orthonormal over all time to the Volterra operators for all orders and all lag sets is introduced. The time series in this class are cyclostationary and complex valued. The orthonormal operators are used to obtain an input-output type of cross-correlation formula for identifying the individual Volterra kernels of arbitrary order for a nonlinear system of possibly infinite order and possibly infinite memory. The real parts of the complex-valued inputs in this class comprise a class of real-valued inputs for which the same sets of specified operators apply. However, the orthogonality for different orders holds for these real inputs only for Volterra operators of order less than the order of the specified operator. Thus, these real inputs can be used to identify Volterra kernels only for finite-order systems. Frequency-domain counterparts of the time-domain methods that can utilize an FFT algorithm are developed