Identification of infinite degree Volterra series in the time and frequency domains

Volterra series (VS) are widely used in non-linear dynamical system identification. Much physical information about a system can be extracted from the corresponding VS model. Most non-linear frequency domain representations have been based on VS models through the application of the Fourier transform. But the fact that the number of the parameters to be identified in a VS model increases exponentially with the size of the VS model restricts its application. The involvement of kernel methods has been shown significantly to reduce the burden of the computation, with the potential to increase the practical usability of VS and the methods that are based on it. This paper presents the identification of infinite degree, finite memory length, time-invariant, discrete VS from the general reproducing kernel Hilbert space point of view and introduces its extension to the estimation of generalized frequency response functions.