  Kernel-based modeling of dynamic systems has garnered a significant amount of
attention in the system identification literature since its introduction to the
field. While the method was originally applied to linear impulse response
estimation in the time domain, the concepts have since been extended to the
frequency domain for estimation of frequency response functions (FRFs), as well
as to the estimation of the Volterra series in time domain. In the latter case,
smoothness and exponential decay was imposed along the hypersurfaces of the
multidimensional impulse responses, allowing lower variance estimates than
could be obtained in a simple least squares framework. The Volterra series can
also be expressed in a frequency domain context, however there are several
competing representations which all possess some unique advantages. Perhaps the
most natural representation is the generalized frequency response function
(GFRF), which is defined as the multidimensional Fourier transform of the
corresponding Volterra kernel in the time-domain series. The representation
leads to a series of frequency domain functions with increasing dimension.
