From first principles, a method is presented to generate the minimal region in the n- dimensional frequency space necessary for a complete nonredundant representation of the support of an N-th order joint cumulant spectral function. This region is commonly referred to as the N-th order principal domain (PD) or the support set of the N-th order cumulant spectral function (which is the Fourier transform of the N-th order joint cumulant function). The procedure is derived from a composition of the symmetry operations inherent to an N-fold product of the Fourier transforms of a random time series. For exposition, we present an example using the second-order cumulant spectral function. Explicit representations of the PDs for cumulant spectra of orders up to and including order five are included.
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