Spectral characterization of n-th order cyclostationarity

The spectral characterization of second-order (or wide-sense) cyclostationarity gives rise to a generalization of the Wiener relation between the power spectral density and the autocorrelation associated with second-order stationary time-series. This generalization, called the cyclic Wiener relation, is a Fourier transform relation between the spectral autocorrelation function and the cyclic temporal autocorrelation function, both defined in terms of time averages on a single time-series. The spectral characterization is generalized from second-order cyclostationarity to n-th order cyclostationarity for n=2,3,4,5,. . ., and some basic properties of the generalised spectral characterization are presented. These include a further generalization of the Wiener relation, called the n-th order cyclic Wiener relation, which relates the n-th order joint cyclic temporal moment function to the n-th order joint spectral moment function.<>