Higher-order statistics for Rice's representation of cyclostationary signals

The role played by the higher-order wide-sense cyclostationarity properties in Rice's representation of a signal is investigated. Specifically, formulas relating higher-order cyclic spectra of signals involved in Rice's representation of a signal exhibiting cyclostationarity are derived. It is shown that some known results relative to second-order cyclic spectra cannot be extended to higher orders. Furthermore, with reference to strictly band-limited signals, inclusion relationships for the spectral supports (in the space of the cycle and spectral frequencies) of the considered higher-order spectra are determined. Finally, as examples of application, the problem of cycloergodicity for the higher-order cyclic spectra of a quadrature amplitude modulated signal and the bandpass linear time-invariant system identification are considered. (C) 1997 Elsevier Science B.V.