Cyclostationarity: Limits and generalizations

Recent developments and applications of cyclostationary signal analysis are reviewed in the companion paper “Cyclostationarity: New trends and applications”. In this paper, limits to the applicability of the cyclostationary model in the presence of relative motion between transmitter and receiver are enlightened. Two new classes of signals that extend the class of the almost-cyclostationary signals and allow one to overcome these limits are reviewed. The new classes are those of the generalized almost-cyclostationary signals and of the spectrally correlated signals. Probabilistic characterization, statistical function estimation, and time-sampling are reviewed for both classes of signals and a comprehensive bibliography commented. The impact of these models on classical problems considered in the cyclostationary framework is illustrated. Finally, the new class of the oscillatory almost-cyclostationary processes is introduced and characterized.