Higher-order cyclostationarity properties of sampled time-series

In this paper, the higher-order wide-sense stationarity or cyclostationarity properties of a continuous-time-series and those of the discrete-time-series of its samples are related in the fraction-of-time probability framework. In particular, for a cyclostationary continuous-time-series, it is shown how the ratio of the sampling period to the cyclostationarity period affects the cyclostationarity properties of the discrete-time-series. Moreover, it is shown that the higher-order wide-sense stationarity or cyclostationarity of a strictly band limited continuous-time-series can be analyzed by examining that exhibited by the discrete-time-series of its samples provided that the sampling rate is sufficiently high. Finally, the derived results are interpreted in the stochastic process framework.