Sampling of generalized almost-cyclostationary signals

In this paper, the problem of sampling a continuous-time generalized almost-cyclostationary (GACS) signal is addressed. The class of such nonstationary signals includes, as a special case, the almost-cyclostationary (ACS) signals. ACS signals filtered by some linear time-variant channels are further examples. It is shown that the discrete-time signal constituted by the samples of a GACS signal is a discrete-time ACS signal. Thus, discrete-time ACS signals can arise not only from the sampling of continuous-time ACS signals but from the sampling of a wider class of nonstationary signals as well, namely, the continuous-time GACS signals. In the paper, relationships between generalized cyclic statistics of a continuous-time GACS signal and cyclic statistics of the discrete-time ACS signal constituted by its samples are derived. The problem of aliasing in the domain of the cycle frequencies is considered, and a condition assuring that the cyclic temporal moment function of the discrete-time signal can be obtained by sampling that of the continuous-time signal is determined. Finally, it is shown that, starting from the sampled signal, the GACS or ACS nature of the continuous-time signal can be conjectured, provided that the analysis parameters such as the sampling period, padding factor, and data-record length are properly chosen.