On discrete-time estimators of second-order moments of generalized almost-cyclostationary processes

In this paper, a discrete-time estimator is proposed for second-order moments of continuous-time generalized almost-cyclostationary (GACS) processes. GACS processes have statistical functions that are almost-periodic functions of time whose Fourier series expansions have both frequencies and coefficients that depend on the lag shifts of the processes. The class of GACS processes includes the almost-cyclostationary (ACS) processes which are obtained as a special case when the frequencies do not depend on the lag shifts. ACS processes filtered by Doppler channels and communications signals with time-varying parameters are further examples. The discrete-time process obtained by uniformly sampling a continuous-time GACS process is considered. It is shown that such discrete-time process is ACS and it is proved that its discrete-time cyclic correlogram is a mean-square consistent estimator of the cyclic autocorrelation function of the continuous-time GACS process, as the sampling period approaches zero and the data-record length approaches infinity.