In this paper we study the estimation of the spectral density functions of a continuous-time parameter almost periodically correlated process from one discrete random-time sampling. Under mixing hypotheses on the cumulant of the process, we establish the quadratic consistency of this estimator and the rate of convergence.

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Processes that exhibit repeatability in their kth-order moments are frequently studied in signal analysis. Such repeatability can be conveniently expressed with the help of almost periodicity. In particular, almost periodically correlated (APC) processes play an important role in the analysis of repeatable signals. This paper presents a study of asymptotic distributions of the estimator of the spectral covariance function for APC processes. It is demonstrated that, for a large class of APC processes, the functional central limit theorem holds.