Spectral Theory for Periodically and Almost Periodically Correlated Random Processes: A Survey

This paper contains a survey of the spectral theory of periodically correlated and almost periodically correlated stochastic processes. These processes are also called cyclostationary and almost cyclostationary, and we give give some remarks concerning the historical development of the two nomenclatures. In this paper we survey the spectral theory of the covariance, the estimation of the Fourier coeecient functions and their corresponding spectral densities, and the spectral representation of the covariance and the process when the process is harmonizable. In addition, we review the role of the unitary operator and the spectral theory for groups of unitary operators in obtaining representations for these processes. This paper appears under the title \Representation and Estimation for Periodically and Almost Periodically Correlated Random Processes" in Cy