Characterization of the Spectra of Periodically Correlated Processes

Abstract

A complete characterization of the spectrum of a locally square integrable periodically correlated (PC) processes is obtained. The result makes use of the author's recent theorem establishing a one to one correspondence between PC processes and a certain class on infinite dimensional stationary processes. In terms of distributions it is proved that the Fourier transform of a positive definite distribution on the plane which is the sum of complex uniformly bounded measures supported on equidistant lines parallel to diagonal is a locally square integrable function.periodically correlated process correlation function spectrum positive definite distribution