Estimation of deviations between the aperiodic and periodic correlation functions of polyphase sequences in vicinity of the zero shift

Methods of constructing sequences with favorable periodic correlation properties are widely known. Unfortunately, even if sequences have perfect periodic auto-correlation functions, their properties with respect to the aperiodic case can be very poor. In this paper, the behavior of the aperiodic correlation function of polyphase sequences is investigated if the corresponding periodic one is known. Particularly, upper bounds are provided that estimate deviations in terms of l^P-norms (p=1, 2, ∞) between these two correlation functions in the vicinity of the zero shift. Then, the aperiodic auto-correlation function of Frank-Zadoff-Chu (1972) sequences is investigated to show that the bounds cannot be considerably improved in a certain neighborhood of the zero shift