Nonuniform Sampling and Periodic Signal Detection

Abstract

We discuss a search strategy for the discovery of periodically variable sources, using small numbers of observations (N ≤ 20) distributed nonuniformly over a finite observing window that is comparable in size to the underlying periods. We explore such topics as sampling-induced errors, magnitude errors, and random and optimal sampling. We give the algorithm designed for optimal sampling as originally employed in the discovery of variables stars using the Hubble Space Telescope. We discuss in some detail a figure of merit designed to describe various sampling strategies and explore what is required to measure quantities such as the mean magnitudes and amplitudes of variables in addition to their periods.