Tests for Periodic Components in Multiple-Block Data and Analysis of Light Curves from Variable Stars
12 January 1987
A major problem in the analysis of the light curves of variable stars is fragmentation of the record. Typically the available time series consists of several sections each a few hours long separated by gaps ranging from hours to months in duration. Use of the variational methods described by Slepian et al. (1061) yields a set of optimum, but unweildy, windows for this problem. These windows are, however, accurately approximated by discrete Slepian sequences (discrete prolate spheroidal sequences) taken over each segment. Using this approximate expansion we define an extension of the harmonic F test to multiple block data. Depending on the setup used this may be used to test for two closely spaced lines as opposed to a single line, a single line as opposed to narrow-band noise, for "frequency modulation", or for a discrete "phase jump", etc.