The Nyquist frequency for time series with slight deviations from regular spacing

Abstract

The paper is based on the notion that the Nyquist frequency νN is a symmetry point of the periodogram of a time series: the power spectrum at frequencies above νN is a mirror image of that below νN. Koen showed that the sum SS(ν) =

k, [sin 2πν(tk −t )]2 (where tk and t range over the time points of observation) is zero when the frequency ν = νN. This property is used to investigate the Nyquist frequency for data which are almost regularly spaced in time. For some configurations, there are deep minima of SS at frequencies νP νN; such νP are dubbed ‘pseudo-Nyquist’ frequencies: the implication is that most of the information about the frequency content of the data is available in the spectrum over (0, νP). Systematic simulation results are presented for two configurations – small random variations in respectively the time points of observation and the lengths of the intervals between successive observations. A few real examples of CCD time series photometry obtained over several hours are also discussed.