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

The paper is based on the notion that the Nyquist frequency ν N is a symmetry point of the periodogram of a time series: the power spectrum at frequencies above ν N is a mirror image of that below ν N . Koen showed that the sum SS(ν) = Σ k,l [sin 2πν(t k ― t l )] 2 (where t k and t l range over the time points of observation) is zero when the frequency ν = ν N . 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 ν p << ν N ; such ν P 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, ν P ). 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.