2010MNRAS.401..586K

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 (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.