The Nyquist frequency for time series with slight deviations from regular spacing |
| |
| Authors: | Chris Koen |
| |
| Institution: | Department of Statistics, University of the Western Cape, Private Bag X17, Bellville, 7535 Cape, South Africa |
| |
| 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  (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. |
| |
| Keywords: | methods: statistical stars: individual: HE 0230-4323 |
|
|
