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FastChi: A Fast Chi-squared Technique For Period Search of Irregularly Sampled Data
The Fast Chi-Squared Algorithm is a fast, powerful technique for detecting periodicity. It was developed for analyzing variable stars, but is applicable to many of the other applications where the Fast Fourier Transforms (FFTs) or other periodograms (such as Lomb-Scargle) are currently used. The Fast Chi-squared technique takes a data set (e.g. the brightness of a star measured at many different times during a series of observations) and finds the periodic function that has the best frequency and shape (to an arbitrary number of harmonics) to fit the data. Among its advantages are:
- Statistical efficiency: all of the data are used, weighted by their individual error bars, giving a result with a significance calibrated in well-understood Chi-squared statistics.
- Sensitivity to harmonic content: many conventional techniques look only at the significance (or the amplitude) of the fundamental sinusoid and discard the power of the higher harmonics.
- Insensitivity to the sample timing: you won't find a period of 24 hours just because you take your observations at night. You do not need to window your data.
- The frequency search is gridded more tightly than the traditional "integer number of cycles over the span of observations", eliminating power loss from peaks that fall between the grid points.
- Computational speed: The complexity of the algorithm is O(NlogN), where N is the number of frequencies searched, due to its use of the FFT.