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A prescription for period analysis of unevenly sampled time series
Horne, J. H.; Baliunas, S. L.
AA(Harvard University, Cambridge, MA), AB(Harvard-Smithsonian Center for Astrophysics, Cambridge, MA)
Astrophysical Journal, Part 1 (ISSN 0004- 637X), vol. 302, March 15, 1986, p. 757-763. Research, supported by the National Geographic Society and, the Smithsonian Institution. (ApJ Homepage)
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NASA/STI Keywords:
Computational Astrophysics, Periodic Functions, Time Series Analysis, Fourier Analysis, Probability Distribution Functions, Sampling, Signal To Noise Ratios, Variance (Statistics)
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A technique is presented for detecting the presence and significance of a period in unequally sampled time series data. The calculation of the modified periodogram for unevenly sampled data is reviewed. The proper definition of the variance that is used to normalize the power of the modified periodogram is clarified. It is proven that the probability that a peak in the periodogram is noise or signal can be easily assessed by the method given here only when the total variance of the data is used to normalize the periodogram power. The crucial choice of independent frequencies in calculating both the periodogram and the false alarm probability from unevenly sampled data is discussed. An empirical formula for estimating the number of independent frequencies is derived. In addition, the formula for the uncertainty of a frequency identified in the periodogram is reviewed. A method for detecting the presence of an alias frequency caused by the interaction of the window and signal is prescribed. With some examples of periodic signals, the minimum number of points required to measure reliably a signal are shown. The signal-to-noise ratio and the number of points required to extract signals when one or two periodicities are present in the time series are investigated.

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