Detecting non-sinusoidal periodicities in observational data using multiharmonic periodograms |
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Authors: | Roman V Baluev |
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Institution: | Sobolev Astronomical Institute, St Petersburg State University, Universitetskij prospekt 28, Petrodvorets, St Petersburg 198504, Russia |
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Abstract: | We address the problem of assessing the statistical significance of candidate periodicities found using the so-called 'multiharmonic' periodogram, which is being used for detection of non-sinusoidal signals and is based on the least-squares fitting of truncated Fourier series. The recent author's investigation made for the Lomb–Scargle periodogram is extended to the more general multiharmonic periodogram. As a result, closed and efficient analytic approximations to the false alarm probability, associated with multiharmonic periodogram peaks, are obtained. The resulting analytic approximations are tested under various conditions using Monte Carlo simulations. The simulations showed a nice precision and robustness of these approximations. |
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Keywords: | methods: data analysis methods: statistical surveys |
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