Journal Article

Detecting non-sinusoidal periodicities in observational data using multiharmonic periodograms

Roman V. Baluev

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 395, issue 3, pages 1541-1548
Published in print May 2009 | ISSN: 0035-8711
Published online May 2009 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2009.14634.x
Detecting non-sinusoidal periodicities in observational data using multiharmonic periodograms

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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.

Keywords: methods: data analysis; methods: statistical; surveys

Journal Article.  5099 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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