Detecting non-sinusoidal periodicities in observational data using multi-harmonic periodograms

Details Detecting non-sinusoidal periodicities in observational data using multi-harmonic periodograms Detecting non-sinusoidal periodicities in observational data using multi-harmonic periodograms

2008-11-06

arxiv.org/abs/0811.0907v2

Mon. Not. R. Astron. Soc., 2009, V. 395, Issue 3, P. 1541-1548

Astronomy and Astrophysics

Astrophysics

8 pages, 6 figures, 1 table. Accepted to MNRAS

Scientific paper

10.1111/j.1365-2966.2009.14634.x

We address the problem of assessing the statistical significance of candidate periodicities found using the so-called `multi-harmonic' 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 investigation (Baluev 2008) made for the Lomb-Scargle periodogram is extended to the more general multi-harmonic periodogram. As a result, closed and efficient analytic approximations to the false alarm probability, associated with multi-harmonic periodogram peaks, are obtained. The resulting analytic approximations are tested under various conditions using Monte Carlo simulations. The simulations showed a suitable precision and robustness of these approximations.

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