EDP Sciences
Free access
Issue A&A
Volume 467, Number 3, June I 2007
Page(s) 1353 - 1371
Section Astronomical instrumentation
DOI http://dx.doi.org/10.1051/0004-6361:20066597

A&A 467, 1353-1371 (2007)
DOI: 10.1051/0004-6361:20066597


I. Frequency- and phase-resolved significance in Fourier space
P. Reegen

Institut für Astronomie, Universität Wien, Türkenschanzstraße 17, 1180 Vienna, Austria
    e-mail: reegen@astro.univie.ac.at

(Received 19 October 2006 / Accepted 6 March 2007)

Context.Identifying frequencies with low signal-to-noise ratios in time series of stellar photometry and spectroscopy, and measuring their amplitude ratios and peak widths accurately, are critical goals for asteroseismology. These are also challenges for time series with gaps or whose data are not sampled at a constant rate, even with modern Discrete Fourier Transform (DFT) software. Also the False-Alarm Probability introduced by Lomb and Scargle is an approximation which becomes less reliable in time series with longer data gaps.
Aims.A rigorous statistical treatment of how to determine the significance of a peak in a DFT, called SIGSPEC, is presented here. SIGSPEC is based on an analytical solution of the probability that a DFT peak of a given amplitude does not arise from white noise in a non-equally spaced data set.
Methods.The underlying Probability Density Function (PDF) of the amplitude spectrum generated by white noise can be derived explicitly if both frequency and phase are incorporated into the solution. In this paper, I define and evaluate an unbiased statistical estimator, the "spectral significance", which depends on frequency, amplitude, and phase in the DFT, and which takes into account the time-domain sampling.
Results.I also compare this estimator to results from other well established techniques and assess the advantages of SIGSPEC, through comparison of its analytical solutions to the results of extensive numerical calculations. According to those tests, SIGSPEC obtains as accurate frequency values as a least-squares fit of sinusoids to data, and is less susceptible to aliasing than the Lomb-Scargle Periodogram, other DFTs, and Phase Dispersion Minimization (PDM). I demonstrate the effectiveness of SIGSPEC with a few examples of ground- and space-based photometric data, illustratring how SIGSPEC deals with the effects of noise and time-domain sampling in determining significant frequencies.

Key words: methods: data analysis -- methods: statistical

© ESO 2007

What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.
  • If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
  • You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
  • You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.

Editor-in-Chief: T. Forveille
Letters Editor-in-Chief: J. Alves
Managing Editor: C. Bertout

ISSN: 0004-6361 ; e-ISSN: 1432-0746
Frequency: 12 volumes per year
Published by: EDP Sciences

Mirror sites: CDS | EDP Sciences
  RSS feeds
© The European Southern Observatory (ESO)