SigSpec - I. Frequency- and Phase-Resolved Significance in Fourier Space

By P. Reegen. 2007

167 citations recorded by the source corpus.

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. 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. 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. I also compare this estimator to results from other well established techniques and 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.

Subfields: Analytical Chemistry, Astronomy and Astrophysics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/aa92eaac3d5e6b532271bf67b2e18e1aa6f13d9f

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In Analytical Chemistry

In Astronomy and Astrophysics

In Statistics and Probability

Citations in the corpus

The Kepler characterization of the variability among A- and F-type stars I. General overview (2011, methodology): “As a comparison, subsamples of the stars were analysed using different analysis methods, such as SigSpec (Reegen, 2007, 2011), Period04 (Lenz & Breger 2005), the generalized Lomb-Scargle periodogram (Zechmeister & Kürster 2009), and the non-interactive code,freqfind (Leroy & Gutiérrez-Soto, in…”
A detection threshold in the amplitude spectra calculated from Kepler data obtained during K2 mission (2014, methodology): “Reegen (2007) provided a tool for reliable computation of significance levels in the frequency domain, based on the fals - alarm probability associated with a peak in the amplitude spectrum.”
The generalised Lomb-Scargle periodogram. A new formalism for the floating-mean and Keplerian periodograms (2009, methodology): “Briefly, approaching from Fourier theory Reegen (2007) defined the zero mean corrected Fourier coefficients4 aZM(ω) = 1 N ∑ yi cosωti − 1 N2 ∑ yi · ∑ cosωti bZM(ω) = 1 N ∑ yi sinωti − 1 N2 ∑ yi · ∑ sinωti which obviously correspond toYCandYS in Eqs.”
RADIAL VELOCITY PLANETS DE-ALIASED: A NEW, SHORT PERIOD FOR SUPER-EARTH 55 Cnc e (2010, methodology): “The standard, general-purpose software SigSpec mentioned in the introduction (Reegen 2007, 2010) agrees with our orbital period distinctions (we used the parameters: depth=2, par = 0.2 and par = 0.5, and a frequency upper limit of 2 day−1).”