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SigSpec is an acronym of "SIGnificance SPECtrum" and addresses a statistical technique to provide the reliability of periodicities in a measured (noisy and not necessarily equidistant) time series.[1] It relies on the amplitude spectrum obtained by the Discrete Fourier transform (DFT) and assigns a quantity called the spectral significance (frequently abbreviated by “sig”) to each amplitude. This quantity is a logarithmic measure of the probability that the given amplitude level is due to white noise, in the sense of a type I error. It represents the answer to the question, “What would be the chance to obtain an amplitude like the measured one or higher, if the analysed time series were random?”

SigSpec may be considered a formal extension to the Lomb-Scargle periodogram,[2][3] appropriately incorporating a time series to be averaged to zero before applying the DFT, which is done in many practical applications. When a zero-mean corrected dataset has to be statistically compared to a random sample, the sample mean (rather than the population mean only) has to be zero.

Probability density function (pdf) of white noise in Fourier space[edit]

Considering a time series to be represented by a set of pairs , the amplitude pdf of white noise in Fourier space, depending on frequency and phase angle may be described in terms of three parameters, , , , defining the “sampling profile”, according to

In terms of the phase angle in Fourier space, , with

the probability density of amplitudes is given by

where the sock function is defined by

and denotes the variance of the dependent variable .

False-alarm probability and spectral significance[edit]

Integration of the pdf yields the false-alarm probability that white noise in the time domain produces an amplitude of at least ,

The sig is defined as the negative logarithm of the false-alarm probability and evaluates to

It returns the number of random time series one would have to examine to obtain one amplitude exceeding at the given frequency and phase.


SigSpec is primarily used in asteroseismology to identify variable stars and to classify stellar pulsation (see references below). The fact that this method incorporates the properties of the time-domain sampling appropriately makes it a valuable tool for typical astronomical measurements containing data gaps.


  1. ^ P. Reegen (2007). "SigSpec - I. Frequency- and phase-resolved significance in Fourier space". Astronomy and Astrophysics. 467: 1353–1371. arXiv:physics/0703160Freely accessible. Bibcode:2007A&A...467.1353R. doi:10.1051/0004-6361:20066597. 
  2. ^ N. R. Lomb (1976). "Least-squares frequency analysis of unequally spaced data". Astrophysics and Space Science. 39: 447–462. Bibcode:1976Ap&SS..39..447L. doi:10.1007/BF00648343. 
  3. ^ J. D. Scargle (1982). "Studies in astronomical time series analysis. II. Statistical aspects of spectral analysis of unevenly spaced data". The Astrophysical Journal. 263: 835–853. Bibcode:1982ApJ...263..835S. doi:10.1086/160554. 
  • M. Breger; S. M. Rucinski; P. Reegen (2007). "The Pulsation of EE Camelopardalis". The Astronomical Journal. 134: 1994–1998. arXiv:0709.3393Freely accessible. Bibcode:2007AJ....134.1994B. doi:10.1086/522795. 
  • M. Gruberbauer; K. Kolenberg; J. F. Rowe; D. Huber; J. M. Matthews; P. Reegen; R. Kuschnig; C. Cameron; T. Kallinger; W. W. Weiss; D. B. Guenther; A. F. J. Moffat; S. M. Rucinski; D. Sasselov; G. A. H. Walker (2007). "MOST photometry of the RRdLyrae variable AQLeo: two radial modes, 32 combination frequencies and beyond". Monthly Notices of the Royal Astronomical Society. 379: 1498–1506. arXiv:0705.4603Freely accessible. Bibcode:2007MNRAS.379.1498G. doi:10.1111/j.1365-2966.2007.12042.x. 
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  • D. B. Guenther; T. Kallinger; K. Zwintz; W. W. Weiss; J. Tanner (2007). "Seismology of Pre-Main-Sequence Stars in NGC 6530". The Astrophysical Journal. 671: 581–591. Bibcode:2007ApJ...671..581G. doi:10.1086/522880. 
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  • T. Kallinger; P. Reegen; W. W. Weiss (2008). "A heuristic derivation of the uncertainty for frequency determination in time series data". Astronomy and Astrophysics. 481: 571–574. arXiv:0801.0683Freely accessible. Bibcode:2008A&A...481..571K. doi:10.1051/0004-6361:20077559. 
  • P. Reegen (2005). "SigSpec - reliable computation of significance in Fourier space", in The A-Star Puzzle, Proceedings IAU Symp. 224, eds. J. Zverko, J. Ziznovsky, S.J. Adelman, W.W. Weiss. The A-Star Puzzle, Proceedings of IAU Symposium 224. Cambridge, UK: Cambridge University Press. pp. 791–798. ISBN 0-521-85018-5. 
  • P. Reegen; M. Gruberbauer; L. Schneider; W. W. Weiss (2008). "Cinderella - Comparison of INDEpendent RELative Least-squares Amplitudes". Astronomy and Astrophysics. 484: 601–608. Bibcode:2008A&A...484..601R. doi:10.1051/0004-6361:20078855. 
  • C. Schoenaers; A. E. Lynas-Gray (2007). "A new slowly pulsating subdwarf-B star: HD 4539". Communications in Asteroseismology. 151: 67–76. Bibcode:2007CoAst.151...67S. doi:10.1553/cia151s67. 
  • M. Zechmeister; M. Kuerster (2009). "The gemeralised Lomb-Scargle periodogram. A new formalism for the floating-mean and Keplerian periodograms". Astronomy and Astrophysics. 496: 577–584. arXiv:0901.2573Freely accessible. Bibcode:2009A&A...496..577Z. doi:10.1051/0004-6361:200811296. 
  • K. Zwintz; T. Kallinger; D. B. Guenther; M. Gruberbauer; D. Huber; J. Rowe; R. Kuschnig; W. W. Weiss; J. M. Matthews; A. F. J. Moffat; S. M. Rucinski; D. Sasselov; G. A. H. Walker; M. P. Casey (2009). "MOST photometry of the enigmatic PMS pulsator HD 142666". Astronomy and Astrophysics. 494: 1031–1040. arXiv:0812.1960Freely accessible. Bibcode:2009A&A...494.1031Z. doi:10.1051/0004-6361:200811116. 
  • K. Zwintz; M. Hareter; R. Kuschnig; P. J. Amado; N. Nesvacil; E. Rodriguez; D. Diaz-Fraile; W. W. Weiss; T. Pribulla; D. B. Guenther; J. M. Matthews; A. F. J. Moffat; S. M. Rucinski; D. Sasselov; G. A. H. Walker (2009). "MOST observations of the young open cluster NGC 2264". Astronomy and Astrophysics. 502: 1239–252. doi:10.1051/0004-6361:200911863. 

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