Least-squares spectral analysis

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Background
The result of fitting a set of data points with a quadratic function

Least-squares spectral analysis (LSSA) is a method of estimating a frequency spectrum based on a least-squares fit of sinusoids to data samples, similar to Fourier analysis.[1][2] Fourier analysis, the most used spectral method in science, generally boosts long-periodic noise in the long and gapped records; LSSA mitigates such problems.[3] Unlike in Fourier analysis, data need not be equally spaced to use LSSA.

Developed in 1969[4] and 1971,[5] LSSA is also known as the Vaníček method and the Gauss-Vaniček method after Petr Vaníček,[6][7] and as the Lomb method[3] or the Lomb–Scargle periodogram,[2][8] based on the simplifications first by Nicholas R. Lomb[9] and then by Jeffrey D. Scargle.[10]

  1. ^ Cafer Ibanoglu (2000). Variable Stars As Essential Astrophysical Tools. Springer. ISBN 0-7923-6084-2.
  2. ^ a b D. Scott Birney; David Oesper; Guillermo Gonzalez (2006). Observational Astronomy. Cambridge University Press. ISBN 0-521-85370-2.
  3. ^ a b Press (2007). Numerical Recipes (3rd ed.). Cambridge University Press. ISBN 978-0-521-88068-8.
  4. ^ P. Vaníček (1 August 1969). "Approximate Spectral Analysis by Least-squares Fit" (PDF). Astrophysics and Space Science. 4 (4): 387–391. Bibcode:1969Ap&SS...4..387V. doi:10.1007/BF00651344. OCLC 5654872875. S2CID 124921449.
  5. ^ P. Vaníček (1 July 1971). "Further development and properties of the spectral analysis by least-squares fit" (PDF). Astrophysics and Space Science. 12 (1): 10–33. Bibcode:1971Ap&SS..12...10V. doi:10.1007/BF00656134. S2CID 109404359.
  6. ^ J. Taylor; S. Hamilton (20 March 1972). "Some tests of the Vaníček Method of spectral analysis". Astrophysics and Space Science. 17 (2): 357–367. Bibcode:1972Ap&SS..17..357T. doi:10.1007/BF00642907. S2CID 123569059.
  7. ^ M. Omerbashich (26 June 2006). "Gauss-Vanicek spectral analysis of the Sepkoski compendium: no new life cycles". Computing in Science & Engineering. 8 (4): 26–30. arXiv:math-ph/0608014. Bibcode:2006CSE.....8d..26O. doi:10.1109/MCSE.2006.68.
  8. ^ Hans P. A. Van Dongen (1999). "Searching for Biological Rhythms: Peak Detection in the Periodogram of Unequally Spaced Data". Journal of Biological Rhythms. 14 (6): 617–620. doi:10.1177/074873099129000984. PMID 10643760. S2CID 14886901.
  9. ^ Cite error: The named reference lomb was invoked but never defined (see the help page).
  10. ^ Cite error: The named reference scar was invoked but never defined (see the help page).