Least Squares Spectral Analysis Algorithm
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See: Least Squares Estimation Algorith, Spectral Analysis Algorithm, Fourier Transform.
References
2012
- http://en.wikipedia.org/wiki/Least-squares_spectral_analysis
- 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] Fourier analysis, the most used spectral method in science, generally boosts long-periodic noise in long gapped records; LSSA mitigates such problems.[2]
LSSA is also known as the Vaníček method[3] after Petr Vaníček, and as the Lomb method (or the Lomb periodogram[4]) and the Lomb–Scargle method[5] (or Lomb–Scargle periodogram[6][7]), based on the contributions of Nicholas R. Lomb and, independently, Jeffrey D. Scargle. Closely related methods have been developed by Michael Korenberg and by Scott Chen and David Donoho.
- 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] Fourier analysis, the most used spectral method in science, generally boosts long-periodic noise in long gapped records; LSSA mitigates such problems.[2]
- ↑ Cafer Ibanoglu (2000). Variable Stars As Essential Astrophysical Tools. Springer. ISBN 0-7923-6084-2. http://books.google.com/?id=QzGbOiZ3OnkC&pg=PA269&dq=vanicek+spectral+sinusoids.
- ↑ Press (2007). Numerical Recipes (3rd ed.). Cambridge University Press. ISBN 0-521-88068-8. http://books.google.com/?id=9GhDHTLzFDEC&pg=PA685&dq=%22spectral+analysis%22+%22vanicek%22+inauthor:press.
- ↑ J. Taylor and S. Hamilton (1972-03-20). "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.
- ↑ Alistair I. Mees (2001). Nonlinear Dynamics and Statistics. Springer. ISBN 0-8176-4163-7. http://books.google.com/?id=pH_OmkD4ZaQC&pg=PA227&dq=Lomb-periodogram.
- ↑ Frank Chambers (2002). Climate Change: Critical Concepts in the Environment. Routledge. ISBN 0-415-27858-9. http://books.google.com/?id=LnqFIpFJ9cwC&pg=PA178&dq=Lomb-Scargle-method.
- ↑ D. Scott Birney, David Oesper, and Guillermo Gonzalez (2006). Observational Astronomy. Cambridge University Press. ISBN 0-521-85370-2. http://books.google.com/?id=cc9L8QWcZWsC&pg=RA3-PA263&dq=Lomb-Scargle-periodogram.
- ↑ 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.