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Frequency Estimation And Generalized Lomb-Scargle Periodograms

G. L. Bretthorst
Published 2003 · Mathematics

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Using Bayesian probability theory we demonstrate that the Lomb-Scargle periodogram may be generalized in a straightforward manner to nonuniformly nonsimultaneously sampled quadrature data when the sinusoid has a arbitrary amplitude modulation. This generalized Lomb-Scargle periodogram is the sufficient statistic for single frequency estimation in real uniformly sampled data, to frequency estimation for a single sinusoid having exponential, Gaussian, or arbitrary amplitude modulation. In addition we define the bandwidth of a nonuniformly sampled data set and show that the phenomenon of aliases exists in both uniformly and nonuniformly sampled data and that the phenomenon has the same cause in both types of data. Finally, we show that nonuniform sampling does not affect the accuracy of the frequency estimates; although it may affect the accuracy of the amplitude estimates.
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This paper is referenced by
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10.1016/j.neunet.2016.07.004
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10.1007/978-3-319-93061-9_4
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10.1002/WICS.1444
Time series clustering and classification via frequency domain methods
S. Holan (2018)
10.1007/S42452-019-1102-3
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THE ASTROPY PROJECT : BUILDING AN INCLUSIVE , OPEN-SCIENCE PROJECT AND STATUS OF THE V 2 . 0 CORE PACKAGE
A. Price-Whelan (2018)
10.1016/J.PALAEO.2018.06.002
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W. Carleton (2018)
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10.1038/srep37237
MathIOmica: An Integrative Platform for Dynamic Omics
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10.3847/1538-4365/aab766
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J. VanderPlas (2018)
10.1016/J.QUASCIREV.2014.09.032
A reassessment of the impact of drought cycles on the Classic Maya
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10.1029/2019jc015974
Improved Internal Wave Spectral Continuum in a Regional Ocean Model
Arin D. Nelson (2020)
10.3847/1538-3881/aabc4f
The Astropy Project: Building an Open-science Project and Status of the v2.0 Core Package
The Astropy Collaboration (2018)
10.1109/TSP.2017.2652391
A Study of Periodograms Standardized Using Training Datasets and Application to Exoplanet Detection
S. Sulis (2017)
10.1103/PhysRevD.85.063505
Statistical Tests of Noise and Harmony in Dark Matter Modulation Signals
S. Chang (2012)
10.3847/1538-4357/ab8bd4
Looking at Blazar Light Curve Periodicities with Gaussian Processes
Stefano Covino (2020)
10.1101/074260
MathIOmica: an integrative platform for dynamic omics
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