Mathematics – Probability
Scientific paper
Dec 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000aas...197.2201b&link_type=abstract
American Astronomical Society, 197th AAS Meeting, #22.01; Bulletin of the American Astronomical Society, Vol. 32, p.1438
Mathematics
Probability
Scientific paper
This talk is a tutorial on spectral analysis of nonuniformly nonsimultaneously sampled data using Bayesian probability theory. In this talk we describe how these data are traditionally analyzed, analyze them using Bayesian probability theory, show that for real, nonquadrature, data the sufficient statistic (a function of the data that summarizes all of the information in the data relevant to the question being asked) is a generalized Lomb-Scargle periodogram. We then show that for uniformly sampled quadrature data the generalized Lomb-Scargle periodogram becomes a Schuster periodogram, and finally show how the Lomb-Scargle periodogram generalizes for nonuniform nonsimultaneous sampled data containing decaying sinusoids. After describing how the Lomb-Scargle periodogram generalizes we discuss the aliasing phenomenon and explicitly calculate the effective bandwidth of nonuniformly nonsimultaneously sampled quadrature data. Finally, we discuss the effect of nonuniform sampling on the estimated parameters and show that for all practical purposes the frequency estimates are unchanged by the nonuniform samples.
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