Generalizing the Lomb-Scargle periodogram
G. Larry Bretthorst · AIP conference proceedings · 2001
This paper is an elaboration of an issue that arose in the paper “Nonuniform Sampling: Bandwidth and Aliasing” [1]. In that paper the single frequency estimation problem was explored using Bayesian probability theory for quadrature data that were sampled nonuniformly and nonsimultaneously. In the process of discussing single frequency estimation, it was shown that the Lomb-Scargle periodogram is the sufficient statistic for single frequency estimation for a stationary sinusoid given real nonuniformly sampled data. Here we demonstrate that the Lomb-Scargle periodogram may be generalized in a straightforward manner to nonuniformly nonsimultaneously sampled quadrature data when the sinusoid has arbitrary decay. This generalized Lomb-Scargle periodogram is the sufficient statistic for single frequency estimation in a wide class of problems ranging from stationary frequency estimation in real uniformly sampled data, to frequency estimation for a single sinusoid having exponential, Gaussian, or arbitrary decay for either real or quadrature data sampled either uniformly or nonuniformly and for quadrature data nonsimultaneously.