Unevenly-sampled signals: a general formalism of the Lomb-Scargle periodogram

Abstract

The periodogram is a popular tool that tests whether a signal consists only of noise or if it also includes other components. The main issue of this method is to define a critical detection threshold that allows identification of a component other than noise, when a peak in the periodogram exceeds it. In the case of signals sampled on a regular time grid, determination of such a threshold is relatively simple. When the sampling is uneven, however, things are more complicated. The most popular solution in this case is to use the "Lomb-Scargle" periodogram, but this method can be used only when the noise is the realization of a zero-mean, white (i.e. flat-spectrum) random process. In this paper, we present a general formalism based on matrix algebra, which permits analysis of the statistical properties of a periodogram independently of the characteristics of noise (e.g. colored and/or non-stationary), as well as the characteristics of sampling.

10 pages, 11 figures, Astronomy and Astrophysics, in press

References in corpus (1)

• The generalised Lomb-Scargle periodogram. A new formalism for the floating-mean and Keplerian periodograms

Cited by in corpus (7)

• Understanding the Lomb-Scargle Periodogram
• A Stochastic Model for the Luminosity Fluctuations of Accreting Black Holes
• Multiwavelength variability study and search for periodicity of PKS 1510-089
• The gamma-ray and Optical Variability Analysis of the BL Lac Object 3FGL J0449.4-4350
• Estimating activity cycles with probabilistic methods I. Bayesian Generalised Lomb-Scargle Periodogram with Trend
• LASR-Guided Stellar Photometric Variability Subtraction: The Linear Algorithm For Significance Reduction
• Searching for unresolved massive black hole pairs through AGN photometric variability