The Lomb-Scargle periodogram is a common tool in the frequency analysis of unequally spaced data equivalent to least-squares fitting of sine waves. We give an analytic solution for the generalisation to a full sine wave fit, including an offset and weights ($χ^{2}$ fitting). Compared to the Lomb-Scargle periodogram, the generalisation is superior as it provides more accurate frequencies, is less susceptible to aliasing, and gives a much better determination of the spectral intensity. Only a few modifications are required for the computation and the computational effort is similar. Our approach brings together several related methods that can be found in the literature, viz. the date-compensated discrete Fourier transform, the floating-mean periodogram, and the "spectral significance" estimator used in the SigSpec program, for which we point out some equivalences. Furthermore, we present an algorithm that implements this generalisation for the evaluation of the Keplerian periodogram that searches for the period of the best-fitting Keplerian orbit to radial velocity data. The systematic and non-random algorithm is capable of detecting eccentric orbits, which is demonstrated by two examples and can be a useful tool in searches for the orbital periods of exoplanets.
Studies in Astronomical Time Series Analysis: The Double Lomb-Scargle Periodogram and Super Resolution
NASA Ames Research Center（NASA 艾姆斯研究中心）；Julius-Maximilians-Universität Würzburg（维尔茨堡大学）；Stanford University（斯坦福大学）；Institut de Física d’Altes Energies (IFAE)（高能物理研究所 (IFAE)）；The Barcelona Institute of Science and Technology (BIST)（巴塞罗那科学技术研究院 (BIST)）
A Multi-instrument Generalized Lomb-Scargle Periodogram Implementation
Max-Planck-Institut für Astronomie（马克斯·普朗克天文学研究所）；Fakultät für Physik und Astronomie, Universität Heidelberg（海德堡大学物理与天文学院）；Department of Astronomy, Universidade de São Paulo（圣保罗大学天文学系）；Space Telescope Science Institute（太空望远镜科学研究所）；William H. Miller III Department of Physics and Astronomy, Johns Hopkins University（约翰斯·霍普金斯大学威廉·H·米勒三世物理与天文系）
本文提出一种多仪器广义 Lomb-Scargle 周期图（GLS）的闭式实现，将其应用于热木星 TOI-481 b 的径向速度数据，能更高显著性地恢复其周期，代码已在 GitHub 开源。
