LombScargle

Lomb-Scargle is a statistical tool for identifying periodic signals in time series data that are irregularly sampled. It generalizes the classical Fourier periodogram to handle uneven sampling and measurement errors, making it well suited for astronomical observations where data gaps are common.

The method originates from Lomb’s 1976 work and was further developed by Scargle in 1982. A widely used extension is the generalized Lomb-Scargle periodogram (GLS), introduced by Zechmeister and Kürster in 2009, which accommodates a floating mean and heteroscedastic uncertainties. The core idea is to fit, at each frequency, a sinusoid (often with an offset) to the observed values using weighted least squares, where weights reflect measurement errors. The resulting power at a given frequency measures how well a sinusoid at that frequency explains the data relative to the overall variance.

Practically, the algorithm searches over a range of frequencies to build a power spectrum P(ω). For uneven data, the Lomb-Scargle formulation yields an unbiased, statistically meaningful estimate of the spectrum, with the significance of peaks commonly assessed through analytic false-alarm probabilities or resampling methods. The method does not interpolate missing observations; instead, it directly utilizes the irregular sampling.

Applications of Lomb-Scargle are widespread in astronomy, where it is used to detect periodicities in light curves and radial-velocity measurements, enabling the discovery of variable stars, pulsations, and exoplanets. It remains a standard tool in time-series analysis for unevenly spaced data due to its robustness, interpretability, and efficient computation.