LombScarglebased

LombScarglebased refers to methods that utilize the Lomb-Scargle periodogram to detect and characterize periodic signals in unevenly sampled time series. The technique was developed independently by Nicolaas R. Lomb in 1976 and Jeffrey D. Scargle in 1982 and has since become a standard tool in time-domain data analysis. Unlike a classical Fourier periodogram, Lomb-Scargle accommodates irregular sampling without requiring interpolation.

In its standard form, Lomb-Scargle computes a periodogram as a function of frequency by fitting, for each angular frequency ω, a sinusoid of the form y = A cos(ω t) + B sin(ω t) to the data, with an optimal phase chosen via a time offset τ to decouple A and B. The resulting power at each frequency is proportional to the reduction in the sum-of-squares and can be interpreted as the likelihood of a sinusoidal component at that frequency. Weights can be added to account for measurement uncertainties, yielding the generalized Lomb-Scargle variant.

Variants include Generalized Lomb-Scargle (GLS) which allows a floating mean and heteroscedastic errors, the floating-mean Lomb-Scargle, multi-harmonic extensions to model non-sinusoidal shapes, and Bayesian Lomb-Scargle formulations that provide posterior probability distributions for amplitude and frequency. Efficient algorithms enable fast computation on large data sets.

Applications include detection of periodic signals in astronomical time series: variable stars, pulsations, and radial velocity surveys for exoplanets; it is also used in geosciences, climatology, and other fields dealing with irregularly spaced measurements. Limitations include sensitivity to the sampling window, potential for aliasing and spectral leakage, reliance on the assumption of sinusoidal or near-sinusoidal signals, and the need for careful false alarm probability calibration.

Software implementations are widely available in scientific libraries, such as Python's Astropy and SciPy, R's lomb package, and MATLAB toolboxes. The Lomb-Scargle framework remains a foundational approach for time-domain signal analysis when data are unevenly sampled.