statistics

lomb scargle periodogram

Finding periods in unevenly sampled data, where the ordinary Fourier transform cannot be used.
13 related articles

Description

The Lomb–Scargle periodogram is a method for detecting periodic signals in data that is unevenly sampled in time. Unlike the classical Fourier transform, which requires equally spaced samples, the Lomb–Scargle approach fits sinusoids of different frequencies directly to the observed data points, weighting each measurement by its uncertainty. It is the workhorse for finding exoplanets, variable stars, and other periodic phenomena in astronomical time-series data.

History

The method was developed independently by Norman Lomb in 1976 and Jeffrey Scargle in 1982, building on earlier work by Barning in 1963. It has since become a standard tool in astrophysics.

How it works

For each trial frequency, the method computes a power value that measures how well a sinusoid of that frequency fits the data, after accounting for the uneven sampling. The key trick is to shift the sinusoid's phase so that it is orthogonal to a constant offset, which makes the fit independent of the mean of the data. The resulting periodogram shows peaks at frequencies where the signal is strong, and the significance of each peak can be assessed against a false-alarm probability.

In practice

It is used to discover exoplanets by detecting the periodic Doppler shift of their host stars, to measure the rotation periods of stars, and to analyze variable star light curves.

Fun fact

The Lomb–Scargle periodogram is mathematically equivalent to a least-squares fit of a sinusoid, which means it gives the same result as a full nonlinear fit but at a fraction of the computational cost.

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Related articles · 13

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