A critical comparison of the Lomb-Scargle and the classical periodograms

Abstract

The detection of signals hidden in noise is one of the oldest and common problems in astronomy. Various solutions have been proposed in the past such as the parametric approaches based on the least-squares fit of theoretical templates or the non-parametric techniques as the phase-folding method. Most of them, however, are suited only for signals with specific time evolution. For generic signals the spectral approach based on the periodogram is potentially the most effective. In astronomy the main problem in working with the periodogram is that often the sampling of the signals is irregular. This complicates its efficient computation (the fast Fourier transform cannot be directly used) but overall the determination of its statistical characteristics. The Lomb-Scargle periodogram (LSP) provides a solution to this last important issue, but its main drawback is the assumption of a very specific model of the datawhich is not correct for most of the practical applications. These issues are not always considered in literature with theoretical and practical consequences of no easy solution. Moreover, apart from pathological samplings, it is common believe that the LSP and the classical periodogram (CP) usually provide almost identical results. In general, this is true but here it is shown that there are situations where the LSP is less effective than the CP in the detection of signals in noise. There are no compelling reasons, therefore, to use the LSP instead of the CP which is directly connected to the correlation function of the observed signal with the sinusoidal functions at the various frequencies of interest.