The n-dimensional Extension of the Lomb-Scargle Method

Abstract

The common methods of spectral analysis for n-dimensional time series investigate Fourier transform (FT) to decompose discrete data into a set of trigonometric components, i. e. amplitude and phase. Due to the limitations of discrete FT, the data set is restricted to equidistant sampling. However, in the general situation of non-equidistant sampling FT based methods will cause significant errors in the parameter estimation. Therefore, the classical Lomb-Scargle method (LSM) was developed for one dimensional data to circumvent the incorrect behaviour of FT in case of fragmented and irregularly sampled data. The present work deduces LSM for n-dimensional (multivariate) data sets by a redefinition of the shifting parameter \(\tau\). An analytical derivation shows, that nD LSM extents the traditional 1D case preserving all the statistical features. Applications with ideal test data and experimental data will illustrate the derived method.