Studies in Astronomical Time Series Analysis. III. Fourier Transforms, Autocorrelation Functions, and CrossCorrelation Functions of Unevenly Spaced Data
Abstract
This paper develops techniques to evaluate the discrete Fourier transform (DFT), the autocorrelation function (ACF), and the crosscorrelation function (CCF) of time series which are not evenly sampled. The series may consist of quantized point data (e.g., yes/no processes such as photon arrival). The DFT, which can be inverted to recover the original data and the sampling, is used to compute correlation functions by means of a procedure which is effectively, but not explicitly, an interpolation. The CCF can be computed for two time series not even sampled at the same set of times. Techniques for removing the distortion of the correlation functions caused by the sampling, determining the value of a constant component to the data, and treating unequally weighted data are also discussed. FORTRAN code for the Fourier transform algorithm and numerical examples of the techniques are given.
 Publication:

The Astrophysical Journal
 Pub Date:
 August 1989
 DOI:
 10.1086/167757
 Bibcode:
 1989ApJ...343..874S
 Keywords:

 Bl Lacertae Objects;
 Computational Astrophysics;
 Time Series Analysis;
 Autocorrelation;
 Cross Correlation;
 Fortran;
 Fourier Transformation;
 Astronomy;
 ANALYTICAL METHODS;
 BL LACERTAE OBJECTS;
 NUMERICAL METHODS