Studies in astronomical time series analysis. III - Fourier transforms, autocorrelation functions, and cross-correlation functions of unevenly spaced data

view Abstract Citations (225) References (11) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Studies in Astronomical Time Series Analysis. III. Fourier Transforms, Autocorrelation Functions, and Cross-Correlation Functions of Unevenly Spaced Data Scargle, Jeffrey D. Abstract This paper develops techniques to evaluate the discrete Fourier transform (DFT), the autocorrelation function (ACF), and the cross-correlation 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 full text sources ADS | data products SIMBAD (1) NED (1) Related Materials (5) Part 1: 1981ApJS...45....1S Part 2: 1982ApJ...263..835S Part 4: 1990ApJ...359..469S Part 5: 1998ApJ...504..405S Part 6: 2013ApJ...764..167S