Astrophysics and Space Science

, Volume 36, Issue 1, pp 137–158 | Cite as

Fourier analysis with unequally-spaced data

  • T. J. Deeming


The general problems of Fourier and spectral analysis are discussed. A discrete Fourier transformF N (v) of a functionf(t) is presented which (i) is defined for arbitrary data spacing; (ii) is equal to the convolution of the true Fourier transform off(t) with a spectral window. It is shown that the ‘pathology’ of the data spacing, including aliasing and related effects, is all contained in the spectral window, and the properties of the spectral windows are examined for various kinds of data spacing. The results are applicable to power spectrum analysis of stochastic functions as well as to ordinary Fourier analysis of periodic or quasiperiodic functions.


Spectrum Analysis Fourier Fourier Transform Power Spectrum Convolution 
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  1. Blackman, R. B. and Tukey, J. W.: 1958,The Measurement of Power Spectra, Dover Publications, New York.Google Scholar
  2. Kinman, T. D.: 1973, private communication.Google Scholar
  3. Lighthill, M. J.: 1958,Fourier Theory and Generalized Functions, Cambridge University Press, New York.Google Scholar

Copyright information

© D. Reidel Publishing Company 1975

Authors and Affiliations

  • T. J. Deeming
    • 1
  1. 1.Dept. of AstronomyThe University of Texas at AustinUSA

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