Astrophysics and Space Science

, Volume 36, Issue 1, pp 137-158

First online:

Fourier analysis with unequally-spaced data

  • T. J. DeemingAffiliated withDept. of Astronomy, The University of Texas at Austin

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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.