Fourier Analysis with Unequally-Spaced Data

Details Fourier Analysis with Unequally-Spaced Data Fourier Analysis with Unequally-Spaced Data

Aug 1975

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975ap%26ss..36..137d&link_type=abstract

Astrophysics and Space Science, Volume 36, Issue 1, pp.137-158

Astronomy and Astrophysics

Astrophysics

785

Scientific paper

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.

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