Abstract
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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References
Blackman, R. B. and Tukey, J. W.: 1958,The Measurement of Power Spectra, Dover Publications, New York.
Kinman, T. D.: 1973, private communication.
Lighthill, M. J.: 1958,Fourier Theory and Generalized Functions, Cambridge University Press, New York.
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Astrophysics and Space Science Review Paper.
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Deeming, T.J. Fourier analysis with unequally-spaced data. Astrophys Space Sci 36, 137–158 (1975). https://doi.org/10.1007/BF00681947
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DOI: https://doi.org/10.1007/BF00681947