International Tables for Crystallography

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International Tables for Crystallography (2006). Vol. B, Section 1.3.4.5.1
Fourier transforms in crystallography: theory, algorithms and applications
G. Bricogne. International Tables for Crystallography (2010). Vol. B, ch. 1.3, pp. 24-113  [ doi:10.1107/97809553602060000760 ]

Abstract

In the first part of this chapter, the mathematical theory of the Fourier transformation is cast in the language of Schwartz's theory of distributions, allowing Fourier transforms, Fourier series and discrete Fourier transforms to be treated together. Next the numerical computation of the discrete Fourier transform is discussed. One-dimensional algorithms are examined first, including the Cooley–Tukey algorithm, the Good (or prime factor) algorithm, the Rader algorithm and the Winograd algorithms. Multidimensional algorithms are then covered. The last part of the chapter surveys the crystallographic applications of Fourier transforms.


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About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The multi-volume series comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.