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Discrete Fourier transform in arbitrary dimensions by a generalized Beever—Lipson algorithm

Title data

Schneider, Martin ; van Smaalen, Sander:
Discrete Fourier transform in arbitrary dimensions by a generalized Beever—Lipson algorithm.
In: Acta Crystallographica Section A. Vol. 56 (2000) Issue 3 . - pp. 248-251.
ISSN 1600-5724
DOI: https://doi.org/10.1107/S0108767300000532

Official URL: Volltext

Abstract in another language

The Beevers—Lipson procedure was developed as an economical evaluation of Fourier maps in two- and three-dimensional space. Straightforward generalization of this procedure towards a transformation in n-dimensional space would lead to n nested loops over the n coordinates, respectively, and different computer code is required for each dimension. An algorithm is proposed based on the generalization of the Beevers—Lipson procedure towards transforms in n-dimensional space that contains the dimension as a variable and that results in a single piece of computer code for arbitrary dimensions. The computational complexity is found to scale as Nłog(N), where \it N is the number of pixels in the map, and it is independent of the dimension of the transform. This procedure will find applications in the evaluation of Fourier maps of quasicrystals and other aperiodic crystals, and in the maximum-entropy method for aperiodic crystals.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Beevers-Lipson
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Group Material Sciences > Chair Crystallography
Faculties > Faculty of Mathematics, Physics und Computer Science > Group Material Sciences > Chair Crystallography > Chair Crystallography - Univ.-Prof. Dr. Sander van Smaalen
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Group Material Sciences
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 530 Physics
Date Deposited: 23 Mar 2016 08:19
Last Modified: 23 Mar 2016 08:19
URI: https://eref.uni-bayreuth.de/id/eprint/32008