The crystallographic fast Fourier transform. I. p3 symmetry

Małgorzata Rowicka, Andrzej Kudlicki, Zbyszek Otwinowski

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

An algorithm for computing the discrete Fourier transform of data with threefold symmetry axes is presented. This algorithm is straightforward and easily implemented. It reduces the computational complexity of such a Fourier transform by a factor of 3. There are no restrictive requirements imposed on the initial data. Explicit formulae and a scheme of computing the Fourier transform are given. The algorithm has been tested and benchmarked against FFT on the unit cell, revealing the expected increase in speed. This is a non-trivial example of a more general approach developed recently by the authors.

Original languageEnglish (US)
Pages (from-to)574-579
Number of pages6
JournalActa Crystallographica Section A: Foundations of Crystallography
Volume58
Issue number6
DOIs
StatePublished - Nov 2002

Fingerprint

Fourier Analysis
Fast Fourier transforms
Fourier transforms
symmetry
fast Fourier transformations
Discrete Fourier transforms
Computational complexity
requirements
cells

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Structural Biology

Cite this

The crystallographic fast Fourier transform. I. p3 symmetry. / Rowicka, Małgorzata; Kudlicki, Andrzej; Otwinowski, Zbyszek.

In: Acta Crystallographica Section A: Foundations of Crystallography, Vol. 58, No. 6, 11.2002, p. 574-579.

Research output: Contribution to journalArticle

@article{d6afe51d102843dd9be832d1346251fb,
title = "The crystallographic fast Fourier transform. I. p3 symmetry",
abstract = "An algorithm for computing the discrete Fourier transform of data with threefold symmetry axes is presented. This algorithm is straightforward and easily implemented. It reduces the computational complexity of such a Fourier transform by a factor of 3. There are no restrictive requirements imposed on the initial data. Explicit formulae and a scheme of computing the Fourier transform are given. The algorithm has been tested and benchmarked against FFT on the unit cell, revealing the expected increase in speed. This is a non-trivial example of a more general approach developed recently by the authors.",
author = "Małgorzata Rowicka and Andrzej Kudlicki and Zbyszek Otwinowski",
year = "2002",
month = "11",
doi = "10.1107/S0108767302016744",
language = "English (US)",
volume = "58",
pages = "574--579",
journal = "Acta Crystallographica Section A: Foundations and Advances",
issn = "0108-7673",
publisher = "John Wiley and Sons Inc.",
number = "6",

}

TY - JOUR

T1 - The crystallographic fast Fourier transform. I. p3 symmetry

AU - Rowicka, Małgorzata

AU - Kudlicki, Andrzej

AU - Otwinowski, Zbyszek

PY - 2002/11

Y1 - 2002/11

N2 - An algorithm for computing the discrete Fourier transform of data with threefold symmetry axes is presented. This algorithm is straightforward and easily implemented. It reduces the computational complexity of such a Fourier transform by a factor of 3. There are no restrictive requirements imposed on the initial data. Explicit formulae and a scheme of computing the Fourier transform are given. The algorithm has been tested and benchmarked against FFT on the unit cell, revealing the expected increase in speed. This is a non-trivial example of a more general approach developed recently by the authors.

AB - An algorithm for computing the discrete Fourier transform of data with threefold symmetry axes is presented. This algorithm is straightforward and easily implemented. It reduces the computational complexity of such a Fourier transform by a factor of 3. There are no restrictive requirements imposed on the initial data. Explicit formulae and a scheme of computing the Fourier transform are given. The algorithm has been tested and benchmarked against FFT on the unit cell, revealing the expected increase in speed. This is a non-trivial example of a more general approach developed recently by the authors.

UR - http://www.scopus.com/inward/record.url?scp=0036854312&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036854312&partnerID=8YFLogxK

U2 - 10.1107/S0108767302016744

DO - 10.1107/S0108767302016744

M3 - Article

VL - 58

SP - 574

EP - 579

JO - Acta Crystallographica Section A: Foundations and Advances

JF - Acta Crystallographica Section A: Foundations and Advances

SN - 0108-7673

IS - 6

ER -