### 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 language | English (US) |
---|---|

Pages (from-to) | 574-579 |

Number of pages | 6 |

Journal | Acta Crystallographica Section A: Foundations of Crystallography |

Volume | 58 |

Issue number | 6 |

DOIs | |

State | Published - Nov 2002 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Structural Biology

### Cite this

*Acta Crystallographica Section A: Foundations of Crystallography*,

*58*(6), 574-579. https://doi.org/10.1107/S0108767302016744

**The crystallographic fast Fourier transform. I. p3 symmetry.** / Rowicka-Kudlicka, Malgorzata; Kudlicki, Andrzej; Otwinowski, Zbyszek.

Research output: Contribution to journal › Article

*Acta Crystallographica Section A: Foundations of Crystallography*, vol. 58, no. 6, pp. 574-579. https://doi.org/10.1107/S0108767302016744

}

TY - JOUR

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

AU - Rowicka-Kudlicka, Malgorzata

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

C2 - 12388876

AN - SCOPUS:0036854312

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 -