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.
authors.affiliation: Department of Biochemistry, UT Southwestern Medical Center at Dallas, 5323 Harry Hines Boulevard, Dallas, TX 75390-9038, USA. maga@work.swmed.edu
authors.forename: Małgorzata
authors.initials: M
authors.lastname: Rowicka
authors.forename: Andrzej
authors.initials: A
authors.lastname: Kudlicki
authors.forename: Zbyszek
authors.initials: Z
authors.lastname: Otwinowski
mesh_terms: D000465:Algorithms; D018360:Crystallography, X-Ray / Q000706:statistics & numerical data*; D005583:Fourier Analysis