Factorization method for crystallographic Fourier transforms
type: Item
instance of: scholarly article
title: Factorization method for crystallographic Fourier transforms
zbMATH Open document ID: 0707.65107
DOI: 10.1016/0196-8858(90)90014-P
author: M. An
author: James W. Cooley
author: R. Tolimieri
published in: Advances in Applied Mathematics
publication date: 1990-01-01T00:00:00Z
review text: Let p,q be primes (p\(\neq q)\) and \(n=pq\). Algorithms for computing the 3- dimensional discrete Fourier transform (DFT) of size \(n\times n\times n\) that take advantage of crystal symmetries are developed. The symmetry of a crystal gives rise to redundancy in the sampled data, i.e., the data are invariant under a space group G of the crystal. The DFT of G- invariant data without redundant arithmetic is called a symmetrized DFT. The main result is the orbit exchange. This is a procedure for designing symmetrized DFT-algorithms of size \(n\times n\times n\) which reduce to symmetrized DFT's on the prime factors of n. Note that fast algorithms for symmetrized DFT of prime size are known.
Mathematics Subject Classification ID: 65T50
Mathematics Subject Classification ID: 20H15
Mathematics Subject Classification ID: 42B10
zbMATH DE Number: 4162227
zbMATH Keywords: fast DFT-algorithms
zbMATH Keywords: orbit exchange
zbMATH Keywords: cristallography
zbMATH Keywords: 3-dimensional discrete Fourier transform
zbMATH Keywords: symmetrized DFT
reviewed by: Manfred Tasche
MaRDI profile type: Publication
full work available at URL: 0196-8858(90)90014-p
OpenAlex ID: W2034513738
description: scientific article; zbMATH DE number 4162227