Journal ArticleDOI
Note a note on prime factor FFT algorithms
Clive Temperton,Clive Temperton +1 more
TLDR
It is shown that prime factor FFT algorithms offer little improvement over conventional F FT algorithms on computers such as the Cray-1 and Cyber 205 where the multiplications can be performed in parallel with the additions.About:
This article is published in Journal of Computational Physics.The article was published on 1983-10-01. It has received 37 citations till now. The article focuses on the topics: Prime-factor FFT algorithm & Fast Fourier transform.read more
Citations
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Journal ArticleDOI
The multiconfiguration time-dependent Hartree (MCTDH) method: a highly efficient algorithm for propagating wavepackets
TL;DR: In this article, a review of the multiconfiguration time-dependent Hartree (MCTDH) method for propagating wavepackets is given, and the formal derivation, numerical implementation, and performance of the method are detailed.
Journal ArticleDOI
FFT algorithms for vector computers
TL;DR: Several methods for lengthening vectors are discussed, including the case of multiple and multi-dimensional transforms where M sequences of length N can be transformed as a single sequence of length MN using a 'truncated' FFT.
Journal ArticleDOI
A methodology for designing, modifying, and implementing Fourier transform algorithms on various architectures
TL;DR: Fourier transform algorithms are described using tensor (Kronecker) products and an associated class of permutations to derive variants of the Cooley-Tukey fast Fourier transform algorithm.
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Implementation of a self-sorting in-place prime factor FFT algorithm
TL;DR: A “prime factor” Fast Fourier Transform algorithm is described which is self-sorting and computes the transform in place and it is obtained that the required indexing is actually simpler than that for a conventional FFT.
Journal ArticleDOI
Recursive fast algorithm and the role of the tensor product
TL;DR: The scope of the Tensor product approach is generalized to include a much larger class of fast recursive algorithms, which greatly enhances the versatility of the tensor product technique and brings many different algorithms to the level of understanding and flexibility enjoyed by the FFT.
References
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Journal ArticleDOI
An algorithm for the machine calculation of complex Fourier series
J.W. Cooley,John W. Tukey +1 more
TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
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On computing the discrete Fourier transform
TL;DR: New algorithms for computing the Discrete Fourier Transform of n points are described, which use substantially fewer multiplications than the best algorithm previously known, and about the same number of additions.
Journal ArticleDOI
An algorithm for computing the mixed radix fast Fourier transform
TL;DR: This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey, and includes an efficient method for permuting the results in place.