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Prime-factor FFT algorithm

About: Prime-factor FFT algorithm is a research topic. Over the lifetime, 2346 publications have been published within this topic receiving 65147 citations. The topic is also known as: Prime Factor Algorithm.


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Proceedings ArticleDOI
Denis Donnelly1
01 Oct 2006
TL;DR: In this paper, the authors compare the performance of the fast Fourier (FFT) and Hilbert-Huang (HHT) transforms for time domain data conversion and compare the behavior and flexibility of these two transforms for a number of different time domain signal types.
Abstract: The conversion of time domain data via the fast Fourier (FFT) and Hilbert-Huang (HHT) transforms is compared. The FFT treats amplitude vs. time information globally as it transforms the data to an amplitude vs. frequency description. The HHT is not constrained by the assumptions of stationarity and linearity, required for the FFT, and generates both amplitude and frequency information as a function of time. The behavior and flexibility of these two transforms are examined for a number of different time domain signal types.

20 citations

Journal ArticleDOI
01 Jan 1988
TL;DR: The implementation on the CRAY-1 of a prime factor FFT algorithm which adapts some of these developments to a vector-processing scientific computer and it is shown that worthwhile gains are obtained in both speed and storage requiremennts.
Abstract: Recent developments in algorithm design have made the Fast Fourier Transform even faster. We described the implementation on the CRAY-1 of a prime factor FFT algorithm which adapts some of these developments to a vector-processing scientific computer. Comparative times are given for the new and old versions of the FFT algorithm, applied to the problem of performing multiple simultaneous complex transforms. It is shown that worthwhile gains are obtained in both speed and storage requiremennts. The new algorithm is also vectorizable in the more difficult cases of a single transform. Finally, we use timing measurements of the new routine to estimate the value on the CRAY-1 of Hockney's parameter n 1 2 , which characterizes a computer in terms of its apparent degree of parallelism.

20 citations

Journal ArticleDOI
01 May 1986
TL;DR: An algorithm is described for computing two and three dimensional Fourier transforms on computers of SIMD architecture and the use of the 2-d results in conjunction with base ‘r1 + r2’ FFT algorithms to calculate 3-d Fourier transform on a set of N3 complex data points.
Abstract: An algorithm is described for computing two and three dimensional Fourier transforms on computers of SIMD architecture. The algorithm assumes the existence of a library routine for the calculation of a 2-d Fourier transform on a set of Np2 data points where Np2 is the number of processing elements. The paper discusses how to use this routine to calculate 2-d Fourier transforms on a set of N2 data points where NpN is a power of two, using an interleaving technique. The paper also discusses the use of the 2-d results in conjunction with base ‘r1 + r2’ FFT algorithms to calculate 3-d Fourier transforms on a set of N3 complex data points. In the final section a general program is described to calculate 3-d Fourier transforms for any values of N and Np such that NpN is a power of two. Timings are given for the algorithms run on an ICL Distributed Array Processor.

20 citations

Journal ArticleDOI
TL;DR: The Cooley-Tukey FFT as discussed by the authors algorithm is based on the version of the Goertzel algorithm via Horner's rule, which is suitable for vector processors and any parallel machine such as hypercube.
Abstract: An efficient algorithm that places an optimized DG (dependence graph) for 2/sup n/ points of the discrete Fourier transform (DFT) computation is proposed. A one-dimensional DFT is turned into a multidimensional DFT, consisting of a few short DFTs, which is based on the version of the Goertzel algorithm via Horner's rule. The data sequences in the Cooley-Tukey FFT algorithm are in an order that is easily manageable and well suited for vector processors and any parallel machine such as hypercube. >

20 citations

Patent
21 Jun 2004
TL;DR: A single-path delay feedback pipelined fast Fourier transform processor comprising at least one set of triplet FFT stage means: a first stage means comprising a radix-2 butterfly, a feedback memory, and a multiplication by unity or Wnn/8 ; and a third stage mean comprising a trivial coefficient pre-multiplication, a butterfly and a complex twiddle coefficient multiplication with coefficients determined using a twiddle factor decomposition technique as mentioned in this paper.
Abstract: A single-path delay feedback pipelined fast Fourier transform processor comprising at least one set of triplet FFT stage means: a first FFT stage means comprising a radix-2 butterfly, a feedback memory, and a multiplication by unity; a second FFT stage means comprising a trivial coefficient pre-multiplication, a radix-2 butterfly, a feedback memory, and a multiplication by selectable unity or Wnn/8 ; and a third FFT stage means comprising a trivial coefficient pre-multiplication, a butterfly, a feedback memory, and a complex twiddle coefficient multiplication with coefficients determined using a twiddle factor decomposition technique.

20 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20235
202224
20211
20188
201757
201692