Kolba, D. ; Rice University, Houston, TX ; Parks, T.W. ... Timing for a prime factor fast Fourier transform (FFT) algorithm using high-speed convolution, which was ...

Prime-factor FFT algorithm

The prime-factor algorithm (PFA), also called the Good–Thomas algorithm (1958/1963), is a fast Fourier transform (FFT) algorithm that re-expresses the discrete Fourier transform (DFT) of a size N = N1N2 as a two-dimensional N1×N2 DFT, but only for the case where N1 and N2 are relatively prime. These smaller transforms of size N1 and N2 can then be evaluated by applying PFA recursively or by using some other FFT algorithm.

PFA should not be confused with the mixed-radix generalization of the popular Cooley–Tukey algorithm, which also subdivides a DFT of size N = N1N2 into smaller transforms of size N1 and N2. The latter algorithm can use any factors (not necessarily relatively prime), but it has the disadvantage that it also requires extra multiplications by roots of unity called twiddle factors, in addition to the smaller transforms. On the other hand, PFA has the disadvantages that it only works for relatively prime factors (e.g. it is useless for power-of-two sizes) and that it requires a more complicated re-indexing of the data based on the Chinese remainder theorem (CRT). Note, however, that PFA can be combined with mixed-radix Cooley–Tukey, with the former factorizing N into relatively prime components and the latter handling repeated factors.

PFA is also closely related to the nested Winograd FFT algorithm, where the latter performs the decomposed N1 by N2 transform via more sophisticated two-dimensional convolution techniques. Some older papers therefore also call Winograd's algorithm a PFA FFT.

(Although the PFA is distinct from the Cooley–Tukey algorithm, Good's 1958 work on the PFA was cited as inspiration by Cooley and Tukey in their famous 1965 paper, and there was initially some confusion about whether the two algorithms were different. In fact, it was the only prior FFT work cited by them, as they were not then aware of the earlier research by Gauss and others.)

This is an excerpt from the article Prime-factor FFT algorithm from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.

PFA should not be confused with the mixed-radix generalization of the popular Cooley–Tukey algorithm, which also subdivides a DFT of size N = N1N2 into smaller transforms of size N1 and N2. The latter algorithm can use any factors (not necessarily relatively prime), but it has the disadvantage that it also requires extra multiplications by roots of unity called twiddle factors, in addition to the smaller transforms. On the other hand, PFA has the disadvantages that it only works for relatively prime factors (e.g. it is useless for power-of-two sizes) and that it requires a more complicated re-indexing of the data based on the Chinese remainder theorem (CRT). Note, however, that PFA can be combined with mixed-radix Cooley–Tukey, with the former factorizing N into relatively prime components and the latter handling repeated factors.

PFA is also closely related to the nested Winograd FFT algorithm, where the latter performs the decomposed N1 by N2 transform via more sophisticated two-dimensional convolution techniques. Some older papers therefore also call Winograd's algorithm a PFA FFT.

(Although the PFA is distinct from the Cooley–Tukey algorithm, Good's 1958 work on the PFA was cited as inspiration by Cooley and Tukey in their famous 1965 paper, and there was initially some confusion about whether the two algorithms were different. In fact, it was the only prior FFT work cited by them, as they were not then aware of the earlier research by Gauss and others.)

This is an excerpt from the article Prime-factor FFT algorithm from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.

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Prime-factor FFT algorithm - Wikipedia, the free encyclopedia

The prime-factor algorithm (PFA), also called the Good–Thomas algorithm (1958/ 1963), is a fast Fourier transform (FFT) algorithm that re-expresses the discrete ...

en.wikipedia.org/wiki/Prime-factor_FFT_algorithm

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An In-Place, In-Order Prime Factor FFT Algorithm - IEEE Xplore

An In-Place, In-Order Prime Factor FFT Algorithm. C. SIDNEY BURRUS, FELLOW, IEEE, AND PETER W. ESCHENBACHER. Abktract-This paper presents a ...

ieeexplore.ieee.org/iel6/29/26154/01163645.pdf?arnumber=1163645

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IEEE Xplore - A prime factor FFT algorithm using high-speed ...

Two recently developed ideas, the conversion of a discrete Fourier transform ( DFT) to convolution and the implementation of short convolutions with a minimum ...

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FFT Algorithms - Computational Biology Research Center[CBRC]

There are two main families of FFT algorithms: the Cooley-Tukey algorithm and the Prime Factor algorithm. These differ in the way they map the full FFT into ...

www.cbrc.jp/~tominaga/translations/gsl/gsl-1.6/fftalgorithms.pdf

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Prime-factor FFT algorithm | Facebook

Prime-factor FFT algorithm. 9 likes · 0 talking about this.

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Prime Factor Algorithm (PFA) - CCRMA - Stanford University

a more efficient prime factor algorithm (PFA), also called the Good-Thomas FFT algorithm, can be used [26,80,35,43,10,83]. The Chinese Remainder Theorem is ...

ccrma.stanford.edu/~jos/mdft/Prime_Factor_Algorithm_PFA.html

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Signal Processing 19 - Mathematics

The development of the major algorithms (Cooley-Tukey and split-radix FFT, prime factor algorithm and Winograd fast Fourier transform) is reviewed. Then, an ...

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A general in-place and in-order prime factor FFT algorithm - Springer

Jan 1, 1991 ... Starting from an index mapping for one to multi-dimensions, a general in-place and in-order prime factor FFT algorithm is proposed in this ...

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Implementation of a prime factor FFT algorithm on CRAY-1

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 ...

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A prime factor FFT algorithm using high-speed convolution - CiteSeer

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IEEE Xplore - A prime factor FFT algorithm using high-speed ...

IEEE Xplore - A prime factor FFT algorithm with real valued arithmetic

Kumaresan, R. ; University of Rhode Island, Kingston, RI, USA ; Gupta, P.K. ... A prime factor FFT algorithm involving only real valued arithmetic is devised to ...

IEEE Xplore - A new prime factor FFT algorithm

A modification of this indexing scheme gives a new algorithm with the output both ... A new prime factor FFT algorithm ... Rice University, Houston, TX, USA ...

Cooley–Tukey FFT algorithm - Wikipedia, the free encyclopedia

See also the fast Fourier transform for information on other FFT algorithms, ... what is now called the Prime-factor FFT algorithm (PFA); although Good's algorithm was initially ..... 11, Rice University, Houston TX: Connexions, September 2008.

The Prime Factor and Winograd Fourier Transform Algorithms

Sep 21, 2009 ... The prime factor algorithm (PFA) and the Winograd Fourier transform algorithm ( WFTA) are .... Figure 1: A Prime Factor FFT for N = 15 ..... Department of Electrical Engineering, Rice University, Houston, TX 77251–1892.

[PDF]A general in-place and in-order prime factor FFT algorithm - Springer

PRIME FACTOR. FFT ALGORITHM*. Wang Zhongde(=t= ~ ~). (Beijing University of Po, ts "& Telecommunications, Belting). Abstract. Starting from an index ...

Prime Factorisation A New Approach | Rahulkrishnan ...

Prime factorisation also finds applications in Fast Fourier Transform. ... So, albeit there are many prime factorization algorithms to do this in practice for larger .... Dixon, a mathematician at Carleton University, and was published in 1981 5.2. 2.2.

[PDF]Signal Processing 19 - Mathematics

Dept of EE and CTR, S. W. Mudd Building, Columbia University, 500 W 120th Street, New ... and split-radix FFT, prime factor algorithm and Winograd fast Fourier ...

An in-place, in-order prime factor FFT algorithm | ResearchGate

An in-place, in-order prime factor FFT algorithm. C. Burrus, P. Eschenbacher. Rice University, Houston, TX. IEEE Transactions on Acoustics Speech and Signal ...

C. S. Burrus

C. Sidney Burrus received the PhD degree from Stanford University in 1965 after ... the traditional Cooley-Tukey FFT have been the prime factor algorithm (PFA) ...

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Encyclopaedia of Mathematics: An Updated and Annotated Translation ...

The resulting strategy is usually called the Winograd large Fourier transform algorithm, or Winograd large FFT algorithm [4]. An alternative approach has been suggested in [3], using the Good Thomas prime-factor fast Fourier transform to ...

Computational Frameworks for the Fast Fourier Transform

“An In-Place In-Order Prime Factor FFT Algorithm," IEEE Trans. Acout. ... "A Prime Factor FFT Algorithm Using High-Speed Convolution,” IEEE Trans. Aeoiut. ... “ Implementation of a Self-Sorting In-Place Prime Factor FFT Algorithm," J. Compat .

Signal Processing Quick Study Guide for Smartphones and Mobile Devices

Algorithm | Re-indexing | DFT re-expression The Prime-factor algorithm (PFA), also called the Good- Thomas algorithm (1958/1963), is a fast Fourier transform (FFT) algorithm that re-expresses the discrete Fourier transform (DFT) of a size N ...

The DFT: An Owners' Manual for the Discrete Fourier Transform

The FFTs discussed so far represent conceptually about half of all known FFT algorithms. In this section we attempt to summarize briefly the ideas that lead to the "other half." This task is more difficult since the foundations of prime factor ...

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Prime-factor FFT algorithm

Prime-factor FFT algorithm

CenterSpace Blog » Blog Archive » Modern Fast Fourier Transform

All variants of the original Cooley-Tukey O(n log n) fast Fourier transform fundamentally exploit different ways to factor the discrete Fourier summation of length N.
For example, the split-radix FFT algorithm divides the Fourier summation of length N into three new Fourier summations: one of length N/2 and two of length N/4.

www.centerspace.net/blog/nmath/modern-fast-fourier-transform/
Need help on FFT Algorithms....

Hi , I'm currently working on project that implements Prime Factor Algorithm FFT in FPGAs. I have some knowledge about FFT but not on prime Factor

www.edaboard.com/thread178715.html
Vijayendra (VJ) K Garikapati - Fast Fourier Transform

Fast Fourier transform
A fast Fourier transform (FFT) is an efficient algorithm to compute the discrete Fourier transform (DFT) and its inverse. There are many distinct FFT algorithms involving a wide range of mathematics, from simple complex-number arithmetic to group theory and number theory; this article gives an overview of the available techniques and some of their general properties, while the specific algorithms are described in subsidiary articles linked below.

www.kousik.net/?p=292
Fast Fourier Transform - Algorithms and Applications (Signals and Communication Technology)
book.pdfchm.net/fast-fourier-transform-algorithms-and-applications-signals-and-communication-technology/9781402066283/

Intel® MKL Threaded 1D FFTs | Intel® Developer Zone

This document describes the cases for which the Intel MKL 10.2 and later 1D complex-to-complex FFTs are threaded.

software.intel.com/en-us/articles/mkl-threaded-1d-ffts
How to compile HPC Library-FFTW « Anil Maurya's Blog

HPC & Linux Technical Experience Sharing

anilmaurya.wordpress.com/2010/07/14/how-to-compile-hpc-library-fftw/
So long and thanks for all the fish.
lypyzimy.posterous.com/download-discrete-and-continuous-fourier-tran-39875

The Cooley-Tukey FFT Algorithm for General Factorizations | Numerical Recipes

Just another WordPress.com weblog (by Jaime)

numericalrecipes.wordpress.com/2009/05/29/the-cooley-tukey-fft-algorithm-for-general-factorizations/
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