A prime factor FFT algorithm using high-speed convolution

Kolba, Dean P.; Parks, T.W.

doi:10.1109/tassp.1977.1162973

Cited by 270 publications

(61 citation statements)

References 6 publications

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“…All these results were considered as curiosities when they were first published, but their combination, first done by Winograd and then by Kolba and Parks [39] raised a lot of interest in that class of algorithms. Their overall organization is as follows:…”

Section: Ffts Without Twiddle Factorsmentioning

confidence: 99%

“…This algorithm is known as the Winograd Fourier transform algorithm (WFTA) [54], an algorithm requiring the least known number of multiplications among practical algorithms for moderate lengths DFTs. If the nesting is not used, and the multi-dimensional DFT is performed by the row-column method, the resulting algorithm is known as the prime factor algorithm (PFA) [39] which, while using more multiplications, has less additions and a better structure than the WFTA.…”

Section: Ffts Without Twiddle Factorsmentioning

confidence: 99%

“…[95] Let us now come back to the initial problem of this section: the computation of the bidimensional transform given in (39). Rearranging the data in matrix form, of size NtN2, and F~ (resp.…”

Section: Mnl<2n1mentioning

confidence: 99%

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Fast fourier transforms: A tutorial review and a state of the art

Duhamel¹,

1990

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Rrsum4. La publication de l'algorithme de Cooley-Tukey pour la transformation de Fourier rapide a ouvert une nouvelle ~re dans le traitement num6rique des signaux, en r4duisant l'ordre de complexit6 de probl~mes cruciaux, comme la transformation de Fourier ou la convolution, de N 2 ~ N log2 N (oh N est la taille du probl~me). Le drvelopment des algorithmes principaux (Cooley-Tukey, split-radix FFT, algorithmes des facteurs premiers, et transform6e rapide de Winograd) est drcrit. Ensuite, l'&at de l'art est donn4, et on parle des probl~mes ouverts et des implantations.

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Section: Ffts Without Twiddle Factorsmentioning

confidence: 99%

Section: Ffts Without Twiddle Factorsmentioning

confidence: 99%

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Fast fourier transforms: A tutorial review and a state of the art

Duhamel¹,

1990

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“…This structure is still in use [11], [12] and needs for 5 multipliers. Kolba and Park's design [3] (which we name KolbaWFT) on the other hand needs for only 4 multipliers and a shift operation. Therefore, it is less complex.…”

Section: Comparative Studymentioning

confidence: 99%

“…It is possible to pipeline several short length WFTs to generate transforms of larger sizes [2], [3]. However, realizing a pipelined structure for short length WFTs is difficult due to the irregularity in the flow of the signal within these transforms.…”

Section: Introductionmentioning

confidence: 99%

The design of low complexity low power pipelined short length Winograd Fourier transforms

Coskun

Kale

Morling

et al. 2014

2014 IEEE International Symposium on Circuits and Systems (ISCAS)

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Abstract-In this paper a novel pipelining approach applicable to Winograd Fourier transforms is presented. The novel approach makes use of reconfigurable multiplier blocks to implement the real multipliers required for the transform as well as sharing the hardware resources among additions. The additions are realized using modified forms of butterfly circuits. The novel approach is tested on a 5-point Winograd Fourier transform and the circuit area and power dissipation of the design are estimated using an in-house power estimation tool and compared to the state-of-theart approaches.

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Hypercubic storage layout and transforms in arbitrary dimensions using GPUs and CUDA

Hawick¹,

Playne²

2010

Concurrency and Computation

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SUMMARYMany simulations in the physical sciences are expressed in terms of rectilinear arrays of variables. It is attractive to develop such simulations for use in 1-, 2-, 3-or arbitrary physical dimensions and also in a manner that supports exploitation of data-parallelism on fast modern processing devices. We report on data layouts and transformation algorithms that support both conventional and data-parallel memory layouts. We present our implementations expressed in both conventional serial C code as well as in NVIDIA's Compute Unified Device Architecture concurrent programming language for use on general purpose graphical processing units. We discuss: general memory layouts; specific optimizations possible for dimensions that are powers-of-two and common transformations, such as inverting, shifting and crinkling. We present performance data for some illustrative scientific applications of these layouts and transforms using several current GPU devices and discuss the code and speed scalability of this approach.

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A prime factor FFT algorithm using high-speed convolution

Abstract: Again, the indices in (11), (the exponents of Cl) are taken modulo N-l, By combining (11) with (4) we can always convert the computation of a DFT of prime length into a circular convolution. B. Prime Power Length DFT Winograd [5] and Rader and McClellan [9] have shown

Cited by 270 publications

References 6 publications

Fast fourier transforms: A tutorial review and a state of the art

Fast fourier transforms: A tutorial review and a state of the art

The design of low complexity low power pipelined short length Winograd Fourier transforms

Hypercubic storage layout and transforms in arbitrary dimensions using GPUs and CUDA

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