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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.


Papers
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13 Dec 2016
TL;DR: This paper proposes a method to obtain approximate graph Fourier transforms that can be applied rapidly, based on a greedy approximate diagonalization of the graph Laplacian matrix carried out using a modified version of the famous Jacobi eigenvalues algorithm.
Abstract: The Fast Fourier Transform (FFT) is an algorithm of paramount importance in signal processing as it allows to apply the Fourier transform in O(n log n) instead of O(n 2) arithmetic operations. Graph Signal Processing (GSP) is a recent research domain that generalizes classical signal processing tools, such as the Fourier transform, to situations where the signal domain is given by any arbitrary graph instead of a regular grid. Today, there is no method to rapidly apply graph Fourier transforms. We propose in this paper a method to obtain approximate graph Fourier transforms that can be applied rapidly. It is based on a greedy approximate diagonalization of the graph Laplacian matrix, carried out using a modified version of the famous Jacobi eigenvalues algorithm. The method is described and analyzed in details, and then applied to both synthetic and real graphs, showing its potential.

2 citations

Proceedings ArticleDOI
S. Albrecht1
07 Aug 2002
TL;DR: The properties of the short IFFT (SIFFT) burst-mode processing algorithm and its input and output target space are investigated and a survey on the arithmetic of the SIFFT algorithm using the inverse momentary Fourier transform (IMFT) and the mixed-radix I FFT algorithms is given.
Abstract: Burst-mode data is obtained when a SAR system is operated in ScanSAR mode. First, a detailed description of the characteristics of the received burst-mode data is given. We then investigate the properties of the short IFFT (SIFFT) burst-mode processing algorithm and its input and output target space. A survey on the arithmetic of the SIFFT algorithm using the inverse momentary Fourier transform (IMFT) and the mixed-radix IFFT algorithms is given.

2 citations

Dissertation
07 Jun 2012
TL;DR: This Master Thesis studies the different quantization effects in hardware architecture due to the use of finite word lenght and gives a deterministic analysis with relation to the a finite wordlenght.
Abstract: This Master Thesis studies the different quantization effects in hardware architecture due to the use of finite word lenght. This master thesis gives a deterministic analysis with relation to the a ...

2 citations

Proceedings ArticleDOI
23 May 2005
TL;DR: It is shown that there is a close relationship between the structures of the radix-2/4 decimation-in-time (DIT) fast Hartley transform (FHT) and complex-valued fast Fourier transform (FFT) algorithms.
Abstract: By using an appropriate index mapping and by introducing a unified approach for the development of the radix-2/4 decimation-in-time (DIT) fast Hartley transform (FHT) and complex-valued fast Fourier transform (FFT) algorithms, it is shown that there is a close relationship between the structures of the two algorithms. As a result of this close relationship, it is shown that only a single general butterfly is sufficient to implement the two algorithms. This type of relationship is of significant importance for software and hardware implementations of the algorithms, since this relationship, along with the fact that the DHT (discrete Hartley transform) is an efficient alternative to the DFT (discrete Fourier transform) for real data, makes it possible for a single software or hardware module to be used for the computation of the DHT as well as for the computation of the forward and inverse DFTs for real- or complex-valued data.

2 citations

Journal ArticleDOI
TL;DR: This paper evaluates the implementation of a PFFT on a network of T800 series transputers connected in the form of a linear pipeline and a binary cube and analyzes the speedup obtained, taking into account both computation load and communication overhead.
Abstract: Fast Fourier Transforms (FFTs) are frequently employed in various applications such as image processing and speech recognition. Though FFT calculations can be speeded up considerably, real time processing requirements are well above that of modern day uniprocessor systems. Computing power can be substantially increased through the exploitation of the inherent parallelism available in FFT calculations. However, experimental performance analysis of the Parallel FFT (PFFT) algorithm has not been sufficiently investigated in a loosely coupled multiprocessor environment. In this paper, we evaluate the implementation of a PFFT on a network of T800 series transputers connected in the form of a linear pipeline and a binary cube. We analyse the speedup obtained, taking into account both computation load and communication overhead. A new load balancing algorithm has been incorporated so that load balancing takes into account both computation and communication loads. Realistic performance figures obtained through ac...

2 citations


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