Topic
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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01 Jul 1977TL;DR: In this article, a 1D algorithm using the Hankel transform of the section of the function is described, which can avoid the use of the 2D FFT algorithm due to the loss of symmetry due to sampling and to a waste in storage requirements.
Abstract: Computing the Fourier transform of a circularly symmetric function is often necessary in optics. Use of the 2-D FFT algorithm leads to loss of the symmetry because of the sampling and to a waste in storage requirements; to avoid these inconveniences, a 1-D algorithm is described using the Hankel transform of the section of the function.
20 citations
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TL;DR: The eigensystem for the Fast Fourier transform, FFT, known for several years, can be used to design FFT algorithms and it is found that for every prime number transform there are only 4 distinct eigenvalues.
20 citations
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TL;DR: The discretization of the 1-D AFD integration via with discrete Fourier transform (DFT), incorporating fast Fouriertransform (FFT) is explored, showing that the new algorithm, called FFT-AFD, reduces the computational complexity from O(MN2) to O( MNlogN), the latter being the same as FFT.
20 citations
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26 Aug 2001TL;DR: The architecture and the implementation of a 2K/4K/8K-point complex fast Fourier transform (FFT) processor for an OFDM system are presented and a new twiddle factor generation method is proposed for saving the size of ROM required for storing the twiddle factors.
Abstract: The architecture and the implementation of a 2K/4K/8K-point complex fast Fourier transform (FFT) processor for an OFDM system are presented. The processor can perform 8K-point FFT every 273 /spl mu/s, and 2K-point every 68.26 /spl mu/s at 30 MHz which is enough for the OFDM symbol rate. The architecture is based on the Cooley-Tukey (1965) algorithm for decomposing the long DFT into short length multi-dimensional DFTs. The transposition and shuffle memories are used for the implementation of multi-dimensional transforms. The CORDIC processor is employed for the twiddle factor multiplications in each dimension. A new twiddle factor generation method is also proposed for saving the size of ROM required for storing the twiddle factors.
20 citations
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10 Mar 2006
TL;DR: It is shown that, especially in constrained devices where multiplication is expensive, polynomial multiplication in the suggested finite fields using the FFT outperforms both the schoolbook and Karatsuba methods for practically small finite fields, e.g., relevant to elliptic curve cryptography.
Abstract: We introduce an efficient way of performing polynomial multiplication in a class of finite fields GF(pm) in the frequency domain. The Fast Fourier Transform (FFT) based frequency domain multiplication technique, originally proposed for integer multiplication, provides an extremely efficient method for multiplication with the best known asymptotic complexity, i.e. O(n log n log log n). Unfortunately, the original FFT method bears significant overhead due to the conversions between the time and the frequency domains, which makes it impractical to perform multiplication of relatively short (160 - 1024 bits) integer operands as used in many applications. In this work, we introduce an efficient way of performing polynomial multiplication in finite fields using the FFT. We show that, with careful selection of parameters, all the multiplications required for the FFT computations can be avoided and polynomial multiplication in finite fields can be achieved with only O(m) multiplications in addition to O(m log m) simple shift, addition and subtraction operations. We show that, especially in constrained devices where multiplication is expensive, polynomial multiplication in the suggested finite fields using the FFT outperforms both the schoolbook and Karatsuba methods for practically small finite fields, e.g., relevant to elliptic curve cryptography.
20 citations