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Integer Fast Fourier Transform
 IEEE TRANS. SIGNAL PROCESSING
, 2002
"... In this paper, a concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier transform is introduced. Unlike the fixedpoint fast Fourier transform (FxpFFT), the new transform has the properties that it is an integertointeger mapping, is power adaptable and is reversi ..."
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Cited by 27 (4 self)
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In this paper, a concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier transform is introduced. Unlike the fixedpoint fast Fourier transform (FxpFFT), the new transform has the properties that it is an integertointeger mapping, is power adaptable
Dimensionless Fast Fourier Transforms
, 1997
"... This paper shows that there are fast Fourier transform (FFT) algorithms that work, for a fixed number of points, independent of the dimension. Changing the dimension is achieved by relabeling the input and the output and changing the “twiddle factors. ” An important consequence of this result, is th ..."
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Cited by 5 (1 self)
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This paper shows that there are fast Fourier transform (FFT) algorithms that work, for a fixed number of points, independent of the dimension. Changing the dimension is achieved by relabeling the input and the output and changing the “twiddle factors. ” An important consequence of this result
Nonuniform fast Fourier transform
 Geophysics
, 1999
"... The nonuniform discrete Fourier transform (NDFT) can be computed with a fast algorithm, referred to as the nonuniform fast Fourier transform (NFFT). In L dimensions, the NFFT requires O(N(ln #) L + ( Q L #=1 M # ) P L #=1 log M # ) operations, where M # is the number of Fourier components ..."
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Cited by 52 (2 self)
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The nonuniform discrete Fourier transform (NDFT) can be computed with a fast algorithm, referred to as the nonuniform fast Fourier transform (NFFT). In L dimensions, the NFFT requires O(N(ln #) L + ( Q L #=1 M # ) P L #=1 log M # ) operations, where M # is the number of Fourier components
Fast Fourier Transforms of,.
, 1993
"... We present an algorithm for the evaluation of the Fourier transform of piecewise constant functions of two variables. The algorithm overcomes the accuracy problems associated with computing the Fourier transform of discontinuous functions; in fact, its time complexity is O(log 3 (l/)N 2 + log2 (1/E) ..."
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)N 2]logN), where t is the accuracy and N is the size of the problem. The algorithm is based on the Lagrange interpolation formula and the Green's theorem, which are used to preprocess the data before applying the Fast Fourier transform. It admits natural generalizations to higher dimensions
Gauss and the History of the Fast Fourier Transform
"... THE fast Fourier transform (Fm has become well known. as a very efficient algorithm for calculating the discrete Fourier Transform (Om of a sequence of N numbers. The OFT is used in many disciplines to obtain the spectrum or. ..."
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THE fast Fourier transform (Fm has become well known. as a very efficient algorithm for calculating the discrete Fourier Transform (Om of a sequence of N numbers. The OFT is used in many disciplines to obtain the spectrum or.
Fast Fourier transforms
, 1991
"... S ien
e in partial fulllment of the requirements for the degree of Master of Engineering in Ele
tri
al Engineering and Computer S
ien
e at the ..."
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Cited by 40 (0 self)
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S ien
e in partial fulllment of the requirements for the degree of Master of Engineering in Ele
tri
al Engineering and Computer S
ien
e at the
A Fast Fourier Transform Compiler
, 1999
"... FFTW library for computing the discrete Fourier transform (DFT) has gained a wide acceptance in both academia and industry, because it provides excellent performance on a variety of machines (even competitive with or faster than equivalent libraries supplied by vendors). In FFTW, most of the perform ..."
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Cited by 199 (5 self)
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FFTW library for computing the discrete Fourier transform (DFT) has gained a wide acceptance in both academia and industry, because it provides excellent performance on a variety of machines (even competitive with or faster than equivalent libraries supplied by vendors). In FFTW, most
Fast Fourier transforms for the rook monoid
 Trans. Amer. Math. Soc
"... We define the notion of the Fourier transform for the rook monoid (also called the symmetric inverse semigroup) and provide two efficient divideandconquer algorithms (fast Fourier transforms, or FFTs) for computing it. This paper marks the first extension of group FFTs to nongroup semigroups. 1 ..."
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Cited by 6 (3 self)
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We define the notion of the Fourier transform for the rook monoid (also called the symmetric inverse semigroup) and provide two efficient divideandconquer algorithms (fast Fourier transforms, or FFTs) for computing it. This paper marks the first extension of group FFTs to nongroup semigroups. 1
The future fast fourier transform
 SIAM J. Sci. Computing
, 1999
"... It seems likely that improvements in arithmetic speed will continue to outpace advances in communications bandwidth. Furthermore, as more and more problems are working on huge datasets, it is becoming increasingly likely that data will be distributed across many processors because one processor does ..."
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Cited by 20 (0 self)
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It seems likely that improvements in arithmetic speed will continue to outpace advances in communications bandwidth. Furthermore, as more and more problems are working on huge datasets, it is becoming increasingly likely that data will be distributed across many processors because one processor does not have sufficient storage capacity. For these reasons, we propose that an inexact DFT such as an approximate matrixvector approach based on singular values or a variation of the DuttRokhlin fastmultipolebased algorithm [9] may outperform any exact parallel FFT. The speedup may be as large as a factor of three in situations where FFT run time is dominated by communication. For the multipole idea we further propose that a method of “virtual charges ” may improve accuracy, and we provide an analysis of the singular values that are needed for the approximate matrixvector approaches. 1
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