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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 4 (0 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 53 (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 39 (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
Recursive Fast Fourier Transform Algorithm
, 2008
"... The basis of this report is to cover the Fast Fourier Transform (FFT) algorithm. The Fourier Transform is used mainly in the field of signal processing. The use of the Fourier Transform, and the FFT, is to convert a given input signal from the time domain to the frequency domain. This report will no ..."
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The basis of this report is to cover the Fast Fourier Transform (FFT) algorithm. The Fourier Transform is used mainly in the field of signal processing. The use of the Fourier Transform, and the FFT, is to convert a given input signal from the time domain to the frequency domain. This report
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 193 (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
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
ALGORITHM IN PARALLEL FOR THE FAST FOURIER TRANSFORM
, 2008
"... It has been designed, built and executed a code for the Fast Fourier Transform (FFT), compiled and executed in a cluster of 2n computers under the operating system MacOS and using the routines MacMPI. As practical application, the code has been used to obtain the transformed from an astronomic image ..."
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It has been designed, built and executed a code for the Fast Fourier Transform (FFT), compiled and executed in a cluster of 2n computers under the operating system MacOS and using the routines MacMPI. As practical application, the code has been used to obtain the transformed from an astronomic
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