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On vectorizing the fast fourier transform
BIT, 1980A variant of the Cooley-Tukey algorithm due to Stockham is derived and vectorized and is shown to be on a par with the Pease algorithm. The Stockham algorithm is then proposed for the entire computation of the two-dimensional fast Fourier transform on a vector computer.
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Linear Bijections and the Fast Fourier Transform
Applicable Algebra in Engineering, Communication and Computing, 1997Fast Fourier transform (FFT) algorithms are among the most important applications of scientific computing, and since the 1960's they have revolutionized signal processing and computational science. These algorithms can be based on the algebraic idea of group representation of cyclic groups, and in this framework FFT algorithms have been generalized to ...
Markus Hegland, W. W. Wheeler
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Recursive Fast Fourier Transforms
Proceedings of the December 9-11, 1968, fall joint computer conference, part I on - AFIPS '68 (Fall, part I), 1968The development of the Fast Fourier Transform in complex notation has obscured the savings that can be made through the use of recursive properties of trigometric functions. A disadvantage of the Fast Fourier Transform is that all samples of the function must be stored in memory before processing can start. The computation in the Fast Fourier Transform
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Fast Fourier Transforms for Nonequispaced Data
SIAM Journal on Scientific Computing, 1993The paper presents interesting fast algorithms generalizing the fast Fourier transform to the case of noninteger frequencies and nonequidistant nodes on the interval \([-\pi,\pi]\). The described algorithms are approximate ones, i.e. the calculations are performed with a fixed relative accuracy \(\varepsilon \geq 0\). They are based on a combination of
A. Dutt, Vladimir Rokhlin
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The Discrete Fourier Transform and the Fast Fourier Transform
1998The preceding chapters have made extensive mention of the Fourier transform (FT), the discrete Fourier transform (DFT), and the fast Fourier transform (FFT). This chapter examines the relationship between the FT and the DFT, discusses the FFT algorithm as a means of computing the DFT much more rapidly than can be achieved with the DFT algorithm ...
T. M. Peters, J. H. T. Bates
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Multidimensional Fourier interpolation and fast Fourier transforms
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâThe equality of the coefficients of the interpolation polynomial over a parallelepipedal grid for a multidimensional function to the coefficients of the interpolation polynomial over a uniform grid for a one-dimensional function is proved, for which the fast Fourier transform can be applied according to various schemes.
Basalov, Yu. A. +2 more
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Fast Fourier Transforms for Metabelian Groups
SIAM Journal on Computing, 1989Summary: Let G be a finite group. Then \(L_ S(G)\), the minimal number of arithmetic operations to evaluate a Fourier transform corresponding to G, is smaller than \(2\cdot | G|^ 2\). The fast Fourier transform algorithms improve this trivial upper bound by showing that for a cyclic group G, \(L_ S(G)\leq c\cdot | G| \cdot \log | G|\). This last result
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Computation of the Fast Walsh-Fourier Transform
IEEE Transactions on Computers, 1969Summary: The discrete, orthogonal Walsh functions can be generated by a multiplicative iteration equation. Using this iteration equation, an efficient Walsh transform computation algorithm is derived which is analogous to the Cooley-Tukey algorithm for the complex-exponential Fourier transform.
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2018
As was defined in a previous chapter, the discrete Fourier transform (DFT) is the sampled version of the discrete-time Fourier transform (DTFT), with a finite number of samples taken around the unit circle in the Z-domain. DFT is very useful in the analysis of discrete-time signals and linear time-invariant discrete-time systems.
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As was defined in a previous chapter, the discrete Fourier transform (DFT) is the sampled version of the discrete-time Fourier transform (DTFT), with a finite number of samples taken around the unit circle in the Z-domain. DFT is very useful in the analysis of discrete-time signals and linear time-invariant discrete-time systems.
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