Gauss and the history of the fast fourier transform

@article{Heideman1984GaussAT,
  title={Gauss and the history of the fast fourier transform},
  author={M. Heideman and D. Johnson and C. Burrus},
  journal={IEEE ASSP Magazine},
  year={1984},
  volume={1},
  pages={14-21}
}
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 . frequency content of a Signal, and to facilitate the computation of discrete convolution and correlation. Indeed, published work on the FFT algorithm as a means of calculating the OFT, by J. W. Cooley and J. W. Tukey in 1965 [1], was a turning point in digital signal… Expand
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References

SHOWING 1-10 OF 117 REFERENCES
An algorithm for the machine calculation of complex Fourier series
An efficient method for the calculation of the interactions of a 2' factorial ex- periment was introduced by Yates and is widely known by his name. The generaliza- tion to 3' was given by Box et al.Expand
Note on the calculation of Fourier series
Cooley and Tukey have recently presented an algorithm for the machine calculation of Fourier series [1]. In this connection mention should be made of the similar method described by Danielson andExpand
The Fourier Transform and its Applications.
This paper analyses Fourier transform used for spectral analysis of periodical signals and emphasizes some of its properties. It is demonstrated that the spectrum is strongly depended of signalExpand
How the Fast Fourier Transform Got its Name
TLDR
The time has now come to publish this historical account to quiet all rumors and hearsay about the true history of the Fast Fourier Transform. Expand
FFT pruning
TLDR
It is shown that for situations in which the relative number of zero-valued samples is quite large, significant time-saving can be obtained by pruning the FFT algorithm. Expand
A New Method of Approximate Harmonic Analysis by Selected Ordinates
Assume with Fourier that the curve representing any periodic single-valued function of x may be expressed by the harmonic series; y=A1 sin x + A2 sin 2x + A3 sin 3x +..... + B1 cos x + B2 cos 2x + B3Expand
On computing the Discrete Fourier Transform.
  • S. Winograd
  • Medicine, Mathematics
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1976
TLDR
New algorithms for computing the Discrete Fourier Transform of n points are described, which use substantially fewer multiplications than the best algorithm previously known, and about the same number of additions. Expand
On computing the Discrete Fourier Transform.
TLDR
New algorithms for computing the Discrete Fourier Transform of n points use substantially fewer multiplications than the best algorithm previously known, and about the same number of additions. Expand
A fast Gaussian method for Fourier transform evaluation
  • L.L. Hope
  • Mathematics
  • Proceedings of the IEEE
  • 1975
A Gaussian method for fast evaluation of approximations to Fourier integral transforms is presented. This method is faster than the FFT for transforms of functions that require considerable computerExpand
The inversion of the discrete gauss transform
A study is made of the matrix , especially for the efficient calculation of its inverse and for the solution of the corresponding set of linear equations. Applications are mentioned, especially toExpand
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2
3
4
5
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