Gauss and the history of the fast Fourier transform

  title={Gauss and the history of the fast Fourier transform},
  author={Michael T. Heideman and Don H. Johnson and C. Sidney Burrus},
  journal={Archive for History of Exact Sciences},
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… 
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The quick discrete Fourier transform
  • Haitao Guo, G. Sitton, C. Burrus
  • Computer Science
    Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing
  • 1994
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Some applications of generalized FFT's
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Discrete Fourier Analysis
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It is concluded that mid-low level optimizations can significantly improve an FFT implementation and that a modern general-purpose compiler does not generate optimal code without significant support from the programmer.
Fast Fourier Transforms
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An algorithm that derives fast versions for a broad class of discrete signal transforms symbolically by finding fast sparse matrix factorizations for the matrix representations of these transforms by using the defining matrix as its sole input.
The Algebraic Approach to the Discrete Cosine and Sine Transforms and Their Fast Algorithms
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The Fast Fourier Transform


An algorithm for the machine calculation of complex Fourier series
Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
Note on the calculation of Fourier series
A small-computer program has been written in this laboratory which uses the Danielson-Lanezos method with one minor modification, described below, and yields the same results as the binary form of the Cooley-Tukey algorithm with a comparable number of arithmetical operations.
How the Fast Fourier Transform Got its Name
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.
FFT pruning
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.
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 + B3
The Fourier Transform and its Applications.
1 Introduction 2 Groundwork 3 Convolution 4 Notation for Some Useful Functions 5 The Impulse Symbol 6 The Basic Theorems 7 Obtaining Transforms 8 The Two Domains 9 Waveforms, Spectra, Filters and
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  • L.L. Hope
  • Computer Science
    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 computer
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Index mappings for multidimensional formulation of the DFT and convolution
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