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The re-discovery of the fast Fourier transform algorithm

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Abstract

The discovery of the fast Fourier transform (FFT) algorithm and the subsequent development of algorithmic and numerical methods based on it have had an enormous impact on the ability of computers to process digital representations of signals, or functions. At first, the FFT was regarded as entirely new. However, attention and wide publicity led to an unfolding of its pre-electronic computer history going back to Gauss. The present paper describes the author's own involvement and experience with the FFT algorithm.

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References

  1. M. T. Heideman, D. H. Johnson, C. S. Burrus,The ASSP Magazine (Oct.) 1984,1, 14.

    Google Scholar 

  2. J. W. Cooley, J. W. Tukey,Math. Comp. 1965,19, 297.

    Google Scholar 

  3. I. J. Good,J. Royal Statist. Soc., Ser. B. 1958,20, 361;1960,22, 371 (MR 21 1674; MR 23 A4231).

    Google Scholar 

  4. C. S. Burrus, P. W. Eschenbacher,IEEE Trans. Acoust. Speech and Signal Processing 1981,ASSP-29, 806.

    Google Scholar 

  5. R. B. Blackman, J. W. Tukey,The Measurement of Power Spectra, Dover, New York, 1959.

    Google Scholar 

  6. W. M. Gentleman, G. Sande,Fast Fourier Transforms for Fun and Profit (1966 Fall Joint Computer Conf., AFIPS Proc. Vol. 29), Spartan, Washington, DC, 1966, pp. 563–578.

    Google Scholar 

  7. L. R. Welch,Computation of Finite Fourier Series (Tech. Report No. SPS 37-37, Vol. 4), Jet Propulsion Lab, Pasadena, CA, 1966. Also,A Program for Finite Fourier Transforms (Tech. Report No. SPS 37-40, Vol. 3), Jet Propulsion Lab, Pasadena, CA, 1966.

    Google Scholar 

  8. J. W. Cooley, P. A. Lewis, P. D. Welch,IEEE Trans. Audio Electroacoustics 1969,AU-17, 77.

    Google Scholar 

  9. J. W. Cooley, P. A. W. Lewis, P. D. Welch,IEEE Trans, on Education 1969,E-12, 27.

    Google Scholar 

  10. P. D. Welch,IEEE Trans. Audio Electroacoustics 1969,AU-15, 209.

    Google Scholar 

  11. J. W. Cooley, P. A. W. Lewis, P. D. Welch,J. Sound Vib. 1970,12, 339.

    Google Scholar 

  12. R. W. Hockney,J. Assoc. Computing Machinery 1965,12, 95.

    Google Scholar 

  13. R. W. Hockney,The Potential Calculation and Some Applications (Methods in Computational Physics, Vol.9), Academic Press, New York, 1970;I.B.M. Research Report R.C. 2870, 1970.

    Google Scholar 

  14. Special Issue on Fast Fourier Transform and Its Application to Digital Filtering and Spectral Analysis,IEEE Trans. Audio Electroacoustics 1967,AU-15, 43.

  15. Special Issue on Fast Fourier Transform,IEEE Trans. Audio Electroacoustics 1969,AU-17, 65.

  16. J. Connes, P. Connes, J.-P. Maillard,Atlas des Spectres dans le Proche Infrarouge de Vénus, Mars, Jupiter et Saturne, Éditions du Centre de la Recherche Scientifique, Paris, 1969.

    Google Scholar 

  17. L. H. Thomas, in:Applications of Digital Computers, Ginn, Boston, 1963.

    Google Scholar 

  18. K. Stumpff,Grundlagen und Methoden der Periodenforschung, Springer, Berlin, 1937; K. Stumpff,Tafeln und Aufgaben zur Harmonischen Analyse und Periodogrammrechnung, Springer, Berlin, 1939.

    Google Scholar 

  19. G. C. Danielson, C. Lanczos,J. Franklin Inst. 1942,233, 365 and 435.

    Google Scholar 

  20. P. Rudnick,Math. Comp. 1966,20, 429.

    Google Scholar 

  21. R. L. Garwin,IEEE Trans. Audio Electroacoustics 1969,AU-17, 69.

    Google Scholar 

  22. J. W. Cooley, P. A. Lewis, P. D. Welch,IEEE Trans. Audio Electroacoustics 1967,AU-15, 76.

    Google Scholar 

  23. C. Runge, H. König,Vorlesungen über Numerisches Rechnen (Die Grundlehren der Mathematischen Wissenschaften, Band XI), Springer, Berlin, 1924.

    Google Scholar 

  24. C. Lanczos,Applied Analysis, Prentice Hall, Englewood Cliffs, NJ, 1956.

    Google Scholar 

  25. C. Lanczos,Discourse on Fourier Series, Oliver and Boyd, Edinburgh-London, 1966.

    Google Scholar 

  26. H. H. Goldstine,A History of Numerical Analysis from the 16th Through the 19th Century, Springer, New York-Heidelberg-Berlin, 1977, pp. 249–253.

    Google Scholar 

  27. C. F. Gauss,Nachlaβ: Theoria interpolationis methodo nova tractata (Carl Friedrich Gauss, Werke, Band 3), Königliche Gesellschaft der Wissenschaften, Göttingen, 1866, pp. 265–303.

    Google Scholar 

  28. J. W. Cooley,How the FFT Gained Acceptance, Proceedings of the Association for Computing Machinery Conference on the History of Scientific and Numeric Computation, Princeton, NJ, May 13–15, 1987.

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The author is grateful for permission from the Association for Computing Machinery to allow the present paper to bear some similarity with the paper,How the FFT Gained Acceptance, ref. [28]

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Cooley, J.W. The re-discovery of the fast Fourier transform algorithm. Mikrochim Acta 93, 33–45 (1987). https://doi.org/10.1007/BF01201681

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  • DOI: https://doi.org/10.1007/BF01201681

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