The Discrete Fourier Transform and the Fast Fourier Transform

  • T. M. Peters
  • J. H. T. Bates
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


The 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 directly, and presents some practical guidelines for using the FFT.


Fast Fourier Transform Discrete Fourier Transform Convolution Theorem Fast Fourier Transform Algorithm Output Array 
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    IEEE Signal Processing Magazine, January 1992. (Special Issue on the FFT).Google Scholar
  2. 2.
    R. N. Bracewell The Fourier Transform and its Applications, 2nd ed. McGraw-Hill, New York, 1986.Google Scholar
  3. 3.
    E. O. Brigham The Fast Fourier Transform. Prentice-Hall, Englewood Cliffs, N.J., 1974.MATHGoogle Scholar
  4. 4.
    J. W. Cooley and J. W. Tukey. “An Algorithm for the Machine Calculation of Complex Fourier Series.” Mathematical Computation 19: 297–301, 1965.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • T. M. Peters
  • J. H. T. Bates

There are no affiliations available

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