Shuffle/exchange is the natural interconnection scheme for the parallel fast fourier transform

  • Frank Wagner
Architectural Aspects (Session 5.1)
Part of the Lecture Notes in Computer Science book series (LNCS, volume 237)


It is known, that the Shuffle/Exchange-Network (S/E) is well suited to perform the parallel Fast Fourier Transform (FFT). In this paper we show, that it is optimal for this purpose in a quite general sense:

We assume, that a parallel FFT consists of a sequence of (parallel) butterfly-operations on and permutations of the given data vector. It is shown, that only the S/E and a slight variation thereof guarantee a maximum of regularity of the data flow. It follows, that the S/E is best suited for a realisation of a parallel FFT by specialized hardware.


Fast Fourier Transform Arithmetical Operation Fast Fourier Transform Algorithm Data Flow Graph Dataflow Graph 
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  1. J. Cooley, J. Tukey: An algorithm for machine computation of complex Fourier Series. Math. Comput. 19 (1965), p. 297–301.Google Scholar
  2. D. Kleitman, F. T. Leighton, M. Lepley, G. L. Miller: New Layouts for the Shuffle-Exchange Graph. Proceedings of the 13th Annual ACM Symp. on the Theory of Computing (1981), p. 278–292.Google Scholar
  3. H. Nussbaumer: Fast Fourier Transform and Convolution Algorithms. Springer, Berlin (1981).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Frank Wagner
    • 1
  1. 1.Lehrstuhl für angewandte Mathematik insbesondere InformatikRWTH AachenAachen

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