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A fast flutter by the Fourier transform

  • Conference paper
IV Higher Order Workshop, Banff 1990

Part of the book series: Workshops in Computing ((WORKSHOPS COMP.))

Abstract

This paper explains some familiar but intricate circuit forms that are used to implement the fast Fourier transform. They are shown to be solutions to a recursion equation that defines the transform. An earlier paper [6] showed that the essence of the fast Fourier transform is captured by an equation characteristic of divide-and-conquer algorithms. Butterfly circuits have been shown [8] to be solutions to such equations, and in this paper solutions are derived to the particular equation defining the fast Fourier transform.

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References

  1. A. V. Aho, J. E. Hoperoft and J. D. Ullman, The design and analysis of computer algorithms, Addison-Wesley, 1974.

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  5. P. Denyer and D. Renshaw, VLSI signal processing; a bit-serial approach, Addison-Wesley, 1985.

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  6. G. Jones, Deriving the fast Fourier algorithm by calculation,in [4]. (Programming Research Group technical report PRG-TR-4–89)

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  7. G. Jones and M. Sheeran, Circuit design in Ruby,in [10].

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  8. G. Jones and M. Sheeran, The study of butterflies,in this volume.

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  9. S. G. Smith, Fourier transform machines,pp. 147–199 in [5].

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  10. Jurgen Staunstrup (ed.), Formal methods for VLSI design,North-Holland, 1990.

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Author information

Authors and Affiliations

  1. Programming Research Group, Oxford University Computing Laboratory, 11 Keble Road, Oxford, OX1 3QD, England

    Geraint Jones

Authors
  1. Geraint Jones
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Calgary, 2500 University Drive, T2N 1N4, Calgary, Alberta, Canada

    Graham Birtwistle BSc, PhD, DSc

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© 1991 British Computer Society

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Jones, G. (1991). A fast flutter by the Fourier transform. In: Birtwistle, G. (eds) IV Higher Order Workshop, Banff 1990. Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3182-3_6

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  • DOI: https://doi.org/10.1007/978-1-4471-3182-3_6

  • Publisher Name: Springer, London

  • Print ISBN: 978-3-540-19660-0

  • Online ISBN: 978-1-4471-3182-3

  • eBook Packages: Springer Book Archive

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