skip to main content
10.1145/2465506.2465957acmconferencesArticle/Chapter ViewAbstractPublication PagesissacConference Proceedingsconference-collections
research-article

A new truncated fourier transform algorithm

Published:26 June 2013Publication History

ABSTRACT

Truncated Fourier Transforms (TFTs), first introduced by van der Hoeven, refer to a family of algorithms that attempt to smooth ``jumps'' in complexity exhibited by FFT algorithms. We present an in-place TFT whose time complexity, measured in terms of ring operations, is asymptotically equivalent to existing not-in-place TFT methods. We also describe a transformation that maps between two families of TFT algorithms that use different sets of evaluation points.

References

  1. J. W. Cooley and J. W. Tukey. An algorithm for the machine calculation of complex Fourier series. Math. Comp., 19:297--301, 1965.Google ScholarGoogle ScholarCross RefCross Ref
  2. R. Crandall. Advanced Topics in Scientic Computation. Springer-Verlag, 1996. ISBN 0-387-94473-7. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. R. Crandall and B. Fagin. Discrete weighted transforms and large-integer arithmetic. Math. Comp., 62(205):305--324, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. J. V. Z. Gathen and J. Gerhard. Modern Computer Algebra. Cambridge University Press, New York, NY, USA, 2nd edition, 2003. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. D. Harvey and D. S. Roche. An in-place truncated Fourier transform and applications to polynomial multiplication. In Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC '10, pages 325{329, New York, NY, USA, 2010. ACM. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. M. Heideman, D. Johnson, and C. Burrus. Gauss and the history of the fast Fourier transform. ASSP Magazine, IEEE, 1(4):14--21, 1984.Google ScholarGoogle ScholarCross RefCross Ref
  7. T. Mateer. Fast Fourier Transform Algorithms with Applications. Master's thesis, Clemson University, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. D. Roche. Efficient Computation With Sparse and Dense Polynomials. PhD thesis, University of Waterloo, 2011.Google ScholarGoogle Scholar
  9. I. S. Sergeev. Regular estimates for the complexity of polynomial multiplication and truncated Fourier transform. Prikl. Diskr. Mat., pages 72--88, 2011. (Russian) http://mi.mathnet.ru/eng/pdm347.Google ScholarGoogle Scholar
  10. J. van der Hoeven. The Truncated Fourier Transform and Applications. In J. Gutierrez, editor, Proc. ISSAC 2004, pages 290{296, Univ. of Cantabria, Santander, Spain, July 4-7 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. J. van der Hoeven. Notes on the Truncated Fourier Transform. Technical Report 2005-5, Universitá Paris-Sud, Orsay, France, 2005.Google ScholarGoogle Scholar

Index Terms

  1. A new truncated fourier transform algorithm

    Recommendations

    Comments

    Login options

    Check if you have access through your login credentials or your institution to get full access on this article.

    Sign in
    • Published in

      cover image ACM Conferences
      ISSAC '13: Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation
      June 2013
      400 pages
      ISBN:9781450320597
      DOI:10.1145/2465506

      Copyright © 2013 ACM

      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 26 June 2013

      Permissions

      Request permissions about this article.

      Request Permissions

      Check for updates

      Qualifiers

      • research-article

      Acceptance Rates

      Overall Acceptance Rate395of838submissions,47%

    PDF Format

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader