Skip to main content
SpringerLink
Log in

Distribution of WHT Recurrences

  • Conference paper
Mathematics and Computer Science III

Part of the book series: Trends in Mathematics ((TM))

  • 598 Accesses

Abstract

This work explores the performance ofafamily of algorithms for computing the Walsh-Hadamard transform (WHT), ausefulcomputationin signal and image processing [1, 2, 5].The algorithms exhibit a wide range of performance and it is non-trivialtodetermine which algorithm is optimalon agiven computer[4].This paper providesatheoretical basis fortheperformanceanalysis.Performance is modelledby afamily of recurrence relations that determine the number of instructions required to executeagiven algorithm,and are related to standard divide and conquer recurrences[6, 3].However,since thereare a variablenumber of recursive parts which can grow to infinity as theinputsize increases, new techniquesare required for their analysis. In the full version of this paper,the minimum,maximum,expected values,and variances are calculated and the limiting distribution is obtained.

Article Footnote

Supported in part by NSA #MSPF-02G-043 and NSF ITR/NGS #0325687.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. K.G. Beauchamp.Applications of Walsh and related functions.Academic Press, 1984.

    Google Scholar 

  2. D. F. Elliott and K. R. Rao.Fast Transforms: Algorithms Analyses Applications. Academic Press, 1982.

    MATH  Google Scholar 

  3. H-K. Hwang and R. Neininger. Phase change of limit laws in the quicksort recurrence under varying toll functions.SIAM J. Comput.31:1687–1722, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Johnson and M. Puschel. In Search for the Optimal Walsh-Hadamard Transform. InProceedings ICASSPvolume IV, pages 3347–3350, 2000.

    Google Scholar 

  5. F.J. MacWilliams and N.J. Sloane.The theory of error-correcting codes.North-Holland Publ.Comp., 1992.

    Google Scholar 

  6. H. Mahmoud.Sorting. A Distribution Theory.Wiley, 2000.

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Drexel University, Philadelphia, 19104, PA

    Pawel Hitczenko

  2. Department of Computer Science, Drexel University, Philadelphia, 19104, PA, USA

    Jeremy R. Johnson

  3. Department of Computer Science, Drexel University, Philadelphia, 19104, PA, USA

    Hung-Jen Huang

Authors
  1. Pawel Hitczenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jeremy R. Johnson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hung-Jen Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstrasse 8-10, Wien, 1040, Austria

    Michael Drmota  & Bernhard Gittenberger  & 

  2. INRIA Rocquencourt, Le Chesnay, 78153, France

    Philippe Flajolet

  3. PRISM, Université de Versailles-St-Quentin, Bâtiment Descartes 45 avenue des Etats-Unis, Versailles Cedex, 78035, France

    Danièle Gardy

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer Basel AG

About this paper

Cite this paper

Hitczenko, P., Johnson, J.R., Huang, HJ. (2004). Distribution of WHT Recurrences. In: Drmota, M., Flajolet, P., Gardy, D., Gittenberger, B. (eds) Mathematics and Computer Science III. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7915-6_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-7915-6_16

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9620-7

  • Online ISBN: 978-3-0348-7915-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation