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Full recursive form of the algorithms for fast generalized fourier transforms

  • B. J. Jechev
Namertal Algorithms (Session 1.2)
Part of the Lecture Notes in Computer Science book series (LNCS, volume 237)

Abstract

In this paper the full recursive forms of the discrete Fourier, Hadamard, Paley and Walsh transforms are developed. The algebraic properties and computational complexity of the GFT are investigated on the basis of a theoretical group approach and a matrix pseudoinversion. The approach considered reveals common and sometimes unexpected features of these transforms, the parallel realization of the algorithms becoming thus possible.

Keywords

Discrete Fourier Transform Digital Signal Processing Unexpected Feature Parallel Realization Theoretical Group Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Kasabov, N.K., G.T. Bijev. B.J. Jechev, Hierarchical Discrete Systems and the Realisation of Parallel Algorithms, Lecture Notes in Computer Science, CONPAR 81, Springer Verlag, Berlin, Heidelberg, New York.Google Scholar
  2. 2.
    Wallach Y., Alternating Sequential /Parallel Processing, Springer-Verlag, Berlin, Heid., New York, 1982.Google Scholar
  3. 3.
    Morris, S.A., Pontryagin Duality and the Structure of Locally Compact Abelian Groups, Cambridge University Press, London, New York, 1977.Google Scholar
  4. 4.
    Hewitt E., K. Ross, Abstract Harmonic Analysis, v. II, Springer Verlag, Berlin, Heidelberg, New York, 1970Google Scholar
  5. 5.
    Serre J.-P., Representations Lineaires des Groupes Finis, Herman Paris, 1967.Google Scholar
  6. 6.
    Albert A., Regression and the Moor-Pentrouse Pseudoinverse, Academic Press, New York and London, 1972.Google Scholar
  7. 7.
    Curtis C.W., I. Reiner, Represantation Theory of Finite Groups and Associative Algebras, Int. Publ., John Wiley and Sons, New York, London, 1962.Google Scholar
  8. 8.
    Grossman I., W. Magnus, Group and Their Graphs, Random House, 1964.Google Scholar
  9. 9.
    Strang, G., Linear Algebra and its applications, Academic Press New York, 1976.Google Scholar
  10. 10.
    McClellan, J.H., C.M. Rader, Number Theory in Digital Signal Processing, Prentice-Hall, Inc. Englewood Cliffs, New Jersey 07632.Google Scholar
  11. 11.
    Oppenheim A.V., R.W. Schafer, Digital Signal Processing, Prentice Hall, Inc. Englewood Cliffs, New Jersey.Google Scholar
  12. 12.
    Nussbaumer H.J., Fast Fourier Transform and Convolution Algorithms, Springer-Verlag, 1982Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • B. J. Jechev
    • 1
  1. 1.Center of Robotics, Higher Institute of Mechanical and Electrical EngineeringSofiaBulgaria

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