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.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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.
Wallach Y., Alternating Sequential /Parallel Processing, Springer-Verlag, Berlin, Heid., New York, 1982.
Morris, S.A., Pontryagin Duality and the Structure of Locally Compact Abelian Groups, Cambridge University Press, London, New York, 1977.
Hewitt E., K. Ross, Abstract Harmonic Analysis, v. II, Springer Verlag, Berlin, Heidelberg, New York, 1970
Serre J.-P., Representations Lineaires des Groupes Finis, Herman Paris, 1967.
Albert A., Regression and the Moor-Pentrouse Pseudoinverse, Academic Press, New York and London, 1972.
Curtis C.W., I. Reiner, Represantation Theory of Finite Groups and Associative Algebras, Int. Publ., John Wiley and Sons, New York, London, 1962.
Grossman I., W. Magnus, Group and Their Graphs, Random House, 1964.
Strang, G., Linear Algebra and its applications, Academic Press New York, 1976.
McClellan, J.H., C.M. Rader, Number Theory in Digital Signal Processing, Prentice-Hall, Inc. Englewood Cliffs, New Jersey 07632.
Oppenheim A.V., R.W. Schafer, Digital Signal Processing, Prentice Hall, Inc. Englewood Cliffs, New Jersey.
Nussbaumer H.J., Fast Fourier Transform and Convolution Algorithms, Springer-Verlag, 1982
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jechev, B.J. (1986). Full recursive form of the algorithms for fast generalized fourier transforms. In: Händler, W., Haupt, D., Jeltsch, R., Juling, W., Lange, O. (eds) CONPAR 86. CONPAR 1986. Lecture Notes in Computer Science, vol 237. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16811-7_160
Download citation
DOI: https://doi.org/10.1007/3-540-16811-7_160
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16811-9
Online ISBN: 978-3-540-44856-3
eBook Packages: Springer Book Archive