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Proceedings Paper

Nonlinear signal solitaire
Author(s): Ekaterina V. Labunets-Rundblad; Laura Astola; Valeri G. Labunets; Jaakko T. Astola; Karen O. Egiazarian
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Paper Abstract

Integral transforms and the signal representations associated with them are important tools in applied mathematics and signal theory. The Fourier transform and the Laplace transform are certainly the best known and most commonly used integral transforms. However, the Fourier transform is just one of many ways of signal representation and there are many other transforms of interest. In the past 20 years, other analytical methods have been proposed and applied, for example, wavelet, Walsh, Legandre, Hermite, Gabor, fractional Fourier analysis, etc. Regardless of their particular merits they are not as useful as the classical Fourier representation that is closely connected to such powerful concepts of signal theory as linear and nonlinear convolutions, classical and high-order correlations, invariance with respect to shift, ambiguity and Wigner distributions, etc. To obtain the general properties and important tools of the classical Fourier transform for an arbitrary orthogonal transform we associate to it generalized shift operators and develop the theory of abstract harmonic analysis of signals and linear and nonlinear systems that are invariant with respect to these generalized shift operators.

Paper Details

Date Published: 3 March 2000
PDF: 12 pages
Proc. SPIE 3961, Nonlinear Image Processing XI, (3 March 2000); doi: 10.1117/12.379384
Show Author Affiliations
Ekaterina V. Labunets-Rundblad, Tampere Univ. of Technology (Finland)
Laura Astola, Tampere Univ. of Technology (Finland)
Valeri G. Labunets, Tampere Univ. of Technology (Finland)
Jaakko T. Astola, Tampere Univ. of Technology (Finland)
Karen O. Egiazarian, Tampere Univ. of Technology (Finland)

Published in SPIE Proceedings Vol. 3961:
Nonlinear Image Processing XI
Edward R. Dougherty; Jaakko T. Astola, Editor(s)

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