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Proceedings Paper

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

It is well known that nonlinear time-invariant filtering may be viewed as a nonlinear superposition of time-shifted versions of the input signal, that is described as a time invariant Volterra convolution. Nonlinear superposition of time- and frequency shifted versions of the input signal is called Volterra-Weyl convolution. In the present paper, we associate with each orthogonal transform (Legandre, Hermite, Laguerre, Walsh, Haar, Gabor, fractional Fourier, wavelet, etc.) a family of generalized shift operators. Using them we construct a nonlinear superposition of generalized time-shifted versions of the input signal. We call such a superposition a generalized Volterra-Weyl convolution (VWC). Particular cases of the VWC are nonlinear Gabor and Zak transformations, generalized higher-order Wigner distribution and ambiguity functions.

Paper Details

Date Published: 3 March 2000
PDF: 12 pages
Proc. SPIE 3961, Nonlinear Image Processing XI, (3 March 2000); doi: 10.1117/12.379383
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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