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Proceedings Paper

Discretization of the Gabor-type scheme by sampling of the Zak transform
Author(s): Meir Zibulski; Yehoshua Y. Zeevi
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Paper Abstract

The matrix algebra approach was previously applied in the analysis of the continuous Gabor representation in the Zak transform domain. In this study we analyze the discrete and finite (periodic) scheme by the same approach. A direct relation that exists between the two schemes, based on the sampling of the Zak transform, is established. Specifically, we show that sampling of the Gabor expansion in the Zak transform domain yields a discrete scheme of representation. Such a derivation yields a simple relation between the schemes by means of the periodic extension of the signal. We show that in the discrete Zak domain the frame operator can be expressed by means of a matrix-valued function which is simply the sampled version of the matrix-valued function of the continuous scheme. This result establishes a direct relation between the frame properties of the two schemes.

Paper Details

Date Published: 16 September 1994
PDF: 11 pages
Proc. SPIE 2308, Visual Communications and Image Processing '94, (16 September 1994); doi: 10.1117/12.185873
Show Author Affiliations
Meir Zibulski, Technion--Israel Institute of Technology (Israel)
Yehoshua Y. Zeevi, Technion--Israel Institute of Technology (Israel)

Published in SPIE Proceedings Vol. 2308:
Visual Communications and Image Processing '94
Aggelos K. Katsaggelos, Editor(s)

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