Discretization of the Gabor-type scheme by sampling of the Zak transform

Meir Zibulski; Yehoshua Y. Zeevi

doi:10.1117/12.185873

16 September 1994 Discretization of the Gabor-type scheme by sampling of the Zak transform

Meir Zibulski, Yehoshua Y. Zeevi

Proceedings Volume 2308, Visual Communications and Image Processing '94; (1994) https://doi.org/10.1117/12.185873
Event: Visual Communications and Image Processing '94, 1994, Chicago, IL, United States

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.

Citation Download Citation

Meir Zibulski and Yehoshua Y. Zeevi "Discretization of the Gabor-type scheme by sampling of the Zak transform", Proc. SPIE 2308, Visual Communications and Image Processing '94, (16 September 1994); https://doi.org/10.1117/12.185873

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