Kyoto Journal of Mathematics

Gabor families in l2(Zd)

Qiao-Fang Lian and Yun-Zhang Li

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Abstract

This paper addresses Gabor families in l2(Zd). The discrete Gabor families have interested many researchers due to their good potential for digital signal processing. Gabor analysis in l2(Zd) is more complicated than that in l2(Z) since the geometry of the lattices generated by time-frequency translation matrices can be quite complex in this case. In this paper, we characterize window functions such that they correspond to complete Gabor families (Gabor frames) in l2(Zd); obtain a necessary and sufficient condition on time-frequency translation for the existence of complete Gabor families (Gabor frames, Gabor Riesz bases) in l2(Zd); characterize duals with Gabor structure for Gabor frames; derive an explicit expression of the canonical dual for a Gabor frame; and prove its norm minimality among all Gabor duals.

Article information

Source
Kyoto J. Math., Volume 52, Number 1 (2012), 179-204.

Dates
First available in Project Euclid: 19 February 2012

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1329684747

Digital Object Identifier
doi:10.1215/21562261-1503800

Mathematical Reviews number (MathSciNet)
MR2892772

Zentralblatt MATH identifier
1242.42026

Subjects
Primary: 42C15: General harmonic expansions, frames

Citation

Lian, Qiao-Fang; Li, Yun-Zhang. Gabor families in $l^{2}(\mathbb{Z}^{d})$. Kyoto J. Math. 52 (2012), no. 1, 179--204. doi:10.1215/21562261-1503800. https://projecteuclid.org/euclid.kjm/1329684747


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