Super Gabor frames on discrete periodic sets

Authors:
Yun-Zhang Li;Qiao-Fang Lian
Affiliations:
College of Applied Sciences, Beijing University of Technology, Beijing, People's Republic of China 100124;Department of Mathematics, Beijing Jiaotong University, Beijing, People's Republic of China 100044
Venue:
Advances in Computational Mathematics
Year:
2013

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Abstract

Due to its potential applications in multiplexing techniques such as time division multiple access and frequency division multiple access, superframe has interested some mathematicians and engineering specialists. In this paper, we investigate super Gabor systems on discrete periodic sets in terms of a suitable Zak transform matrix, which can model signals to appear periodically but intermittently. Complete super Gabor systems, super Gabor frames and Gabor duals for super Gabor frames on discrete periodic sets are characterized; An explicit expression of Gabor duals is established, and the uniqueness of Gabor duals is characterized. On the other hand, discrete periodic sets admitting complete super Gabor systems, super Gabor frames, super Gabor Riesz bases are also characterized. Some examples are also provided to illustrate the general theory.