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Super Gabor frames on discrete periodic sets

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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.

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Authors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Yun-Zhang Li

  2. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Qiao-Fang Lian

Authors
  1. Yun-Zhang Li
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  2. Qiao-Fang Lian
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Corresponding author

Correspondence to Qiao-Fang Lian.

Additional information

Communicated by Qiyu Sun.

Supported by the National Natural Science Foundation of China (Grant No. 10901013), Beijing Natural Science Foundation (Grant No. 1092001), the Scientific Research Common Program of Beijing Municipal Commission of Education (Grant No. KM201110005030), the Fundamental Research Funds for the Central Universities (Grant No. 2011JBM299).

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Li, YZ., Lian, QF. Super Gabor frames on discrete periodic sets. Adv Comput Math 38, 763–799 (2013). https://doi.org/10.1007/s10444-011-9259-3

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  • DOI: https://doi.org/10.1007/s10444-011-9259-3

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