Gabor systems on discrete periodic sets |
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Authors: | YunZhang Li QiaoFang Lian |
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Institution: | (1) College of Applied Sciences, Beijing University of Technology, Beijing, 100124, China;(2) Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, China |
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Abstract: | Due to its good potential for digital signal processing, discrete Gabor analysis has interested some mathematicians. This
paper addresses Gabor systems on discrete periodic sets, which can model signals to appear periodically but intermittently.
Complete Gabor systems and Gabor frames on discrete periodic sets are characterized; a sufficient and necessary condition
on what periodic sets admit complete Gabor systems is obtained; this condition is also proved to be sufficient and necessary
for the existence of sets E such that the Gabor systems generated by χ
E
are tight frames on these periodic sets; our proof is constructive, and all tight frames of the above form with a special
frame bound can be obtained by our method; periodic sets admitting Gabor Riesz bases are characterized; some examples are
also provided to illustrate the general theory.
This work was supported by National Natural Science Foundation of China (Grant No. 10671008), Beijing Natural Science Foundation
(Grant No. 1092001), PHR (IHLB) and the project sponsored by SRF for ROCS, SEM of China |
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Keywords: | Gabor systems periodic sets discrete Zak transform |
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