Super Gabor frames on discrete periodic sets

被引：10

作者：

Li, Yun-Zhang ^{[1
]}

Lian, Qiao-Fang ^{[2
]}

机构：

[1] Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China

[2] Beijing Jiaotong Univ, Dept Math, Beijing 100044, Peoples R China

来源：

ADVANCES IN COMPUTATIONAL MATHEMATICS | 2013年 / 38卷 / 04期

基金：

中国国家自然科学基金; 北京市自然科学基金;

关键词：

Superframe; Super Gabor frame; Gabor dual; Discrete periodic sets; Discrete Zak transform; WEYL-HEISENBERG FRAMES; TRANSFORM; SIGNALS;

D O I：

10.1007/s10444-011-9259-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：763 / 799

页数：37

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