Rational time–frequency super Gabor frames and their duals☆
Rational time–frequency super Gabor frames and their duals☆
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DOI：
10.1016/j.jmaa.2013.02.057
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发表时间：
2013-07
影响因子：
1.3
通讯作者：
Yun‐Zhang Li;Fengying Zhou
中科院分区：
文献类型：
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作者：
Yun‐Zhang Li;Fengying Zhou
本文研究了具有有理时频乘积格的一般超Gabor系统。针对这类超Gabor系统，提出了一种Zak变换矩阵方法。我们刻画了完备的超Gabor系统和超Gabor框架。给出了一个超Gabor框架，得到了它的标准对偶的显式表达式和它的所有超Gabor对偶的一个参数化式，并证明了该标准对偶是所有超Gabor对偶中的范数极小对偶.我们还证明了超Gabor框架存在唯一的超Gabor对偶当且仅当它是Riesz基。
This paper addresses general super Gabor systems with rational time–frequency product lattices. A Zak transform matrix method is developed for such super Gabor systems. We characterize complete super Gabor systems and super Gabor frames. Given a super Gabor frame, we obtain an explicit expression of its canonical dual and a parametrization of all its super Gabor duals and prove that the canonical dual is the norm-minimal one among all super Gabor duals. We also prove that a super Gabor frame has a unique super Gabor dual if and only if it is a Riesz basis.