Simple quasicrystals are sets of stable sampling
Simple quasicrystals are sets of stable sampling
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简单的准晶体是稳定采样的集合
DOI：
10.1080/17476930903394689
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发表时间：
2010
影响因子：
0.9
通讯作者：
Y. Meyer
中科院分区：
文献类型：
--
作者：
Basarab Matei;Y. Meyer
这一贡献是解决信号处理中的一个问题。设是一个格，是对偶格。然后，标准的香农-奈奎斯特定理说，任何信号f的傅里叶变换是由一个紧凑的子集支持，可以从样本中恢复，当且仅当平移集是成对不相交的。这个关于K的充分条件也是必要的。当它不满足可能发生。Olevskii和Ulanovskii设计了不规则的抽样策略。然后，可以最佳地减少恢复信号或图像所需的措施的数量，该信号或图像的傅里叶变换由具有给定措施的紧致集K支持。目前的贡献是为了弥合这一进步之间的差距差距不规则采样和准晶理论。
This contribution is addressing an issue named in signal processing. Let be a lattice and be the dual lattice. Then the standard Shannon–Nyquist theorem says that any signal f whose Fourier transform is supported by a compact subset can be recovered from the samples if and only if the translated sets are pairwise disjoint. This sufficient condition on K is also necessary. When it is not satisfied may occur. Olevskii and Ulanovskii designed irregular sampling strategies which remedy . Then one can optimally reduce the number of measures needed to recover a signal or an image whose Fourier transform is supported by a compact set K with a given measure. The present contribution is aimed at bridging the gap between this advance on irregular sampling and the theory of quasicrystals.