Uncertainty in time–frequency representations on finite Abelian groups and applications
Uncertainty in time–frequency representations on finite Abelian groups and applications
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DOI：
10.1016/j.acha.2007.09.008
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发表时间：
2006-11
影响因子：
2.5
通讯作者：
F. Krahmer;G. Pfander;Peter Rashkov
中科院分区：
文献类型：
--
作者：
F. Krahmer;G. Pfander;Peter Rashkov
关于有限阿贝尔群函数的不确定性原理的经典和最新结果将函数支持的基数与其傅里叶变换支持的基数联系起来。我们获得了与函数的支持大小及其短时傅立叶变换相关的相应结果。我们利用我们的发现构建了一类等范紧 Gabor 框架，该框架对擦除具有最大的鲁棒性。此外，我们还讨论了我们的发现对具有稀疏时频表示的信号恢复和存储理论的影响。
Classical and recent results on uncertainty principles for functions on finite Abelian groups relate the cardinality of the support of a function to the cardinality of the support of its Fourier transform. We obtain corresponding results relating the support sizes of functions and their short-time Fourier transforms. We use our findings to construct a class of equal norm tight Gabor frames that are maximally robust to erasures. Also, we discuss consequences of our findings to the theory of recovering and storing signals with sparse time–frequency representations.