Extreme Singular Values of Random Time-Frequency Structured Matrices
Extreme Singular Values of Random Time-Frequency Structured Matrices
复制标题
随机时频结构矩阵的极奇异值
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Palina Salanevich
中科院分区：
文献类型：
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作者：
Palina Salanevich
本文研究了具有随机窗口的Gabor框架$(g, Lambda)$的分析矩阵的极值奇异性。这些矩阵的列是$g$的时频移，$Lambdasubset mathbb{Z}_M imesmathbb{Z}_M$是时频移指标的集合。我们的目标是获得这种随机时频结构矩阵的奇异值的界对于不同选择的框架集$Lambda$，并研究它们对$Lambda$结构的依赖，以及对其基数的依赖。我们还将Gabor框架分析矩阵的结果与具有独立同分布条目的矩阵的结果进行了比较。
In this paper, we investigate extreme singular values of the analysis matrix of a Gabor frame $(g, Lambda)$ with a random window $g$. Columns of such matrices are time and frequency shifts of $g$, and $Lambdasubset mathbb{Z}_M imesmathbb{Z}_M$ is the set of time-frequency shift indices. Our aim is to obtain bounds on the singular values of such random time-frequency structured matrices for various choices of the frame set $Lambda$, and to investigate their dependence on the structure of $Lambda$, as well as on its cardinality. We also compare the results obtained for Gabor frame analysis matrices with the respective results for matrices with independent identically distributed entries.