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arXiv · 1902.01062

Extreme Singular Values of Random Time-Frequency Structured Matrices

Palina Salanevich
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Abstract

In this paper, we investigate extreme singular values of the analysis matrix of a Gabor frame $(g, Λ)$ with a random window $g$. Columns of such matrices are time and frequency shifts of $g$, and $Λ\subset \mathbb{Z}_M\times\mathbb{Z}_M$ 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 $Λ$, and to investigate their dependence on the structure of $Λ$, 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.

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Palina Salanevich. 2019-02-04. Extreme Singular Values of Random Time-Frequency Structured Matrices. https://arxiv.org/abs/1902.01062

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