Extreme Singular Values of Random Time-Frequency Structured Matrices

Research output: Working paperAcademic

Abstract

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 $\Lambda\subset \mathbb{Z}_M\times\mathbb{Z}_M$ 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 $\Lambda$, 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.
Original languageEnglish
PublisherarXiv
Pages1-21
DOIs
Publication statusPublished - 4 Feb 2019
Externally publishedYes

Keywords

  • math.PR
  • math.FA
  • 60B20, 15B52, 15A18, 42C15, 43A32

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