Time-frequency analysis on flat tori and Gabor frames in finite dimensions

10.10.2022 15:00 - 16:00

Michael Speckbacher (Universität Wien)


Abstract: In this talk, we will introduce the concept of time-frequency analysis on the flat torus and present some of its basic properties. In particular, we show that it can be understood as a continuous extension of the finite Gabor transform on the lattice to the entire flat torus, and use this observation (in combination with complex analysis methods) to fully characterize the frame set of finite Gabor systems using periodized and sampled Gaussians as its window. This can be seen as an analogue of the results of Lyubarskii and Seip-Wallstén to the finite setting of $\C^N$.



SR 10, 2. OG., OMP 1

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