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arXiv · 2605.16139

Block-equivalent finite Gabor frames

Oleg Asipchuk·Laura De Carli·Luis Rodriguez
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Abstract

We study finite systems of vectors whose frame operator matrices are unitarily equivalent, via explicit and computationally efficient unitary transformations, to block-diagonal matrices. We call such systems block-equivalent. We show that a Gabor system $\mathcal{G}=\mathcal{G}(g,L\times K)\subset \mathbb C^N$ is block-equivalent when either the modulation set $L$ or the translation set $K$ is a subgroup of $\mathbb Z_N$. We also characterize situations in which the frame operator matrix becomes diagonal. Finally, we show that geometric conditions on subsets of $\mathbb Z_N$ force certain diagonals of the frame operator matrix of $\mathcal{G}$ to vanish, yielding additional sparsity and block structures.

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Oleg Asipchuk, Laura De Carli, Luis Rodriguez. 2026-05-15. Block-equivalent finite Gabor frames. https://arxiv.org/abs/2605.16139

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