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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 𝒒=𝒒(g,LΓ— K)βŠ‚ β„‚N is block-equivalent when either the modulation set L or the translation set K is a subgroup of β„€N. We also characterize situations in which the frame operator matrix becomes diagonal. Finally, we show that geometric conditions on subsets of β„€N force certain diagonals of the frame operator matrix of 𝒒 to vanish, yielding additional sparsity and block structures.

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Cite

BibTeXRIS
BibTeX
@misc{asipchuk2026blockequivalent,
  title = {{Block-equivalent finite Gabor frames}},
  author = {Oleg Asipchuk and Laura De Carli and Luis Rodriguez},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.16139},
  eprint = {2605.16139},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.16139},
}
RIS
TY  - UNPB
TI  - Block-equivalent finite Gabor frames
AU  - Oleg Asipchuk
AU  - Laura De Carli
AU  - Luis Rodriguez
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2605.16139
UR  - https://arxiv.org/abs/2605.16139
AB  - 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 𝒒=𝒒(g,LΓ— K)βŠ‚ β„‚^N is block-equivalent when either the modulation set L or the translation set K is a subgroup of β„€_N. We also characterize situations in which the frame operator matrix becomes diagonal. Finally, we show that geometric conditions on subsets of β„€_N force certain diagonals of the frame operator matrix of 𝒒 to vanish, yielding additional sparsity and block structures.
ER  -