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dc.contributor.author
Antezana, Jorge Abel
dc.contributor.author
Carbajal, Diana Agustina
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Romero, Jose Luis Fernando
dc.date.available
2024-08-05T14:15:55Z
dc.date.issued
2024-06
dc.identifier.citation
Antezana, Jorge Abel; Carbajal, Diana Agustina; Romero, Jose Luis Fernando; Random periodic sampling patterns for shift-invariant spaces; Institute of Electrical and Electronics Engineers; Ieee Transactions On Information Theory; 70; 6; 6-2024; 3855-3863
dc.identifier.issn
0018-9448
dc.identifier.uri
http://hdl.handle.net/11336/241722
dc.description.abstract
We consider multi-variate signals spanned by the integer shifts of a set of generating functions with distinct frequency profiles and the problem of reconstructing them from samples taken on a random periodic set. We show that such a sampling strategy succeeds with high probability provided that the density of the sampling pattern exceeds the number of frequency profiles by a logarithmic factor. The signal model includes bandlimited functions with multi-band spectra. While in this wellstudied setting delicate constructions provide sampling strategies that meet the information theoretic benchmark of Shannon and Landau, the sampling pattern that we consider provides, at the price of a logarithmic oversampling factor, a simple alternative that is accompanied by favorable a priori stability margins (snug frames). More generally, we also treat bandlimited functions with arbitrary compact spectra, and different measures of their complexity and approximation rates by integer tiles. At the technical level, we elaborate on recent work on relevant sampling, with the key difference that the reconstruction guarantees that we provide hold uniformly for all signals, rather than for a subset of well-concentrated ones. This is achieved by methods of concentration of measure formulated on the Zak domain.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Institute of Electrical and Electronics Engineers
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
MULTITILE SPECTRA
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SHIFT INVARIANT SPACES
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ZAK TRANSFORM
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RANDOM SAMPLING
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Matemática Pura
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Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
Random periodic sampling patterns for shift-invariant spaces
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2024-07-26T13:24:58Z
dc.identifier.eissn
1557-9654
dc.journal.volume
70
dc.journal.number
6
dc.journal.pagination
3855-3863
dc.journal.pais
Estados Unidos
dc.journal.ciudad
New York
dc.description.fil
Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
dc.description.fil
Fil: Carbajal, Diana Agustina. Universidad de Viena; Austria. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
dc.description.fil
Fil: Romero, Jose Luis Fernando. Universidad de Viena; Austria. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
dc.journal.title
Ieee Transactions On Information Theory
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://ieeexplore.ieee.org/document/10266375
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1109/TIT.2023.3320289
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/2305.15261
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