Time–frequency shift invariance and the Amalgam Balian–Low theorem
We consider smoothness properties of the generator of a principal Gabor space on the real line which is invariant under some additional translation–modulation pair. We prove that if a Gabor system on a lattice with rational density is a Riesz basis for its closed linear span, and if the closed linea...
| Autores principales: | , |
|---|---|
| Publicado: |
2016
|
| Materias: | |
| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10635203_v41_n3_p677_Cabrelli http://hdl.handle.net/20.500.12110/paper_10635203_v41_n3_p677_Cabrelli |
| Aporte de: |
| id |
paper:paper_10635203_v41_n3_p677_Cabrelli |
|---|---|
| record_format |
dspace |
| spelling |
paper:paper_10635203_v41_n3_p677_Cabrelli2023-06-08T16:03:32Z Time–frequency shift invariance and the Amalgam Balian–Low theorem Cabrelli, Carlos Alberto Molter, Ursula Maria Additional shift invariance Balian–Low theorem Feichtinger algebra Gabor frames Time–frequency analysis Harmonic analysis Balian-Low theorem Gabor frames Gabor systems Linear span Riesz basis Shift invariance Time frequency analysis Time-frequency shift Modulation We consider smoothness properties of the generator of a principal Gabor space on the real line which is invariant under some additional translation–modulation pair. We prove that if a Gabor system on a lattice with rational density is a Riesz basis for its closed linear span, and if the closed linear span, a Gabor space, has any additional translation–modulation invariance, then its generator cannot decay well in time and in frequency simultaneously. © 2015 Elsevier Inc. Fil:Cabrelli, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Molter, U. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10635203_v41_n3_p677_Cabrelli http://hdl.handle.net/20.500.12110/paper_10635203_v41_n3_p677_Cabrelli |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Additional shift invariance Balian–Low theorem Feichtinger algebra Gabor frames Time–frequency analysis Harmonic analysis Balian-Low theorem Gabor frames Gabor systems Linear span Riesz basis Shift invariance Time frequency analysis Time-frequency shift Modulation |
| spellingShingle |
Additional shift invariance Balian–Low theorem Feichtinger algebra Gabor frames Time–frequency analysis Harmonic analysis Balian-Low theorem Gabor frames Gabor systems Linear span Riesz basis Shift invariance Time frequency analysis Time-frequency shift Modulation Cabrelli, Carlos Alberto Molter, Ursula Maria Time–frequency shift invariance and the Amalgam Balian–Low theorem |
| topic_facet |
Additional shift invariance Balian–Low theorem Feichtinger algebra Gabor frames Time–frequency analysis Harmonic analysis Balian-Low theorem Gabor frames Gabor systems Linear span Riesz basis Shift invariance Time frequency analysis Time-frequency shift Modulation |
| description |
We consider smoothness properties of the generator of a principal Gabor space on the real line which is invariant under some additional translation–modulation pair. We prove that if a Gabor system on a lattice with rational density is a Riesz basis for its closed linear span, and if the closed linear span, a Gabor space, has any additional translation–modulation invariance, then its generator cannot decay well in time and in frequency simultaneously. © 2015 Elsevier Inc. |
| author |
Cabrelli, Carlos Alberto Molter, Ursula Maria |
| author_facet |
Cabrelli, Carlos Alberto Molter, Ursula Maria |
| author_sort |
Cabrelli, Carlos Alberto |
| title |
Time–frequency shift invariance and the Amalgam Balian–Low theorem |
| title_short |
Time–frequency shift invariance and the Amalgam Balian–Low theorem |
| title_full |
Time–frequency shift invariance and the Amalgam Balian–Low theorem |
| title_fullStr |
Time–frequency shift invariance and the Amalgam Balian–Low theorem |
| title_full_unstemmed |
Time–frequency shift invariance and the Amalgam Balian–Low theorem |
| title_sort |
time–frequency shift invariance and the amalgam balian–low theorem |
| publishDate |
2016 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10635203_v41_n3_p677_Cabrelli http://hdl.handle.net/20.500.12110/paper_10635203_v41_n3_p677_Cabrelli |
| work_keys_str_mv |
AT cabrellicarlosalberto timefrequencyshiftinvarianceandtheamalgambalianlowtheorem AT molterursulamaria timefrequencyshiftinvarianceandtheamalgambalianlowtheorem |
| _version_ |
1768543957124382720 |