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DC Field | Value | Language |
---|---|---|
dc.citation.endPage | 1140 | - |
dc.citation.number | 4 | - |
dc.citation.startPage | 1119 | - |
dc.citation.title | JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | - |
dc.citation.volume | 24 | - |
dc.contributor.author | Christensen, Ole | - |
dc.contributor.author | Kim, Hong Oh | - |
dc.contributor.author | Kim, Rae Young | - |
dc.date.accessioned | 2023-12-21T20:19:31Z | - |
dc.date.available | 2023-12-21T20:19:31Z | - |
dc.date.created | 2018-08-30 | - |
dc.date.issued | 2018-08 | - |
dc.description.abstract | We prove that Gabor systems generated by certain scaled B-splines can be considered as perturbations of the Gabor systems generated by the Gaussian, with a deviation within an arbitrary small tolerance whenever the order N of the B-spline is sufficiently large. As a consequence we show that for any choice of translation/modulation parameters a, b > 0 with ab < 1, the scaled version of B-N generates Gabor frames for N sufficiently large. Considering the Gabor frame decomposition generated by the Gaussian and a dual window, the results lead to estimates of the deviation from perfect reconstruction that arise when the Gaussian is replaced by a scaled B-spline, or when the dual window of the Gaussian is replaced by certain explicitly given and compactly supported linear combinations of the B-splines. In particular, this leads to a family of approximate dual windows of a very simple form, leading to "almost perfect reconstruction" within any desired error tolerance whenever the product ab is sufficiently small. In contrast, the known (exact) dual windows have a very complicated form. A similar analysis is sketched with the scaled B-splines replaced by certain truncations of the Gaussian. As a consequence of the approach we prove (mostly known) convergence results for the considered scaled B-splines to the Gaussian in the L-P-spaces, as well in the time-domain as in the frequency domain. | - |
dc.identifier.bibliographicCitation | JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, v.24, no.4, pp.1119 - 1140 | - |
dc.identifier.doi | 10.1007/s00041-017-9557-3 | - |
dc.identifier.issn | 1069-5869 | - |
dc.identifier.scopusid | 2-s2.0-85028538690 | - |
dc.identifier.uri | https://scholarworks.unist.ac.kr/handle/201301/24713 | - |
dc.identifier.url | https://link.springer.com/article/10.1007%2Fs00041-017-9557-3 | - |
dc.identifier.wosid | 000441847000008 | - |
dc.language | 영어 | - |
dc.publisher | SPRINGER BIRKHAUSER | - |
dc.title | B-Spline Approximations of the Gaussian, their Gabor Frame Properties, and Approximately Dual Frames | - |
dc.type | Article | - |
dc.description.isOpenAccess | FALSE | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.subject.keywordAuthor | Gaussian | - |
dc.subject.keywordAuthor | B-Splines | - |
dc.subject.keywordAuthor | Frames | - |
dc.subject.keywordAuthor | Dual frames | - |
dc.subject.keywordPlus | BARGMANN-FOCK SPACE | - |
dc.subject.keywordPlus | DENSITY THEOREMS | - |
dc.subject.keywordPlus | INTERPOLATION | - |
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