Gabor Analysis and Algorithms: Theory and Applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1998
|
| Schriftenreihe: | Applied and Numerical Harmonic Analysis
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In his paper Theory of Communication [Gab46], D. Gabor proposed the use of a family of functions obtained from one Gaussian by time-and frequency shifts. Each of these is well concentrated in time and frequency; together they are meant to constitute a complete collection of building blocks into which more complicated time-depending functions can be decomposed. The application to communication proposed by Gabor was to send the coeffi cients of the decomposition into this family of a signal, rather than the signal itself. This remained a proposal-as far as I know there were no seri ous attempts to implement it for communication purposes in practice, and in fact, at the critical time-frequency density proposed originally, there is a mathematical obstruction; as was understood later, the family of shifted and modulated Gaussians spans the space of square integrable functions [BBGK71, Per71] (it even has one function to spare [BGZ75] . . . ) but it does not constitute what we now call a frame, leading to numerical insta bilities. The Balian-Low theorem (about which the reader can find more in some of the contributions in this book) and its extensions showed that a similar mishap occurs if the Gaussian is replaced by any other function that is "reasonably" smooth and localized. One is thus led naturally to considering a higher time-frequency density |
| Beschreibung: | 1 Online-Ressource (XVI, 496 p) |
| ISBN: | 9781461220169 9781461273820 |
| DOI: | 10.1007/978-1-4612-2016-9 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804153091234201600 |
|---|---|
| any_adam_object | |
| author | Feichtinger, Hans G. 1951- |
| author_GND | (DE-588)11810442X (DE-588)1147161585 |
| author_facet | Feichtinger, Hans G. 1951- |
| author_role | aut |
| author_sort | Feichtinger, Hans G. 1951- |
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| building | Verbundindex |
| bvnumber | BV042419959 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1165580347 (DE-599)BVBBV042419959 |
| dewey-full | 519 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519 |
| dewey-search | 519 |
| dewey-sort | 3519 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-2016-9 |
| format | Electronic eBook |
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| id | DE-604.BV042419959 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461220169 9781461273820 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855376 |
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| spelling | Feichtinger, Hans G. 1951- Verfasser (DE-588)11810442X aut Gabor Analysis and Algorithms Theory and Applications edited by Hans G. Feichtinger, Thomas Strohmer Boston, MA Birkhäuser Boston 1998 1 Online-Ressource (XVI, 496 p) txt rdacontent c rdamedia cr rdacarrier Applied and Numerical Harmonic Analysis In his paper Theory of Communication [Gab46], D. Gabor proposed the use of a family of functions obtained from one Gaussian by time-and frequency shifts. Each of these is well concentrated in time and frequency; together they are meant to constitute a complete collection of building blocks into which more complicated time-depending functions can be decomposed. The application to communication proposed by Gabor was to send the coeffi cients of the decomposition into this family of a signal, rather than the signal itself. This remained a proposal-as far as I know there were no seri ous attempts to implement it for communication purposes in practice, and in fact, at the critical time-frequency density proposed originally, there is a mathematical obstruction; as was understood later, the family of shifted and modulated Gaussians spans the space of square integrable functions [BBGK71, Per71] (it even has one function to spare [BGZ75] . . . ) but it does not constitute what we now call a frame, leading to numerical insta bilities. The Balian-Low theorem (about which the reader can find more in some of the contributions in this book) and its extensions showed that a similar mishap occurs if the Gaussian is replaced by any other function that is "reasonably" smooth and localized. One is thus led naturally to considering a higher time-frequency density Mathematics Functional analysis Engineering mathematics Applications of Mathematics Signal, Image and Speech Processing Appl.Mathematics/Computational Methods of Engineering Functional Analysis Mathematik Gabor-Transformation (DE-588)4410111-9 gnd rswk-swf Bildverarbeitung (DE-588)4006684-8 gnd rswk-swf Digitale Signalverarbeitung (DE-588)4113314-6 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Bildverarbeitung (DE-588)4006684-8 s Mathematische Methode (DE-588)4155620-3 s 1\p DE-604 Digitale Signalverarbeitung (DE-588)4113314-6 s 2\p DE-604 Gabor-Transformation (DE-588)4410111-9 s 3\p DE-604 Strohmer, Thomas Sonstige (DE-588)1147161585 oth https://doi.org/10.1007/978-1-4612-2016-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Feichtinger, Hans G. 1951- Gabor Analysis and Algorithms Theory and Applications Mathematics Functional analysis Engineering mathematics Applications of Mathematics Signal, Image and Speech Processing Appl.Mathematics/Computational Methods of Engineering Functional Analysis Mathematik Gabor-Transformation (DE-588)4410111-9 gnd Bildverarbeitung (DE-588)4006684-8 gnd Digitale Signalverarbeitung (DE-588)4113314-6 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| subject_GND | (DE-588)4410111-9 (DE-588)4006684-8 (DE-588)4113314-6 (DE-588)4155620-3 |
| title | Gabor Analysis and Algorithms Theory and Applications |
| title_auth | Gabor Analysis and Algorithms Theory and Applications |
| title_exact_search | Gabor Analysis and Algorithms Theory and Applications |
| title_full | Gabor Analysis and Algorithms Theory and Applications edited by Hans G. Feichtinger, Thomas Strohmer |
| title_fullStr | Gabor Analysis and Algorithms Theory and Applications edited by Hans G. Feichtinger, Thomas Strohmer |
| title_full_unstemmed | Gabor Analysis and Algorithms Theory and Applications edited by Hans G. Feichtinger, Thomas Strohmer |
| title_short | Gabor Analysis and Algorithms |
| title_sort | gabor analysis and algorithms theory and applications |
| title_sub | Theory and Applications |
| topic | Mathematics Functional analysis Engineering mathematics Applications of Mathematics Signal, Image and Speech Processing Appl.Mathematics/Computational Methods of Engineering Functional Analysis Mathematik Gabor-Transformation (DE-588)4410111-9 gnd Bildverarbeitung (DE-588)4006684-8 gnd Digitale Signalverarbeitung (DE-588)4113314-6 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| topic_facet | Mathematics Functional analysis Engineering mathematics Applications of Mathematics Signal, Image and Speech Processing Appl.Mathematics/Computational Methods of Engineering Functional Analysis Mathematik Gabor-Transformation Bildverarbeitung Digitale Signalverarbeitung Mathematische Methode |
| url | https://doi.org/10.1007/978-1-4612-2016-9 |
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