Noch Fragen? 0800 / 33 82 637

Gabor Analysis and Algorithms

Theory and Applications

Produktform: E-Buch Text Elektronisches Buch in proprietärem

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.weiterlesen

Dieser Artikel gehört zu den folgenden Serien

Elektronisches Format: PDF

Sprache(n): Englisch

ISBN: 978-1-4612-2016-9 / 978-1461220169 / 9781461220169

Verlag: Birkhäuser Boston

Erscheinungsdatum: 06.12.2012

Seiten: 496

Herausgegeben von Hans G. Feichtinger, Thomas Strohmer

160,49 € inkl. MwSt.
Recommended Retail Price
kostenloser Versand

lieferbar - Lieferzeit 10-15 Werktage

zurück