Gabor Analysis and Algorithms: Theory and Applications - Couverture rigide

Couverture rigide

ISBN 10 : 0817639594 ISBN 13 : 9780817639594

Editeur : Birkhauser Boston Inc, 1997

Synopsis

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.

Détails de l'édition

• Éditeur: Birkhauser Boston Inc
• Date d'édition: 1997
• Langue: anglais
• ISBN 10: 0817639594
• ISBN 13: 9780817639594
• Reliure: Relié
• Nombre de pages: 512
• Éditeur: Feichtinger Hans G., Strohmer Thomas
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne