Gabor Analysis and Algorithms: Theory and Applications - Couverture souple

Couverture souple

ISBN 10 : 146127382X ISBN 13 : 9781461273820

Editeur : Birkhäuser, 2012

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: Birkhäuser
• Date d'édition: 2012
• Langue: anglais
• ISBN 10: 146127382X
• ISBN 13: 9781461273820
• Reliure: Broché
• Nombre de pages: 516
• Éditeur: Feichtinger Hans G., Strohmer Thomas
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Allemagne