Gabor Analysis and Algorithms: Theory and Applications

. Ed(s): Feichtinger, Hans G.; Strohmer, Thomas

ISBN 10: 0817639594 / ISBN 13: 9780817639594

Published by Birkh?user, 1997

About this Item

This text provides an introduction to mathematicians and engineers who want to learn about the different approaches and aspects of Gabor analysis or want to apply Gabor-based techniques to tasks in signal and image processing. Editor(s): Feichtinger, Hans G.; Strohmer, Thomas. Series: Applied and Numerical Harmonic Analysis. Num Pages: 496 pages, biography. BIC Classification: PBW; TJK; UYS; UYT. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 234 x 156 x 28. Weight in Grams: 896. . 1997. 1998th Edition. hardcover. . . . .

Seller Inventory # V9780817639594

Bibliographic Details

• Title: Gabor Analysis and Algorithms: Theory and Applications
• Publisher: Birkh?user
• Publication Date: 1997
• Language: English
• ISBN 10: 0817639594
• ISBN 13: 9780817639594
• Binding: Hardcover
• Condition: New

About this title

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.

Review

"... a definitive survey of the subject shows connections and interactions between theory, numerical algorithms, and applications." ―Mathematical Reviews