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About this book
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.
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Table of contents (15 chapters)
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Front Matter
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Back Matter
Reviews
"... a definitive survey of the subject shows connections and interactions between theory, numerical algorithms, and applications." —Mathematical Reviews
Editors and Affiliations
Bibliographic Information
Book Title: Gabor Analysis and Algorithms
Book Subtitle: Theory and Applications
Editors: Hans G. Feichtinger, Thomas Strohmer
Series Title: Applied and Numerical Harmonic Analysis
DOI: https://doi.org/10.1007/978-1-4612-2016-9
Publisher: Birkhäuser Boston, MA
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 1998
Hardcover ISBN: 978-0-8176-3959-4Published: 18 December 1997
Softcover ISBN: 978-1-4612-7382-0Published: 11 October 2012
eBook ISBN: 978-1-4612-2016-9Published: 06 December 2012
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number: 1
Number of Pages: XVI, 496
Topics: Applications of Mathematics, Signal, Image and Speech Processing, Mathematical and Computational Engineering, Functional Analysis