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Applied and Numerical Harmonic Analysis

Gabor Analysis and Algorithms

Theory and Applications

Editors: Feichtinger, Hans G., Strohmer, Thomas (Eds.)

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


Table of contents (15 chapters)

Table of contents (15 chapters)

Buy this book

eBook $79.99
price for USA in USD (gross)
  • ISBN 978-1-4612-2016-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-0-8176-3959-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.99
price for USA in USD
  • ISBN 978-1-4612-7382-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

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
Copyright
1998
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-2016-9
DOI
10.1007/978-1-4612-2016-9
Hardcover ISBN
978-0-8176-3959-4
Softcover ISBN
978-1-4612-7382-0
Series ISSN
2296-5009
Edition Number
1
Number of Pages
XVI, 496
Topics