Gabor Analysis and Algorithms: Theory and Applications - Applied and Numerical Harmonic Analysis (Hardback)
  • Gabor Analysis and Algorithms: Theory and Applications - Applied and Numerical Harmonic Analysis (Hardback)
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Gabor Analysis and Algorithms: Theory and Applications - Applied and Numerical Harmonic Analysis (Hardback)

(editor), (editor)
£119.99
Hardback 496 Pages / Published: 18/12/1997
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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.

Publisher: Birkhauser Boston Inc
ISBN: 9780817639594
Number of pages: 496
Weight: 1980 g
Dimensions: 235 x 155 x 28 mm
Edition: 1998 ed.


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