Gabor Analysis and Algorithms - Theory and Applications (Hardcover, 1998 ed.)

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.

General

Imprint:	Birkhauser Boston
Country of origin:	United States
Series:	Applied and Numerical Harmonic Analysis
Release date:	December 1997
First published:	1998
Editors:	Hans G. Feichtinger • Thomas Strohmer
Dimensions:	235 x 155 x 28mm (L x W x T)
Format:	Hardcover
Pages:	496
Edition:	1998 ed.
ISBN-13:	978-0-8176-3959-4
Categories:	Books > Computing & IT > Applications of computing > Signal processing Books > Science & Mathematics > Mathematics > Applied mathematics > General Books > Professional & Technical > Electronics & communications engineering > Communications engineering / telecommunications > General Books > Computing & IT > Applications of computing > Image processing > General Promotions
LSN:	0-8176-3959-4
Barcode:	9780817639594

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