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    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
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Gabor Analysis and Algorithms: Theory and Applications

Gabor Analysis and Algorithms: Theory and Applications

Feichtinger, Hans G.
Strohmer, Thomas

Hardcover

Series: Applied and Numerical Harmonic Analysis

Technology & EngineeringGeneral Mathematics

ISBN10: 0817639594
ISBN13: 9780817639594
Publisher: Springer Nature
Published: Dec 18 1997
Pages: 496
Weight: 1.89
Height: 1.12 Width: 6.39 Depth: 9.52
Language: English
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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