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Více informací o knize Gabor Analysis and Algorithms

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• Anotace
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Anotace knihy

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.

Parametry knihy

Zařazení knihy Knihy v angličtině Mathematics & science Mathematics Calculus & mathematical analysis

• Plný název: Gabor Analysis and Algorithms
• Podnázev: Theory and Applications
• Autor: Hans G. Feichtinger, Thomas Strohmer
• Jazyk: Angličtina
• Vazba: Brožovaná
• Počet stran: 496
• EAN: 9781461273820
• ISBN: 146127382X
• ID: 06795211
• Nakladatelství: Springer-Verlag New York Inc.
• Hmotnost: 783 g
• Rozměry: 235 × 155 × 29 mm
• Datum vydání: 11. October 2012

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