Gabor Analysis and Algorithms is popular PDF and ePub book, written by Hans G. Feichtinger in 2012-12-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Gabor Analysis and Algorithms can be Read Online from any device for your convenience.
Gabor Analysis and Algorithms Book PDF Summary
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.
Detail Book of Gabor Analysis and Algorithms PDF
- Author : Hans G. Feichtinger
- Release : 06 December 2012
- Publisher : Springer Science & Business Media
- ISBN : 9781461220169
- Genre : Mathematics
- Total Page : 507 pages
- Language : English
- PDF File Size : 9,9 Mb
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