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Gabor Analysis and Algorithms : Theory and Applications / edited by Hans G. Feichtinger, Thomas Strohmer
(Applied and Numerical Harmonic Analysis. ISSN:22965017)
版 | 1st ed. 1998. |
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出版者 | (Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser) |
出版年 | 1998 |
本文言語 | 英語 |
大きさ | XVI, 496 p : online resource |
著者標目 | Feichtinger, Hans G editor Strohmer, Thomas editor SpringerLink (Online service) |
件 名 | LCSH:Mathematics LCSH:Signal processing LCSH:Engineering mathematics LCSH:Engineering -- Data processing 全ての件名で検索 LCSH:Functional analysis FREE:Applications of Mathematics FREE:Signal, Speech and Image Processing FREE:Mathematical and Computational Engineering Applications FREE:Functional Analysis |
一般注記 | 1 The duality condition for Weyl-Heisenberg frames -- 2 Gabor systems and the Balian-Low Theorem -- 3 A Banach space of test functions for Gabor analysis -- 4 Pseudodifferential operators, Gabor frames, and local trigonometric bases -- 5 Perturbation of frames and applications to Gabor frames -- 6 Aspects of Gabor analysis on locally compact abelian groups -- 7 Quantization of TF lattice-invariant operators on elementary LCA groups -- 8 Numerical algorithms for discrete Gabor expansions -- 9 Oversampled modulated filter banks -- 10 Adaptation of Weyl-Heisenberg frames to underspread environments -- 11 Gabor representation and signal detection -- 12 Multi-window Gabor schemes in signal and image representations -- 13 Gabor kernels for affine-invariant object recognition -- 14 Gabor’s signal expansion in optics 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 HTTP:URL=https://doi.org/10.1007/978-1-4612-2016-9 |
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Springer eBooks | 9781461220169 |
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EB00234783 |
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