| 书目名称 | Gabor Analysis and Algorithms | | 副标题 | Theory and Applicati | | 编辑 | Hans G. Feichtinger,Thomas Strohmer | | 视频video | | | 丛书名称 | Applied and Numerical Harmonic Analysis | | 图书封面 |  | | 描述 | 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 occ | | 出版日期 | Book 1998 | | 关键词 | Analysis; Signal; algorithm; algorithms; calculus; detection; harmonic analysis; image processing; numerical | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4612-2016-9 | | isbn_softcover | 978-1-4612-7382-0 | | isbn_ebook | 978-1-4612-2016-9Series ISSN 2296-5009 Series E-ISSN 2296-5017 | | issn_series | 2296-5009 | | copyright | Springer Science+Business Media New York 1998 |
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发表于 2025-3-21 17:55:20
