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＜E-Book＞
Foundations of Time-Frequency Analysis / by Karlheinz Gröchenig
(Applied and Numerical Harmonic Analysis. ISSN:22965017)

Edition	1st ed. 2001.
Publisher	(Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser)
Year	2001
Language	English
Size	XVI, 360 p : online resource
Authors	*Gröchenig, Karlheinz author SpringerLink (Online service)
Subjects	LCSH:Signal processing LCSH:Topological groups LCSH:Lie groups LCSH:Operations research LCSH:Management science LCSH:Electrical engineering FREE:Signal, Speech and Image Processing FREE:Topological Groups and Lie Groups FREE:Operations Research, Management Science FREE:Electrical and Electronic Engineering
Notes	Time-frequency analysis is a modern branch of harmonic analysis. It com­ prises all those parts of mathematics and its applications that use the struc­ ture of translations and modulations (or time-frequency shifts) for the anal­ ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym­ metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen­ tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita­ tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori­ entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D HTTP:URL=https://doi.org/10.1007/978-1-4612-0003-1

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