Foundations of Time-Frequency Analysis

Released on by Karlheinz Gröchenig
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  • Foundations of Time-Frequency Analysis Book Detail

  • Author : Karlheinz Gröchenig
  • Release Date : 2013-12-01
  • Publisher : Springer Science & Business Media
  • Genre : Technology & Engineering
  • Pages : 367
  • ISBN 13 : 1461200032
  • File Size : 82,82 MB
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Foundations of Time-Frequency Analysis by Karlheinz Gröchenig PDF Summary

Book Description: 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.

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Covering a period of about 25 years, during which time-frequency has undergone significant developments, this book is principally addressed to researchers and e