Foundations of Time-Frequency Analysis

  • Karlheinz Gröchenig

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Karlheinz Gröchenig
    Pages 1-2
  3. Karlheinz Gröchenig
    Pages 3-20
  4. Karlheinz Gröchenig
    Pages 37-58
  5. Karlheinz Gröchenig
    Pages 59-82
  6. Karlheinz Gröchenig
    Pages 83-101
  7. Karlheinz Gröchenig
    Pages 103-126
  8. Karlheinz Gröchenig
    Pages 127-146
  9. Karlheinz Gröchenig
    Pages 147-174
  10. Karlheinz Gröchenig
    Pages 175-201
  11. Karlheinz Gröchenig
    Pages 203-214
  12. Karlheinz Gröchenig
    Pages 215-244
  13. Karlheinz Gröchenig
    Pages 245-275
  14. Karlheinz Gröchenig
    Pages 277-299
  15. Karlheinz Gröchenig
    Pages 301-327
  16. Back Matter
    Pages 329-360

About this book

Introduction

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.

Keywords

Fourier analysis Fourier transform Modulation Signal analysis harmonic analysis information information theory quantum mechanics signal analysis wavelets

Authors and affiliations

  • Karlheinz Gröchenig
    • 1
  1. 1.Department of MathematicsUniversity of ConnecticutStorrsUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0003-1
  • Copyright Information Birkhäuser Boston 2001
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6568-9
  • Online ISBN 978-1-4612-0003-1
  • Series Print ISSN 2296-5009
  • Series Online ISSN 2296-5017
  • About this book