Foundations of Time-Frequency Analysis

2001
ISBN: 978-0-8176-4022-4
Verlag: Birkhäuser Boston

Buch, Englisch, 360 Seiten, Book w. online files / update, Format (B × H): 160 mm x 241 mm, Gewicht: 1560 g

Reihe: Applied and Numerical Harmonic Analysis

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.

Zielgruppe

Research

Autoren/Hrsg.

Gröchenig, Karlheinz

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Signalverarbeitung, Bildverarbeitung, Scanning