| Foundations of Time-Frequency Analysis 2001 Edition Contributor(s): Gröchenig, Karlheinz (Author) |
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ISBN: 0817640223 ISBN-13: 9780817640224 Publisher: Birkhauser OUR PRICE: $170.99 Product Type: Hardcover - Other Formats Published: December 2000 Annotation: This book presents time-frequency analysis as a beautiful and deep mathematical subject while at the same time giving honor to its interdisciplinary origins and inspirations from signal analysis and from physics. The presentation covers the mathematical theory of time-frequency analysis, including classical Fourier analysis, discussions of the Heisenberg group, the uncertainty principle in its many forms, and the omnipresence of Gaussian functions. |
| Additional Information |
| BISAC Categories: - Mathematics | Probability & Statistics - General - Mathematics | Applied - Technology & Engineering | Electrical |
| Dewey: 512.55 |
| LCCN: 00044508 |
| Series: Applied and Numerical Harmonic Analysis |
| Physical Information: 0.88" H x 6.37" W x 9.56" (1.41 lbs) 360 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |