Time‒frequency and Time‒scale Methods

Adaptive Decompositions, Uncertainty Principles, and Sampling
2005. Auflage 2004
ISBN: 978-0-8176-4276-1
Verlag: Birkhauser Boston

Buch, Englisch, 390 Seiten, Format (B × H): 164 mm x 244 mm, Gewicht: 1280 g

Reihe: Applied and Numerical Harmonic Analysis

Developed in this book are several deep connections between time-frequency (Fourier/Gabor) analysis and time-scale (wavelet) analysis, emphasizing the powerful adaptive methods that emerge when separate techniques from each area are properly assembled in a larger context. While researchers at the forefront of developments in time-frequency and time-scale analysis are well aware of the benefits of such a unified approach, there remains a knowledge gap in the larger community of practitioners about the precise strengths and limitations of Fourier/Gabor analysis versus wavelets. This book fills that gap by presenting the interface of time-frequency and time-scale methods as a rich area of work.

Zielgruppe

Research

Autoren/Hrsg.

Hogan, Jeffrey A

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Inhaltsverzeichnis

Wavelets: Basic properties, parameterizations and sampling.- Derivatives and multiwavelets.- Sampling in Fourier and wavelet analysis.- Bases for time-frequency analysis.- Fourier uncertainty principles.- Function spaces and operator theory.- Uncertainty principles in mathematical physics.