Jeffrey A. Hogan Livres

Increasingly important in the field of communications, the study of time and band limiting is crucial for the modeling and analysis of multiband signals. This concise but comprehensive monograph is the first to be devoted specifically to this subdiscipline, providing a thorough investigation of its theory and applications. Through cutting-edge numerical methods, it develops the tools for applications not only to communications engineering, but also to optical engineering, geosciences, planetary sciences, and biomedicine. With broad coverage and a careful balance between rigor and readability, Duration and Bandwidth Limiting is a particularly original and valuable resource both for mathematicians interested in the field and for professional engineers with an interest in theory. While its main target audience is practicing scientists, the book may also serve as useful supplemental reading material for mathematically-based graduate courses in communications and signal processing.

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. TOC:Preface.- Wavelets: Basic properties, parametrizations 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.- A Appendix.- References.- Index