Synopses & Reviews
This unified, self-contained volume provides insight into the richness of Gabor analysis and its potential for future development in applied mathematics and engineering. Mathematicians and engineers treat a range of topics covering theory as well as applications in eleven survey chapters. Taken as a whole, the work demonstrates interactions and connections among different areas in which Gabor analysis plays a critical role, including harmonic analysis, operator theory, quantum physics, numerical analysis, electrical engineering, and signal/image processing. Key features of the work: * Gives an overview of recent developments in Gabor analysis, an important tool in the understanding and use of time-frequency analysis methods in a variety of disciplines * Provides sufficient background material along with many new and previously unpublished results * Presents applications to areas such as digital and wireless communications * Up-to-date bibliographies for each chapter; useful subject index for the entire volume * Specific topics covered include: Uncertainty Principles for Time-Frequency Representations; Zak Transforms; Bracket Products for Weyl--Heisenberg Frames; Gabor Multipliers; Gabor Analysis and Operator Algebras; Integral Operators, Pseudodifferential Operators and Gabor Frames; Methods for Approximation of the Inverse (Gabor) Frame Operator; Wilson Bases Graduate students, professionals, and researchers in pure and applied mathematics, mathematical physics, electrical and communications engineering will find Advances in Gabor Analysis a comprehensive resource. Contributors: J.-P. Antoine, F. Bagarello, R. Balan, K. Bittner, H. Bölcskei, P.G. Casazza, O. Christensen, I. Daubechies, H.G. Feichtinger, J.-P. Gabardo, K. Gröchenig, D. Han, C. Heil, A.J.E.M. Janssen, M.C. Lammers, K. Nowak, T. Strohmer Also edited by Feichtinger and Strohmer---Gabor Analysis and Algorithms: Theory and Applications, ISBN 0-8176-3959-4, 1998
Synopsis
Unified, self-contained volume providing insight into the richness of Gabor analysis and its potential for development in applied mathematics and engineering. Mathematicians and engineers treat a range of topics, and cover theory and applications to areas such as digital and wireless communications. The work demonstrates interactions and connections among areas in which Gabor analysis plays a role: harmonic analysis, operator theory, quantum physics, numerical analysis, signal/image processing. For graduate students, professionals, and researchers in pure and applied mathematics, math physics, and engineering.
Table of Contents
Foreword/H. Landau
Contributors
Introduction /H.G. Feichtinger and T. Strohmer
Uncertainty Principles for Time-Frequency Representations /K. Gröchenig
Zak Transforms with Few Zeros and the Tie /A.J.E.M Janssen
Bracket Products for Weyl--Heisenberg Frames /P.G. Casazza and M.C. Lammers
A First Survey of Gabor Multipliers /H.G. Feichtinger and K. Nowak
Aspects of Gabor Analysis and Operator Algebras /J.-P. Gabardo and D. Han
Integral Operators, Pseudodifferential Operators, and Gabor Frames /C. Heil
Methods for Approximation of the Inverse (Gabor) Frame Operator /O. Christensen and T. Strohmer
Wilson Bases on the Interval /K. Bittner
Localization Properties and Wavelet-Like Orthonormal Bases for the Lowest Landau Level /J.-P. Antoine and F. Bagarello
Optimal Stochastic Encoding and Approximation Schemes using Weyl--Heisenberg Sets /R. Balan and I. Daubechies
Orthogonal Frequency Division Multiplexing Based on Offset QAM /H. Bölcskei
Index