Ebook: Advances in Gabor Analysis
- Tags: Analysis, Computational Mathematics and Numerical Analysis, Computational Intelligence, Signal Image and Speech Processing
- Series: Applied and Numerical Harmonic Analysis
- Year: 2003
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scientific communities with significant developments in harmonic analysis, ranging from abstract har monic analysis to basic applications. The title of the series reflects the im portance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the interleaving of theory and applications and their creative symbi otic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has flour ished, developed, and deepened over time within many disciplines and by means of creative cross-fertilization with diverse areas. The intricate and fundamental relationship between harmonic analysis and fields such as sig nal processing, partial differential equations (PDEs), and image processing is reflected in our state of the art ANHA series. Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time frequency analysis, and fractal geometry, as well as the diverse topics that impinge on them.
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.
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.
Content:
Front Matter....Pages i-xix
Introduction....Pages 1-9
Uncertainty Principles for Time-Frequency Representations....Pages 11-30
Zak Transforms with Few Zeros and the Tie....Pages 31-70
Bracket Products for Weyl—Heisenberg Frames....Pages 71-98
A First Survey of Gabor Multipliers....Pages 99-128
Aspects of Gabor Analysis and Operator Algebras....Pages 129-152
Integral Operators, Pseudodifferential Operators, and Gabor Frames....Pages 153-169
Methods for Approximation of the Inverse (Gabor) Frame Operator....Pages 171-195
Wilson Bases on the Interval....Pages 197-221
Localization Properties and Wavelet-Like Orthonormal Bases for the Lowest Landau Level....Pages 223-258
Optimal Stochastic Encoding and Approximation Schemes using Weyl—Heisenberg Sets....Pages 259-320
Orthogonal Frequency Division Multiplexing Based on Offset QAM....Pages 321-352
Back Matter....Pages 353-356
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.
Content:
Front Matter....Pages i-xix
Introduction....Pages 1-9
Uncertainty Principles for Time-Frequency Representations....Pages 11-30
Zak Transforms with Few Zeros and the Tie....Pages 31-70
Bracket Products for Weyl—Heisenberg Frames....Pages 71-98
A First Survey of Gabor Multipliers....Pages 99-128
Aspects of Gabor Analysis and Operator Algebras....Pages 129-152
Integral Operators, Pseudodifferential Operators, and Gabor Frames....Pages 153-169
Methods for Approximation of the Inverse (Gabor) Frame Operator....Pages 171-195
Wilson Bases on the Interval....Pages 197-221
Localization Properties and Wavelet-Like Orthonormal Bases for the Lowest Landau Level....Pages 223-258
Optimal Stochastic Encoding and Approximation Schemes using Weyl—Heisenberg Sets....Pages 259-320
Orthogonal Frequency Division Multiplexing Based on Offset QAM....Pages 321-352
Back Matter....Pages 353-356
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