Advances in Gabor Analysis / Edition 1

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Gabor Analysis constitutes a central part of time-frequency analysis. While preserving the symmetry between the time (location) domain and the frequency (wave number) domain it avoids the high degree of redundancy inherent in the continuous short-time Fourier transform. The ability to resolve details of a signal ( or a system impulse response) in a two-dimensional representation, whose coefficients have a very natural interpretation, is the basis for many interesting applications in electrical engineering, or signal-and image processing in general, and thus makes Gabor Analysis an important branch of applied mathematics, whose full recognition lies ahead of us. The proposed book contributes positively to this devleopment.

The aim of the book is to provide an overview of recent developments in the area of Gabor analysis by bringing together the leading scientists of various disciplines related to this subject. Covering theory, numerics, as well as applications of Gabor analysis, the book will not merely be a collection of articles but a nice blend of invited chapters with a consistent presentation. Each chapter contains the most recent research while providing enough background material to put the work into proper context.

Graduate students, practitioners and other researchers in the areas of numerical analysis, electrical engineering and applied mathematics will find this book a current and useful resource.

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Editorial Reviews

From the Publisher

"The authors have put their effort into writing articles with the necessary background to make their presentations attractive and including a complete set of references. Good introductions and detailed expositions of ideas are given in all the presentations. These features make this book an invaluable tool for researchers interested in signal analysis. The research community will benefit greatly from this publication." —Mathematical Reviews

"The present book can be considered as a continuation of two previous ones: Gabor Analysis and Algorithms: Theory and Applications, H. G. Feichtinger and T. Strohmer, Eds., Birkhäuser 1998, and the book by K. Gröchenig, Foundations of Time-Frequency Analysis, Birkhäuser 2001. It contains survey chapters, but new results that have not been published previously are also included. The introductory chapter of the book, written by H. G. Feichtinger and T. Strohmer, contains a clear outline of the contents as well as some comments on the future developments in Gabor analysis.

Written by leading experts in the field, the volume appeals, by its interdisciplinary character, to a large audience, both novices and experts, theoretically inclined researchers and practitioners as well. It brilliantly illustrates how application areas and pure and applied mathematics can work together with profit for all." —Revue D'Analyse Numérique et de Théorie de L'Approximation, 2004

"A mathematically sound and self-contained presentation on recent advances in the highly applicable field of Gabor analysis.… This book is a must for all interested in signal analysis, and, of course, in particular in Gabor analysis." —Monatschefte für Mathematik

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Product Details

  • ISBN-13: 9780817642396
  • Publisher: Birkhauser Verlag
  • Publication date: 12/17/2002
  • Series: Applied and Numerical Harmonic Analysis Series
  • Edition description: 2003
  • Edition number: 1
  • Pages: 356
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.88 (d)

Table of Contents

1 Introduction 1
2 Uncertainty Principles for Time-Frequency Representations 11
3 Zak Transforms with Few Zeros and the Tie 31
4 Bracket Products for Weyl-Heisenberg Frames 71
5 A First Survey of Gabor Multipliers 99
6 Aspects of Gabor Analysis and Operator Algebras 129
7 Integral Operators, Pseudodifferential Operators, and Gabor Frames 153
8 Methods for Approximation of the Inverse (Gabor) Frame Operator 171
9 Wilson Bases on the Interval 197
10 Localization Properties and Wavelet-Like Orthonormal Bases for the Lowest Landau Level 223
11 Optimal Stochastic Encoding and Approximation Schemes using Weyl-Heisenberg Sets 259
12 Orthogonal Frequency Division Multiplexing Based on Offset QAM 321
Index 353
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