Gabor Analysis and Algorithms: Theory and Applications / Edition 1

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Editorial Reviews

Surveys the subject of Gabor analysis, showing the connections and interactions between theory, numerical algorithms, and applications. The first part covers the mathematical foundations of Gabor analysis, including Weyl-Heisenberg frames, duality conditions, the uncertainty principle, and the Balian-Low Theorem, as well as a group theoretical approach. The second part presents numerical algorithms and selected applications in signal and image processing. Annotation c. by Book News, Inc., Portland, Or.
From the Publisher

"... a definitive survey of the subject shows connections and interactions between theory, numerical algorithms, and applications." —Mathematical Reviews

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Product Details

  • ISBN-13: 9780817639594
  • Publisher: Birkhauser Verlag
  • Publication date: 12/18/1997
  • Series: Applied and Numerical Harmonic Analysis Series
  • Edition description: 1998
  • Edition number: 1
  • Pages: 496
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.13 (d)

Table of Contents

Introduction 1
1 The duality condition for Weyl-Heisenberg frames 33
2 Gabor systems and the Balian-Low Theorem 85
3 A Banach space of test functions for Gabor analysis 123
4 Pseudodifferential operators, Gabor frames, and local trigonometric bases 171
5 Perturbation of frames and applications to Gabor frames 193
6 Aspects of Gabor analysis on locally compact abelian groups 211
7 Quantization of TF lattice-invariant operators on elementary LCA groups 233
8 Numerical algorithms for discrete Gabor expansions 267
9 Oversampled modulated filter banks 295
10 Adaptation of Weyl-Heisenberg frames to underspread environments 323
11 Gabor representation and signal detection 353
12 Multi-window Gabor schemes in signal and image representations 381
13 Gabor kernels for affine-invariant object recognition 409
14 Gabor's signal expansion in optics 427
Bibliography 453
Index 489
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