Gabor analysis and algorithms: theory and applications
Saved in:
| Format: | Book |
|---|---|
| Language: | German |
| Published: |
Boston [u.a.]
Birkhäuser
1998
|
| Series: | Applied and numerical harmonic analysis
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 453 - 488 |
| Physical Description: | XVI, 496 S. Ill., graph. Darst. |
| ISBN: | 3764339594 0817639594 |
Staff View
MARC
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| 245 | 1 | 0 | |a Gabor analysis and algorithms |b theory and applications |c Hans G. Feichtinger ... eds. |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1998 | |
| 300 | |a XVI, 496 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Applied and numerical harmonic analysis | |
| 500 | |a Literaturverz. S. 453 - 488 | ||
| 650 | 4 | |a ALGORITHMS | |
| 650 | 4 | |a SIGNAL PROCESSING - DIGITAL TECHNIQUES - MATHEMATICS | |
| 650 | 0 | 7 | |a Gabor-Transformation |0 (DE-588)4410111-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Methode |0 (DE-588)4155620-3 |2 gnd |9 rswk-swf |
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Record in the Search Index
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Contents
Foreword
Ingrid Daubechies xi
Preface xiii
Contributors xv
Introduction
Hans G. Feichtinger and Thomas Strohmer 1
1 The duality condition for Weyl Heisenberg frames
A.J.E.M. Janssen 33
1.1 Introduction 33
1.2 Time continuous shift invariant systems 37
1.3 Weyl Heisenberg systems as shift invariant systems 49
1.4 Weyl Heisenberg systems in the time frequency domain . . 54
1.5 Rational Weyl Heisenberg systems in the Zak transform do¬
main 61
1.6 Time discrete Weyl Heisenberg systems 65
2 Gabor systems and the Balian Low Theorem
John J. Benedetto, Christopher He.il, and David F. Walnut 85
2.1 Introduction 85
2.2 Background 90
2.3 The Zak Transform and the Amalgam BLT 97
2.4 Wilson bases 105
2.5 Distributional calculations and the continuity of the Zak
transform 109
2.6 The Uncertainty Principle approach to the BLT 114
2.7 Appendix: Notation 121
3 A Banach space of test functions for Gabor analysis
Hans G. Feichtinger and Georg Zimmermann 123
3.1 Introduction 123
3.2 Characterizations of the Segal algebra So(Rd) 125
3.3 Continuity of Gabor operators 138
3.4 Riesz bases and frames for Banach spaces 144
viii Contents
3.5 Dual pairs and biorthogonal systems 150
3.6 Dual pairs in Sq 161
4 Pseudodifferential operators, Gabor frames, and
local trigonometric bases
Richard Rochberg and Kazuya Tachizawa 171
4.1 Introduction 171
4.2 Main results 173
4.3 Analysis of elliptic pseudodifferential operators 178
4.4 Approximate diagonalization of a(x, D) 180
4.5 The boundedness of a{x, D) on the Sobolev spaces 182
4.6 Estimates for singular values 185
4.7 Size estimates for eigenfunctions 187
5 Perturbation of frames and applications to Gabor frames
Ole Christensen 193
5.1 Introduction 193
5.2 Frames and Riesz bases 195
5.3 Perturbation of frames 197
5.4 Applications to Gabor frames 205
5.5 Banach frames 209
6 Aspects of Gabor analysis on locally compact abelian groups
Karlheinz Grochenig 211
6.1 Introduction 211
6.2 Basics on locally compact abelian groups 213
6.3 Uncertainty Principles and Lieb's inequalities 220
6.4 Zak transform, Gabor frames, and the Balian Low
phenomenon 222
6.5 Density conditions 229
7 Quantization of TF lattice invariant operators
on elementary LCA groups
Hans G. Feichtinger and Werner Kozek 233
7.1 Introduction 233
7.2 Elementary LCA groups and their TF Shift 234
7.3 The Gelfand triple (So,L2,S(,)(g) 237
7.4 The operator Gelfand triple (B,7i,B') 244
7.5 The generalized KN correspondence 247
7.6 Spreading function 251
7.7 TF Lattice invariant operators . 255
7.8 KN versus Weyl quantization 263
Contents ix
8 Numerical algorithms for discrete Gabor expansions
Thomas Strohmer 267
8.1 Introduction 267
8.2 An Algebraic setting for discrete Gabor theory 268
8.3 Unitary factorizations of the Gabor frame operator 271
8.4 Finite Gabor expansions and number theory 280
8.5 Design of adaptive dual windows 286
8.6 Conjugate gradient methods for Gabor expansions 289
8.7 Preconditioners and Approximate Inverses 291
9 Oversampled modulated filter banks
Helmut Bb'lcskei and Franz Hlawatsch 295
9.1 Introduction and outline 295
9.2 Oversampled filter banks and frames 296
9.3 Oversampled DFT filter banks 306
9.4 Oversampled cosine modulated filter banks 314
9.5 Conclusion 321
10 Adaptation of Weyl Heisenberg frames
to underspread environments
Werner Kozek 323
10.1 Introduction 323
10.2 Time frequency operator representation 325
10.3 Operator analysis and synthesis via STFT 327
10.4 Adaptation of continuous WH frames 331
10.5 Underspread operators 336
10.6 Applying adapted continuous frames 340
10.7 Adaptation of discrete WH frames/bases 345
10.8 Numerical simulation 350
11 Gabor representation and signal detection
Ariela Zeira and Benjamin Friedlander 353
11.1 Introduction 353
11.2 Background 355
11.3 Detection in the transform domain 358
11.4 Detection in the data domain 360
11.5 Sensitivity to mismatch 370
11.6 Robust matched subspace detectors 375
11.7 Summary and conclusions 379
12 Multi window Gabor schemes in signal
and image representations
Yehoshua Y. Zeevi, Meir Zibulski, and Moshe Porat 381
12.1 Motivation for using Gabor type schemes 381
x Contents
12.2 Generalized Gabor type schemes 385
12.3 Applications in image processing and computer vision . . . 400
12.4 Summary and discussion 405
13 Gabor kernels for affine invariant object recognition
Jezekiel Ben Arie and Zhiqian Wang 409
13.1 Introduction 410
13.2 Affine invariant spectral signatures (AISSs) 412
13.3 Affine invariant recognition by multi dimensional indexing
(MDI) 420
13.4 Experimental results 421
14 Gabor's signal expansion in optics
Martin J. Bastiaans 427
14.1 Introduction 427
14.2 Some optics fundamentals 428
14.3 Gabor's signal expansion in optics 431
14.4 Degrees of freedom of an optical signal 440
14.5 Coherent optical generation of the Gabor transform via the
Zak transform 446
Bibliography 453
Index 489 |
| any_adam_object | 1 |
| author_GND | (DE-588)11810442X |
| building | Verbundindex |
| bvnumber | BV011746734 |
| classification_rvk | SK 450 |
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| dewey-full | 621.381542 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 621 - Applied physics |
| dewey-raw | 621.381542 |
| dewey-search | 621.381542 |
| dewey-sort | 3621.381542 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Informatik Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Book |
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| indexdate | 2024-12-06T15:15:34Z |
| institution | BVB |
| isbn | 3764339594 0817639594 |
| language | German |
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| physical | XVI, 496 S. Ill., graph. Darst. |
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| spelling | Gabor analysis and algorithms theory and applications Hans G. Feichtinger ... eds. Boston [u.a.] Birkhäuser 1998 XVI, 496 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied and numerical harmonic analysis Literaturverz. S. 453 - 488 ALGORITHMS SIGNAL PROCESSING - DIGITAL TECHNIQUES - MATHEMATICS Gabor-Transformation (DE-588)4410111-9 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Bildverarbeitung (DE-588)4006684-8 gnd rswk-swf Digitale Signalverarbeitung (DE-588)4113314-6 gnd rswk-swf Gabor-Transformation (DE-588)4410111-9 s DE-604 Digitale Signalverarbeitung (DE-588)4113314-6 s Mathematische Methode (DE-588)4155620-3 s Bildverarbeitung (DE-588)4006684-8 s Feichtinger, Hans G. 1951- Sonstige (DE-588)11810442X oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007925640&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gabor analysis and algorithms theory and applications ALGORITHMS SIGNAL PROCESSING - DIGITAL TECHNIQUES - MATHEMATICS Gabor-Transformation (DE-588)4410111-9 gnd Mathematische Methode (DE-588)4155620-3 gnd Bildverarbeitung (DE-588)4006684-8 gnd Digitale Signalverarbeitung (DE-588)4113314-6 gnd |
| subject_GND | (DE-588)4410111-9 (DE-588)4155620-3 (DE-588)4006684-8 (DE-588)4113314-6 |
| title | Gabor analysis and algorithms theory and applications |
| title_auth | Gabor analysis and algorithms theory and applications |
| title_exact_search | Gabor analysis and algorithms theory and applications |
| title_full | Gabor analysis and algorithms theory and applications Hans G. Feichtinger ... eds. |
| title_fullStr | Gabor analysis and algorithms theory and applications Hans G. Feichtinger ... eds. |
| title_full_unstemmed | Gabor analysis and algorithms theory and applications Hans G. Feichtinger ... eds. |
| title_short | Gabor analysis and algorithms |
| title_sort | gabor analysis and algorithms theory and applications |
| title_sub | theory and applications |
| topic | ALGORITHMS SIGNAL PROCESSING - DIGITAL TECHNIQUES - MATHEMATICS Gabor-Transformation (DE-588)4410111-9 gnd Mathematische Methode (DE-588)4155620-3 gnd Bildverarbeitung (DE-588)4006684-8 gnd Digitale Signalverarbeitung (DE-588)4113314-6 gnd |
| topic_facet | ALGORITHMS SIGNAL PROCESSING - DIGITAL TECHNIQUES - MATHEMATICS Gabor-Transformation Mathematische Methode Bildverarbeitung Digitale Signalverarbeitung |
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