Computational signal processing with wavelets:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
1998
|
| Schriftenreihe: | Applied and numerical harmonic analysis
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 313 - 320 |
| Beschreibung: | XXIV, 324 S. Ill., graph. Darst. |
| ISBN: | 3764339098 0817639098 9781461286721 |
Internformat
MARC
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| 100 | 1 | |a Teolis, Anthony |d 1964- |e Verfasser |0 (DE-588)120165864 |4 aut | |
| 245 | 1 | 0 | |a Computational signal processing with wavelets |c Anthony Teolis |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1998 | |
| 300 | |a XXIV, 324 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. 313 - 320 | ||
| 650 | 4 | |a Signalverarbeitung - Wavelet | |
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| 689 | 0 | 0 | |a Signalverarbeitung |0 (DE-588)4054947-1 |D s |
| 689 | 0 | 1 | |a Wavelet |0 (DE-588)4215427-3 |D s |
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| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008118752&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1809999093337948160 |
|---|---|
| adam_text |
Contents
Preface xiii
List of Tables xvii
List of Figures xix
1 Introduction 1
1.1 Motivation and Objectives 1
1.2 Core Material and Development 1
1.3 Hybrid Media Components 2
1.4 Signal Processing Perspective 3
1.4.1 Analog Signals 3
1.4.2 Digital Processing of Analog Signals 3
1.4.3 Time Frequency Limitedness 5
2 Mathematical Preliminaries 7
2.1 Basic Symbols and Notation 7
2.2 Basic Concepts 8
2.2.1 Norm 8
2.2.2 Inner Product 8
2.2.3 Convergence 9
2.2.4 Hilbert Spaces 9
2.3 Basic Spaces 10
2.3.1 Bounded Functions 10
2.3.2 Absolutely Integrable Functions 10
2.3.3 Finite Energy Functions 11
2.3.4 Finite Energy Periodic Functions 11
2.3.5 Time Frequency Concentrated Functions 11
2.3.6 Finite Energy Sequences 12
2.3.7 Bandlimited Functions 12
2.3.8 Hardy Spaces 12
2.4 Operators 13
2.4.1 Bounded Linear Operators 13
viii Contents
2.4.2 Properties 14
2.4.3 Useful Unitary Operators 15
2.5 Bases and Completeness in Hilbert Space 16
2.6 Fourier Transforms 17
2.6.1 Continuous Time Fourier Transform 18
2.6.2 Continuous Time Periodic Fourier Transform . 18
2.6.3 Discrete Time Fourier Transform 20
2.6.4 Discrete Fourier Transform 20
2.6.5 Fourier Dual Spaces 20
2.7 Linear Filters 21
2.7.1 Continuous Filters and Fourier Transforms 21
2.7.2 Discrete Filters and Z Transforms 22
2.8 Analog Signals and Discretization 22
2.8.1 Classical Sampling Theorem 23
2.8.2 What Can Be Computed Exactly? 24
Problems 27
3 Signed Representation and Frames 29
3.1 Inner Product Representation (Atomic Decomposition) . 29
3.2 Orthonormal Bases 30
3.2.1 Parseval and Plancherel 31
3.2.2 Reconstruction 31
3.2.3 Examples 32
3.3 Riesz Bases 33
3.3.1 Reconstruction 34
3.3.2 Examples 35
3.4 General Frames 36
3.4.1 Basic Frame Theory 37
3.4.2 Frame Representation 40
3.4.3 Frame Correlation and Pseudo Inverse 42
3.4.4 Pseudo Inverse 46
3.4.5 Best Frame Bounds 48
3.4.6 Duality 49
3.4.7 Iterative Reconstruction 50
Problems 55
4 Continuous Wavelet and Gabor Transforms 59
4.1 What Is a Wavelet? 60
4.2 Example Wavelets 62
4.2.1 Haar Wavelet 62
4.2.2 Shannon Wavelet 62
4.2.3 Frequency B spline Wavelets 63
4.2.4 Morlet Wavelet 65
4.2.5 Time Frequency Tradeoffs 66
4.3 Continuous Wavelet Transform 67
Contents ix
4.3.1 Definition 67
4.3.2 Properties 69
4.4 Inverse Wavelet Transform 70
4.4.1 The Idea Behind the Inverse 70
4.4.2 Derivation for L2(R) 73
4.4.3 Analytic Signals 74
4.4.4 Admissibility 77
4.5 Continuous Gabor Transform 78
4.5.1 Definition 78
4.5.2 Inverse Gabor Transform 79
4.6 Unified Representation and Groups 80
4.6.1 Groups 80
4.6.2 Weighted Spaces 81
4.6.3 Representation 82
4.6.4 Reproducing Kernel 83
4.6.5 Group Representation Transform 84
Problems 88
5 Discrete Wavelet Transform 89
5.1 Discretization of the CWT 90
5.2 Multiresolution Analysis 92
5.2.1 Multiresolution Design 92
5.2.2 Resolution and Dilation Invariance 93
5.2.3 Definition 94
5.3 Multiresolution Representation 94
5.3.1 Projection 95
5.3.2 Fourier Transforms 95
5.3.3 Between Scale Relations 97
5.3.4 Haar MRA 99
5.4 Orthonormal Wavelet Bases 101
5.4.1 Characterizing Wo 102
5.4.2 Wavelet Construction 104
5.4.3 The Scaling Function 107
5.5 Compactly Supported (Daubechies) Wavelets 108
5.5.1 Main Idea 109
5.5.2 Trigonometric Half Band Filters 109
5.5.3 Examples 112
5.6 Fast Wavelet Transform Algorithm 116
5.6.1 Filter Bank Decomposition of the Identity 116
5.6.2 Down and Up Sampling 117
5.6.3 Examples 120
Problems 125
6 Overcomplete Wavelet Transform 127
6.1 Discretization of the CWT Revisited 129
x Contents
6.1.1 Definition 129
6.1.2 Semilog Regular Time Scale Sampling 130
6.1.3 Invertibility 131
6.1.4 Overcompleteness and Redundancy 132
6.2 Filter Bank Implementation 136
6.2.1 Analysis 137
6.2.2 Synthesis 138
6.3 Time Frequency Localization and Wavelet Design 145
6.3.1 The Uncertainty Principle 145
6.3.2 Parametric Bandlimited Wavelets 148
6.4 OCWT Examples 150
6.5 Irregular Sampling and Frames 156
6.5.1 Paley Wiener Frames 156
6.5.2 Wavelet Frames 160
6.5.3 Irregular Sampling in the Time Scale Domain . 163
Problems 167
7 Wavelet Signal Processing 171
7.1 Noise Suppression 171
7.1.1 Noise Domains 172
7.1.2 Problem 172
7.1.3 Approach 173
7.1.4 Coherence 178
7.1.5 Frame Localization and Coherence 184
7.1.6 Reconstruction Error from Thresholded OCWTs . . 190
7.1.7 Numerical Experiment 192
7.1.8 Coefficient Noise and Overcompleteness 206
7.1.9 Measuring Noise (SNR) 210
7.2 Compression 212
7.2.1 Problem 212
7.2.2 Performance Measures 212
7.2.3 Approach 213
7.2.4 Numerical Experiment 216
7.2.5 Remarks 223
7.3 Digital Communication 224
7.3.1 Problem 224
7.3.2 Objectives 225
7.3.3 Approach 226
7.3.4 Performance Measures 229
7.3.5 Computer Implementation 232
7.3.6 Wavelet Communication Testbed 236
7.3.7 Numerical Experiments 241
7.3.8 Remarks 253
7.4 Identification 254
7.4.1 Approach 254
Contents xi
7.4.2 Performance Indicators 256
7.4.3 Numerical Experiment 256
7.4.4 Remarks 260
7.5 Conclusion 260
Problems 261
8 Object Oriented Wavelet Analysis with MATLAB 5 263
8.1 Wavelet Signal Processing Workstation 264
8.2 MATLAB Coding 267
8.2.1 Object Oriented Programming 267
8.2.2 Designed Classes 268
8.3 The sampled_signal Object 268
8.3.1 Class Construction 268
8.3.2 sampled_signal Methods 271
8.4 Wavelet Transform Implementation 295
8.4.1 Overcomplete Wavelet Transform (OCWT) 295
8.4.2 GUI for Filter Bank Specification 296
8.5 The wavelet Object 298
8.5.1 Class Construction 298
8.5.2 wavelet Methods 300
8.6 Processing Example 304
8.6.1 Forward OCWT 304
8.6.2 Inverse OCWT 307
8.7 Supporting Functions and Globals 308
8.7.1 Frequency and Time Units 308
8.7.2 Graphical 309
8.7.3 Wavelet 311
References 313
Index 321 |
| any_adam_object | 1 |
| author | Teolis, Anthony 1964- |
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| dewey-sort | 3621.3822 815152433 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Book |
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| id | DE-604.BV011996269 |
| illustrated | Illustrated |
| indexdate | 2024-09-12T14:00:47Z |
| institution | BVB |
| isbn | 3764339098 0817639098 9781461286721 |
| language | German |
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| physical | XXIV, 324 S. Ill., graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
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| publisher | Birkhäuser |
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| series2 | Applied and numerical harmonic analysis |
| spelling | Teolis, Anthony 1964- Verfasser (DE-588)120165864 aut Computational signal processing with wavelets Anthony Teolis Boston [u.a.] Birkhäuser 1998 XXIV, 324 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied and numerical harmonic analysis Literaturverz. S. 313 - 320 Signalverarbeitung - Wavelet Signalverarbeitung (DE-588)4054947-1 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Signalverarbeitung (DE-588)4054947-1 s Wavelet (DE-588)4215427-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008118752&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Teolis, Anthony 1964- Computational signal processing with wavelets Signalverarbeitung - Wavelet Signalverarbeitung (DE-588)4054947-1 gnd Wavelet (DE-588)4215427-3 gnd |
| subject_GND | (DE-588)4054947-1 (DE-588)4215427-3 |
| title | Computational signal processing with wavelets |
| title_auth | Computational signal processing with wavelets |
| title_exact_search | Computational signal processing with wavelets |
| title_full | Computational signal processing with wavelets Anthony Teolis |
| title_fullStr | Computational signal processing with wavelets Anthony Teolis |
| title_full_unstemmed | Computational signal processing with wavelets Anthony Teolis |
| title_short | Computational signal processing with wavelets |
| title_sort | computational signal processing with wavelets |
| topic | Signalverarbeitung - Wavelet Signalverarbeitung (DE-588)4054947-1 gnd Wavelet (DE-588)4215427-3 gnd |
| topic_facet | Signalverarbeitung - Wavelet Signalverarbeitung Wavelet |
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