Wavelet theory and its applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Kluwer
1994
|
| Ausgabe: | 3. print. |
| Schriftenreihe: | The Kluwer international series in engineering and computer science
189 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 223 S. Ill., graph. Darst. |
| ISBN: | 079239271X |
Internformat
MARC
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| 245 | 1 | 0 | |a Wavelet theory and its applications |c by Randy K. Young |
| 250 | |a 3. print. | ||
| 264 | 1 | |a Boston [u.a.] |b Kluwer |c 1994 | |
| 300 | |a XIV, 223 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Foreword xi
Preface xiii
Chapter 1: Introduction/Background
1
Wavelet Theory Basics Scaling and Translation 4
Appendix 1 A: Time Referencing 16
Chapter 2: The Wavelet Transform
19
Wavelet Transform Definitions and Operators 19
Wavelet Transform Examples 22
The Resolution of Identity 27
Continuous Inverse Wavelet Transform Theorem 30
Energy Distribution in the Wavelet Transform Domain 34
Discrete Wavelet Transform (Continuous Time Wavelet Series) ... 35
Wideband Matched Filter Interpretation of the Lattice Density .... 38
Review of the Inverse Discrete Wavelet Transform: Scale
translation Lattice Density and Mother Wavelet
Constraints 41
Discrete Wavelet Mathematics Rigorous Justification 44
Discrete Time Wavelet Series 50
Multiresolution, Orthogonal, and Biorthogonal Wavelet
Transforms (and PR QMFs) 51
Discrete Time Wavelet Series A Specific Structure 52
Multiresolution 55
Orthogonal and Biorthogonal Wavelet Transforms 57
An Image Processing Example 60
Appendix 2 A: Nonunique Wavelet Domain Representations 64
Chapter 3: Practical Resolution, Gain, and Processing Structures
71
Introduction 71
Fourier/Narrowband Gain and Resolution Comparisons 72
Multiple Mother Wavelets Gain and Resolution Properties
Only 77
Mother Wavelet Properties Relationships to Established
Theories 79
Signal Analysis Time frequency or time scale Applications 80
A Physical Interpretation of Scale translation Resolution:
Wideband Ambiguity Function Conditions 81
Wideband Conditions 82
Wideband Signals and the Analytic Signal Model 83
Effective rms Time bandwidth Product 85
Wideband Systems and Signals 87
Active and Passive Sensing 92
Ambiguity Functions 95
Reformulation of the WBCAF with Wavelet Transforms 101
Properties of the Reformulated WBCAF 105
Cross Wavelet Transforms and Signal Commonalities 110
Appendix 3 A: Wideband/Narrowband Ambiguity Functions:
Assumptions, Tradeoffs and Efficiencies 113
Appendix 3 B: Narrowband Ambiguity Function Theory 119
Chapter 4: Wavelet Theory Extensions and Ambiguity Functions
123
Introduction 123
Multiresolution/Orthogonal Wavelets versus Unconstrained
Wavelets 123
Sampling Grids 126
Unconstrained Wavelet Transforms Mother Wavelet Freedom . . . 127
The Mother Mapper Operator 128
Unconstrained Wavelet Transforms/Mother Mapper Operator
Properties and Applications 133
Mother Mapper Operator Applications 137
Mother Mapper Operator Final Considerations 139
Further Research and Applications of the Mother Mapper
Operator 140
Chapter 5: Linear Systems Modelling with Wavelet Theory
141
Introduction and Motivation 141
Wideband/Nonstationary/Time varying System Modelling 143
The Wideband Signal Reflection Process 146
Common Framework of System or Channel Characterizations: ... 151
The STV Wavelet Operator Space time varying System Model . . 156
STV Wavelet Operator s Energy Distribution 159
Estimation of the Wideband System Characterization 160
Properties of the STV Wavelet Operator 160
Examples of the STV Wavelet Operator 164
Wideband Reflection: Comparing the LTI and STV Models 169
Justification for the STV Operator Instead of Convolution for
Signals Represented by Wavelet Transforms 174
The STV Wavelet Operator in the Wavelet Transform Domain ... 175
Space time varying System Identification Problem with
Wideband/Nonstationary Input/Outputs 180
viii
Limitations of the STV Wavelet Operator Time Referencing and
Nonlinear Time Variations 181
Bi wavelet System Representation: Time variation of the Time
varying System Model 184
Chapter 6: Wideband Scattering and Environmental Imaging
189
Introduction 189
Scattering Theory 192
General Scattering Function Background 193
Narrowband Scattering Theory 194
Wideband Correlation Receiver and its Output 198
Wideband Point Scatterer Example 201
Wideband Scattering Functions and Resolutions 203
Physical Form of the WBCAF 205
Time Delay and Scale Estimation 208
WBAAF Moments and Assumptions 209
Wideband Scattering Review 210
Related Research 211
References 215
Subject Index 221
ix
|
| adam_txt |
Contents
Foreword xi
Preface xiii
Chapter 1: Introduction/Background
1
Wavelet Theory Basics Scaling and Translation 4
Appendix 1 A: Time Referencing 16
Chapter 2: The Wavelet Transform
19
Wavelet Transform Definitions and Operators 19
Wavelet Transform Examples 22
The Resolution of Identity 27
Continuous Inverse Wavelet Transform Theorem 30
Energy Distribution in the Wavelet Transform Domain 34
Discrete Wavelet Transform (Continuous Time Wavelet Series) . 35
Wideband Matched Filter Interpretation of the Lattice Density . 38
Review of the Inverse Discrete Wavelet Transform: Scale
translation Lattice Density and Mother Wavelet
Constraints 41
Discrete Wavelet Mathematics Rigorous Justification 44
Discrete Time Wavelet Series 50
Multiresolution, Orthogonal, and Biorthogonal Wavelet
Transforms (and PR QMFs) 51
Discrete Time Wavelet Series A Specific Structure 52
Multiresolution 55
Orthogonal and Biorthogonal Wavelet Transforms 57
An Image Processing Example 60
Appendix 2 A: Nonunique Wavelet Domain Representations 64
Chapter 3: Practical Resolution, Gain, and Processing Structures
71
Introduction 71
Fourier/Narrowband Gain and Resolution Comparisons 72
Multiple Mother Wavelets Gain and Resolution Properties
Only 77
Mother Wavelet Properties Relationships to Established
Theories 79
Signal Analysis Time frequency or time scale Applications 80
A Physical Interpretation of Scale translation Resolution:
Wideband Ambiguity Function Conditions 81
Wideband Conditions 82
Wideband Signals and the Analytic Signal Model 83
Effective rms Time bandwidth Product 85
Wideband Systems and Signals 87
Active and Passive Sensing 92
Ambiguity Functions 95
Reformulation of the WBCAF with Wavelet Transforms 101
Properties of the Reformulated WBCAF 105
Cross Wavelet Transforms and Signal Commonalities 110
Appendix 3 A: Wideband/Narrowband Ambiguity Functions:
Assumptions, Tradeoffs and Efficiencies 113
Appendix 3 B: Narrowband Ambiguity Function Theory 119
Chapter 4: Wavelet Theory Extensions and Ambiguity Functions
123
Introduction 123
Multiresolution/Orthogonal Wavelets versus Unconstrained
Wavelets 123
Sampling Grids 126
Unconstrained Wavelet Transforms Mother Wavelet Freedom . . . 127
The Mother Mapper Operator 128
Unconstrained Wavelet Transforms/Mother Mapper Operator
Properties and Applications 133
Mother Mapper Operator Applications 137
Mother Mapper Operator Final Considerations 139
Further Research and Applications of the Mother Mapper
Operator 140
Chapter 5: Linear Systems Modelling with Wavelet Theory
141
Introduction and Motivation 141
Wideband/Nonstationary/Time varying System Modelling 143
The Wideband Signal Reflection Process 146
Common Framework of System or Channel Characterizations: . 151
The STV Wavelet Operator Space time varying System Model . . 156
STV Wavelet Operator's Energy Distribution 159
Estimation of the Wideband System Characterization 160
Properties of the STV Wavelet Operator 160
Examples of the STV Wavelet Operator 164
Wideband Reflection: Comparing the LTI and STV Models 169
Justification for the STV Operator Instead of Convolution for
Signals Represented by Wavelet Transforms 174
The STV Wavelet Operator in the Wavelet Transform Domain . 175
Space time varying System Identification Problem with
Wideband/Nonstationary Input/Outputs 180
viii
Limitations of the STV Wavelet Operator Time Referencing and
Nonlinear Time Variations 181
Bi wavelet System Representation: Time variation of the Time
varying System Model 184
Chapter 6: Wideband Scattering and Environmental Imaging
189
Introduction 189
Scattering Theory 192
General Scattering Function Background 193
Narrowband Scattering Theory 194
Wideband Correlation Receiver and its Output 198
Wideband Point Scatterer Example 201
Wideband Scattering Functions and Resolutions 203
Physical Form of the WBCAF 205
Time Delay and Scale Estimation 208
WBAAF Moments and Assumptions 209
Wideband Scattering Review 210
Related Research 211
References 215
Subject Index 221
ix |
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| index_date | 2024-07-02T16:16:37Z |
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| institution | BVB |
| isbn | 079239271X |
| language | English |
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| spelling | Young, Randy K. Verfasser aut Wavelet theory and its applications by Randy K. Young 3. print. Boston [u.a.] Kluwer 1994 XIV, 223 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Kluwer international series in engineering and computer science 189 Wellenausbreitung (DE-588)4121912-0 gnd rswk-swf Wellenpaket (DE-588)4127186-5 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Wellenausbreitung (DE-588)4121912-0 s DE-604 Wellenpaket (DE-588)4127186-5 s Wavelet (DE-588)4215427-3 s 1\p DE-604 The Kluwer international series in engineering and computer science 189 (DE-604)BV023545171 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015343266&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Young, Randy K. Wavelet theory and its applications The Kluwer international series in engineering and computer science Wellenausbreitung (DE-588)4121912-0 gnd Wellenpaket (DE-588)4127186-5 gnd Wavelet (DE-588)4215427-3 gnd |
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| title | Wavelet theory and its applications |
| title_auth | Wavelet theory and its applications |
| title_exact_search | Wavelet theory and its applications |
| title_exact_search_txtP | Wavelet theory and its applications |
| title_full | Wavelet theory and its applications by Randy K. Young |
| title_fullStr | Wavelet theory and its applications by Randy K. Young |
| title_full_unstemmed | Wavelet theory and its applications by Randy K. Young |
| title_short | Wavelet theory and its applications |
| title_sort | wavelet theory and its applications |
| topic | Wellenausbreitung (DE-588)4121912-0 gnd Wellenpaket (DE-588)4127186-5 gnd Wavelet (DE-588)4215427-3 gnd |
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