Ripples in mathematics: the discrete wavelet transform
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2001
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 246 S. graph. Darst. |
| ISBN: | 3540416625 |
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MARC
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| 100 | 1 | |a Jensen, Arne |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Ripples in mathematics |b the discrete wavelet transform |c A. Jensen ; A. la Cour-Harbo |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2001 | |
| 300 | |a IX, 246 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Ondelettes | |
| 650 | 7 | |a Wavelets |2 gtt | |
| 650 | 4 | |a Wavelets (Mathematics) | |
| 650 | 0 | 7 | |a Wavelet |0 (DE-588)4215427-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Wavelet |0 (DE-588)4215427-3 |D s |
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| 700 | 1 | |a La Cour-Harbo, Anders |d 1973- |e Verfasser |0 (DE-588)123075300 |4 aut | |
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Record in the Search Index
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Contents
1. Introduction 1
1.1 Prerequisites 1
1.2 Guide to the Book 2
1.3 Background Information 3
2. A First Example 7
2.1 The Example 7
2.2 Generalizations 10
Exercises 10
3. The Discrete Wavelet Transform via Lifting 11
3.1 The First Example Again 11
3.2 Definition of Lifting 13
3.3 A Second Example 17
3.4 Lifting in General 19
3.5 DWT in General 21
3.6 Further Examples 23
Exercises 24
4. Analysis of Synthetic Signals 25
4.1 The Haar Transform 25
4.2 The CDF(2,2) Transform 31
Exercises 33
5. Interpretation 37
5.1 The First Example 37
5.2 Further Results on the Haar Transform 40
5.3 Interpretation of General DWT 45
Exercises 50
6. Two Dimensional Transforms 51
6.1 One Scale DWT in Two Dimensions 51
6.2 Interpretation and Examples 53
6.3 A 2D Transform Based on Lifting 57
VIII Contents
Exercises 60
7. Lifting and Filters I 61
7.1 Fourier Series and the ^ Transform 61
7.2 Lifting in the ^ Transform Representation 64
7.3 Two Channel Filter Banks 69
7.4 Orthonormal and Biorthogonal Bases 74
7.5 Two Channel Filter Banks in the Time Domain 76
7.6 Summary of Results on Lifting and Filters 79
7.7 Properties of Orthogonal Filters 79
7.8 Some Examples 82
Exercises 86
8. Wavelet Packets 87
8.1 From Wavelets to Wavelet Packets 87
8.2 Choice of Basis 90
8.3 Cost Functions 96
Exercises 98
9. The Time Frequency Plane 99
9.1 Sampling and Frequency Contents 99
9.2 Definition of the Time Frequency Plane 102
9.3 Wavelet Packets and Frequency Contents 107
9.4 More about Time Frequency Planes Ill
9.5 More Fourier Analysis. The Spectrogram 121
Exercises 125
10. Finite Signals 127
10.1 The Extent of the Boundary Problem 127
10.2 DWT in Matrix Form 130
10.3 Gram Schmidt Boundary Filters 134
10.4 Periodization 140
10.5 Moment Preserving Boundary Filters 144
Exercises 148
11. Implementation 151
11.1 Introduction to Software 151
11.2 Implementing the Haar Transform Through Lifting 152
11.3 Implementing the DWT Through Lifting 155
11.4 The Real Time Method 160
11.5 Filter Bank Implementation 171
11.6 Construction of Boundary Filters 175
11.7 Wavelet Packet Decomposition 180
11.8 Wavelet Packet Bases 181
11.9 Cost Functions 185
Contents IX
Exercises 185
12. Lifting and Filters II 189
12.1 The Three Basic Representations 189
12.2 From Matrix to Equation Form 190
12.3 From Equation to Filter Form 192
12.4 From Filters to Lifting Steps 193
12.5 Factoring Daubechies 4 into Lifting Steps 202
12.6 Factorizing Coiflet 12 into Lifting Steps 204
Exercises 209
13. Wavelets in Matlab 211
13.1 Multiresolution Analysis 212
13.2 Frequency Properties of the Wavelet Transform 216
13.3 Wavelet Packets Used for Denoising 220
13.4 Best Basis Algorithm 225
13.5 Some Commands in Uvi.Wave 230
Exercises 232
14. Applications and Outlook 233
14.1 Applications 233
14.2 Outlook 235
14.3 Some Web Sites 237
References 239
Index 241 |
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| id | DE-604.BV013703086 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T07:38:58Z |
| institution | BVB |
| isbn | 3540416625 |
| language | English |
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| physical | IX, 246 S. graph. Darst. |
| publishDate | 2001 |
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| spelling | Jensen, Arne Verfasser aut Ripples in mathematics the discrete wavelet transform A. Jensen ; A. la Cour-Harbo Berlin [u.a.] Springer 2001 IX, 246 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ondelettes Wavelets gtt Wavelets (Mathematics) Wavelet (DE-588)4215427-3 gnd rswk-swf Wavelet (DE-588)4215427-3 s DE-604 La Cour-Harbo, Anders 1973- Verfasser (DE-588)123075300 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009365557&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jensen, Arne La Cour-Harbo, Anders 1973- Ripples in mathematics the discrete wavelet transform Ondelettes Wavelets gtt Wavelets (Mathematics) Wavelet (DE-588)4215427-3 gnd |
| subject_GND | (DE-588)4215427-3 |
| title | Ripples in mathematics the discrete wavelet transform |
| title_auth | Ripples in mathematics the discrete wavelet transform |
| title_exact_search | Ripples in mathematics the discrete wavelet transform |
| title_full | Ripples in mathematics the discrete wavelet transform A. Jensen ; A. la Cour-Harbo |
| title_fullStr | Ripples in mathematics the discrete wavelet transform A. Jensen ; A. la Cour-Harbo |
| title_full_unstemmed | Ripples in mathematics the discrete wavelet transform A. Jensen ; A. la Cour-Harbo |
| title_short | Ripples in mathematics |
| title_sort | ripples in mathematics the discrete wavelet transform |
| title_sub | the discrete wavelet transform |
| topic | Ondelettes Wavelets gtt Wavelets (Mathematics) Wavelet (DE-588)4215427-3 gnd |
| topic_facet | Ondelettes Wavelets Wavelets (Mathematics) Wavelet |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009365557&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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