Wavelets made easy:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2001
|
| Ausgabe: | 2. print. with corr. |
| Schriftenreihe: | Modern Birkhäuser Classics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIII, 297 S. Ill., graph. Darst. |
| ISBN: | 0817640614 3764340614 9781461460053 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV013561946 | ||
| 003 | DE-604 | ||
| 005 | 20181113 | ||
| 007 | t | ||
| 008 | 010131s2001 ad|| |||| 00||| eng d | ||
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| 020 | |a 3764340614 |9 3-7643-4061-4 | ||
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| 041 | 0 | |a eng | |
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| 100 | 1 | |a Nievergelt, Yves |d 1954- |e Verfasser |0 (DE-588)121171108 |4 aut | |
| 245 | 1 | 0 | |a Wavelets made easy |c Yves Nievergelt |
| 250 | |a 2. print. with corr. | ||
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2001 | |
| 300 | |a XIII, 297 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Modern Birkhäuser Classics | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 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 |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4614-6006-0 |
| 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=009261649&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009261649 | ||
Datensatz im Suchindex
| _version_ | 1804128361173221376 |
|---|---|
| adam_text | Contents
Preface ix
Outline xi
A Algorithms for Wavelet Transforms 1
1 Haar s Simple Wavelets 3
1.0 Introduction 3
1.1 Simple Approximation 4
1.2 Approximation with Simple Wavelets 8
1.2.1 The Basic Haar Wavelet Transform 8
1.2.2 Significance of the Basic Haar Wavelet Transform .... 10
1.2.3 Shifts and Dilations of the Basic Haar Transform 11
1.3 The Ordered Fast Haar Wavelet Transform 14
1.3.1 Initialization 14
1.3.2 The Ordered Fast Haar Wavelet Transform 15
1.4 The In Place Fast Haar Wavelet Transform 21
1.4.1 In Place Basic Sweep 22
1.4.2 The In Place Fast Haar Wavelet Transform 23
1.5 The In Place Fast Inverse Haar Wavelet Transform 28
1.6 Examples 31
1.6.1 Creek Water Temperature Analysis 31
1.6.2 Financial Stock Index Event Detection 33
2 Multidimensional Wavelets and Applications 36
2.0 Introduction 36
2.1 Two Dimensional Haar Wavelets 37
2.1.1 Two Dimensional Approximation with Step Functions . . 37
2.1.2 Tensor Products of Functions 39
2.1.3 The Basic Two Dimensional Haar Wavelet Transform . . 42
2.1.4 Two Dimensional Fast Haar Wavelet Transform 46
2.2 Applications of Wavelets 49
2.2.1 Noise Reduction 49
v
vi Contents
2.2.2 Data Compression 52
2.2.3 Edge Detection 58
2.3 Computational Notes 60
2.3.1 Fast Reconstruction of Single Values 60
2.3.2 Operation Count 63
2.4 Examples 65
2.4.1 Creek Water Temperature Compression 65
2.4.2 Financial Stock Index Image Compression 67
2.4.3 Two Dimensional Diffusion Analysis 68
2.4.4 Three Dimensional Diffusion Analysis 69
3 Algorithms for Daubechies Wavelets 73
3.0 Introduction 73
3.1 Calculation of Daubechies Wavelets 73
3.2 Approximation of Samples with Daubechies Wavelets 82
3.2.1 Approximate Interpolation 83
3.2.2 Approximate Averages 84
3.3 Extensions to Alleviate Edge Effects 85
3.3.1 Zigzag Edge Effects from Extensions by Zeros 85
3.3.2 Medium Edge Effects from Mirror Reflections 88
3.3.3 Small Edge Effects from Smooth Periodic Extensions ... 90
3.4 The Fast Daubechies Wavelet Transform 95
3.5 The Fast Inverse Daubechies Wavelet Transform 101
3.6 Multidimensional Daubechies Wavelet Transforms 107
3.7 Examples 110
3.7.1 Hangman Creek Water Temperature Analysis 110
3.7.2 Financial Stock Index Image Compression 112
B Basic Fourier Analysis 115
4 Inner Products and Orthogonal Projections 117
4.0 Introduction 117
4.1 Linear Spaces 117
4.1.1 NumberFields 117
4.1.2 Linear Spaces 120
4.1.3 Linear Maps 122
4.2 Projections 123
4.2.1 Inner Products 124
4.2.2 Gram Schmidt Orthogonalization 129
4.2.3 Orthogonal Projections 131
4.3 Applications of Orthogonal Projections 134
4.3.1 Application to Three Dimensional Computer Graphics . . 134
4.3.2 Application to Ordinary Least Squares Regression .... 136
Contents vii
4.3.3 Application to the Computation of Functions 138
4.3.4 Applications to Wavelets 142
5 Discrete and Fast Fourier Transforms 147
5.0 Introduction 147
5.1 The Discrete Fourier Transform (DFT) 147
5.1.1 Definition and Inversion 148
5.1.2 Unitary Operators 155
5.2 The Fast Fourier Transform (FFT) 157
5.2.1 The Forward Fast Fourier Transform 157
5.2.2 The Inverse Fast Fourier Transform 161
5.2.3 Interpolation by the Inverse Fast Fourier Transform .... 161
5.2.4 Bit Reversal 163
5.3 Applications of the Fast Fourier Transform 165
5.3.1 Noise Reduction Through the Fast Fourier Transform . . . 165
5.3.2 Convolution and Fast Multiplication 167
5.4 Multidimensional Discrete and Fast Fourier Transforms 171
6 Fourier Series for Periodic Functions 175
6.0 Introduction 175
6.1 Fourier Series 176
6.1.1 Orthonormal Complex Trigonometric Functions 176
6.1.2 Definition and Examples of Fourier Series 177
6.1.3 Relation Between Series and Discrete Transforms 182
6.1.4 Multidimensional Fourier Series 183
6.2 Convergence and Inversion of Fourier Series 185
6.2.1 The Gibbs Wilbraham Phenomenon 185
6.2.2 Piecewise Continuous Functions 187
6.2.3 Convergence and Inversion of Fourier Series 191
6.2.4 Convolutions and Dirac s Function S 192
6.2.5 Uniform Convergence of Fourier Series 194
6.3 Periodic Functions 200
C Computation and Design of Wavelets 203
7 Fourier Transforms on the Line and in Space 205
7.0 Introduction 205
7.1 The Fourier Transform 205
7.1.1 Definition and Examples of the Fourier Transform . . . .205
7.2 Convolutions and Inversion of the Fourier Transform 209
7.3 Approximate Identities 213
7.3.1 Weight Functions 214
7.3.2 Approximate Identities 215
7.3.3 Dirac Delta (5) Function 219
viii Contents
7.4 Further Features of the Fourier Transform 220
7.4.1 Algebraic Features of the Fourier Transform 221
7.4.2 Metric Features of the Fourier Transform 223
7.4.3 Uniform Continuity of Fourier Transforms 227
7.5 The Fourier Transform with Several Variables 229
7.6 Applications of Fourier Analysis 234
7.6.1 Shannon s Sampling Theorem 234
7.6.2 Heisenberg s Uncertainty Principle 236
8 Daubechies Wavelets Design 238
8.0 Introduction 238
8.1 Existence, Uniqueness, and Construction 238
8.1.1 The Recursion Operator and Its Adjoint 239
8.1.2 The Fourier Transform of the Recursion Operator 243
8.1.3 Convergence of Iterations of the Recursion Operator . . .245
8.2 Orthogonality of Daubechies Wavelets 253
8.3 Mallat s Fast Wavelet Algorithm 258
9 Signal Representations with Wavelets 262
9.0 Introduction 262
9.1 Computational Features of Daubechies Wavelets 262
9.1.1 Initial Values of Daubechies Scaling Function 263
9.1.2 Computational Features of Daubechies Function 266
9.1.3 Exact Representation of Polynomials by Wavelets 273
9.2 Accuracy of Signal Approximation by Wavelets 274
9.2.1 Accuracy of Taylor Polynomials 274
9.2.2 Accuracy of Signal Representations by Wavelets 278
9.2.3 Approximate Interpolation by Daubechies Function . . .281
D Directories 285
Acknowledgments 287
Collection of Symbols 289
Bibliography 291
Index 295
|
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| ctrlnum | (OCoLC)47816074 (DE-599)BVBBV013561946 |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515.2433 |
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| discipline | Mathematik |
| edition | 2. print. with corr. |
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| id | DE-604.BV013561946 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:48:01Z |
| institution | BVB |
| isbn | 0817640614 3764340614 9781461460053 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009261649 |
| oclc_num | 47816074 |
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| owner | DE-355 DE-BY-UBR DE-M347 DE-384 DE-92 |
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| physical | XIII, 297 S. Ill., graph. Darst. |
| publishDate | 2001 |
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| publisher | Birkhäuser |
| record_format | marc |
| series2 | Modern Birkhäuser Classics |
| spelling | Nievergelt, Yves 1954- Verfasser (DE-588)121171108 aut Wavelets made easy Yves Nievergelt 2. print. with corr. Boston [u.a.] Birkhäuser 2001 XIII, 297 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Modern Birkhäuser Classics Hier auch später erschienene, unveränderte Nachdrucke Wavelets (Mathematics) Wavelet (DE-588)4215427-3 gnd rswk-swf Wavelet (DE-588)4215427-3 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4614-6006-0 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009261649&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| subject_GND | (DE-588)4215427-3 |
| title | Wavelets made easy |
| title_auth | Wavelets made easy |
| title_exact_search | Wavelets made easy |
| title_full | Wavelets made easy Yves Nievergelt |
| title_fullStr | Wavelets made easy Yves Nievergelt |
| title_full_unstemmed | Wavelets made easy Yves Nievergelt |
| title_short | Wavelets made easy |
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| topic | Wavelets (Mathematics) Wavelet (DE-588)4215427-3 gnd |
| topic_facet | Wavelets (Mathematics) Wavelet |
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