Wavelet transforms and their applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2002
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 565 S. graph. Darst. |
| ISBN: | 0817642048 3764342048 |
Staff View
MARC
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Record in the Search Index
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Titel: Wavelet transforms and their applications
Autor: Debnath, Lokenath
Jahr: 2002
Contents
Preface xi
Chapter 1 Brief Historical Introduction 1
1.1 Fourier Series and Fourier Transforms 1
1.2 Gabor Transforms 4
1.3 The Wigner-Ville Distribution and Time-Frequency
Signal Analysis 7
1.4 Wavelet Transforms 12
1.5 Wavelet Bases and Multiresolution Analysis 17
1.6 Applications of Wavelet Transforms 20
Chapter 2 Hilbert Spaces and Orthonormal Systems 23
2.1 Introduction 23
2.2 Normed Spaces 25
2.3 The U Spaces 28
2.4 Generalized Functions with Examples 35
2.5 Definition and Examples of an Inner Product Space 46
2.6 Norm in an Inner Product Space 50
2.7 Definition and Examples of a Hilbert Space 53
2.8 Strong and Weak Convergences 59
2.9 Orthogonal and Orthonormal Systems 62
vi Contents
2.10 Properties of Orthonormal Systems 68
2.11 Trigonometric Fourier Series 79
2.12 Orthogonal Complements and the Projection Theorem 83
2.13 Linear Funtionals and the Riesz Representation Theorem 89
2.14 Separable Hilbert Spaces 92
2.15 Linear Operators on Hilbert Spaces 95
2.16 Eigenvalues and Eigenvectors of an Operator 117
2.17 Exercises 130
Chapter 3 Fourier Transforms and Their Applications 143
3.1 Introduction 143
3.2 Fourier Transforms in L'(B?) 145
3.3 Basic Properties of Fourier Transforms 150
3.4 Fourier Transforms in L2(R) 166
3.5 Poisson's Summation Formula 182
3.6 The Shannon Sampling Theorem and Gibbs's Phenomenon 187
3.7 Heisenberg's Uncertainty Principle 200
3.8 Applications of Fourier Transforms in Mathematical Statistics 202
3.9 Applications of Fourier Transforms to Ordinary
Differential Equations 210
3.10 Solutions of Integral Equations 214
3.11 Solutions of Partial Differential Equations 218
3.12 Applications of Multiple Fourier Transforms to
Partial Differential Equations 230
3.13 Construction of Green's Functions by the Fourier
Transform Method 236
3.14 Exercises 249
Contents vii
Chapter 4 The Gabor Transform and Time-Frequency 257
Signal Analysis
4.1 Introduction 257
4.2 Classification of Signals and the Joint Time-Frequency
Analysis of Signals 258
4.3 Definition and Examples of the Gabor Transforms 264
4.4 Basic Properties of Gabor Transforms 269
4.5 Frames and Frame Operators 274
4.6 Discrete Gabor Transforms and the Gabor
Representation Problem 284
4.7 The Zak Transform and Time-Frequency Signal Analysis 287
4.8 Basic Properties of Zak Transforms 290
4.9 Applications of Zak Transforms and the Balian-Low Theorem 295
4.10 Exercises 304
Chapter 5 The Wigner-Ville Distribution and
Time-Frequency Signal Analysis 307
5.1 Introduction 307
5.2 Definitions and Examples of the Wigner-Ville Distribution 308
5.3 Basic Properties of the Wigner-Ville Distribution 319
5.4 The Wigner-Ville Distribution of Analytic Signals and
Band-Limited Signals 328
5.5 Definitions and Examples of the Woodward
Ambiguity Functions 331
5.6 Basic Properties of Ambiguity Functions 339
5.7 The Ambiguity Transformation and Its Properties 346
5.8 Discrete Wigner-Ville Distributions 350
5.9 Cohen's Class of Time-Frequency Distributions 354
5.10 Exercises 357
viii Contents
Chapter 6 Wavelet Transforms and Basic Properties 361
6.1 Introduction 361
6.2 Continuous Wavelet Transforms and Examples 365
6.3 Basic Properties of Wavelet Transforms 378
6.4 The Discrete Wavelet Transforms 382
6.5 Orthonormal Wavelets 392
6.6 Exercises 399
Chapter 7 MuItiresolution Analysis and Construction 403
of Wavelets
7.1 Introduction 403
7.2 Definition of Multiresolution Analysis and Examples 405
7.3 Properties of Scaling Functions and Orthonormal Wavelet Bases 412
7.4 Construction of Orthonormal Wavelets 431
7.5 Daubechies" Wavelets and Algorithms 447
7.6 Discrete Wavelet Transforms and Mallat's Pyramid Algorithm 466
7.7 Exercises 471
Chapter 8 Newland's Harmonic Wavelets 475
8.1 Introduction 475
8.2 Harmonic Wavelets 475
8.3 Properties of Harmonic Scaling Functions 482
8.4 Wavelet Expansions and Parseval's Formula 485
8.5 Concluding Remarks 487
8.6 Exercises 487
Chapter 9 Wavelet Transform Analysis of Turbulence 491
9.1 Introduction 492
Contents ix
9.2 Fourier Transforms in Turbulence and the
Navier-Stokes Equations 495
9.3 Fractals, Multifractals, and Singularities in Turbulence 505
9.4 Farge's Wavelet Transform Analysis of Turbulence 512
9.5 Adaptive Wavelet Method for Analysis of Turbulent Flows 515
9.6 Meneveau's Wavelet Analysis of Turbulence 519
Answers and Hints for Selected Exercises 525
Bibliography 539
Index 555 |
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| illustrated | Illustrated |
| indexdate | 2024-08-15T00:17:24Z |
| institution | BVB |
| isbn | 0817642048 3764342048 |
| language | English |
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| physical | XV, 565 S. graph. Darst. |
| publishDate | 2002 |
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| publishDateSort | 2002 |
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| spelling | Debnath, Lokenath 1935- Verfasser (DE-588)115600663 aut Wavelet transforms and their applications Lokenath Debnath Boston [u.a.] Birkhäuser 2002 XV, 565 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ondelettes Traitement du signal - Mathématiques Mathematik Signal processing Mathematics Wavelets (Mathematics) Wavelet (DE-588)4215427-3 gnd rswk-swf 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=009528700&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Debnath, Lokenath 1935- Wavelet transforms and their applications Ondelettes Traitement du signal - Mathématiques Mathematik Signal processing Mathematics Wavelets (Mathematics) Wavelet (DE-588)4215427-3 gnd |
| subject_GND | (DE-588)4215427-3 |
| title | Wavelet transforms and their applications |
| title_auth | Wavelet transforms and their applications |
| title_exact_search | Wavelet transforms and their applications |
| title_full | Wavelet transforms and their applications Lokenath Debnath |
| title_fullStr | Wavelet transforms and their applications Lokenath Debnath |
| title_full_unstemmed | Wavelet transforms and their applications Lokenath Debnath |
| title_short | Wavelet transforms and their applications |
| title_sort | wavelet transforms and their applications |
| topic | Ondelettes Traitement du signal - Mathématiques Mathematik Signal processing Mathematics Wavelets (Mathematics) Wavelet (DE-588)4215427-3 gnd |
| topic_facet | Ondelettes Traitement du signal - Mathématiques Mathematik Signal processing Mathematics Wavelets (Mathematics) Wavelet |
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