Wavelet theory and harmonic analysis in applied sciences:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
1997
|
| Series: | Applied and numerical harmonic analysis
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 345 S. graph. Darst. |
| ISBN: | 0817639535 3764339535 |
Staff View
MARC
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| 245 | 1 | 0 | |a Wavelet theory and harmonic analysis in applied sciences |c C. E. D'Attellis ... eds. |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 1997 | |
| 300 | |a XVIII, 345 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Record in the Search Index
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| adam_text | Contents
Preface xiii
List of Contributors xv
I Theory and Implementations 1
1 Singular integrals related to the Monge Ampere
equation 3
L. A. Caffarelli, C. Gutierrez
1 Introduction 3
2 The maximal function 7
3 Application to singular integral operators 9
4 References 13
2 Wavelet characterization of functions with conditions
on the mean oscillation 15
H. Aimar, A. Bernardis
1 Introduction 15
2 Wavelet Bases 16
3 Functions with conditions on the mean oscillation:
MO spaces 17
4 Sequential spaces of Carleson type: C spaces 19
5 C as a necessary condition for the wavelet coefficients
of MO functions 21
5.1 The Daubechies wavelet case 21
5.2 The Meyer wavelet case 22
6 C as a sufficient condition for MO: The finite case . . 24
6.1 The Daubechies wavelet case 24
6.2 The Meyer wavelet case 26
vi Contents
7 C as sufficient condition for M.O: The general case . . 26
8 Acknowledgements 31
9 References 31
3 Undecimated Wavelet Transform from Orthogonal
Spline Wavelets 33
E. P. Serrano, M. A. Fabio
1 Introduction 33
2 The Undecimated Discrete Wavelet Transform .... 35
3 Undecimate Cardinal Algorithm 39
4 Properties of the Undecimated Discrete Transform . . 48
5 Extended Multiresolution Analysis for Vo 56
6 Decomposition of a Signal in Vo 62
7 Conclusion 67
8 References 68
4 Oblique Multiwavelet Bases 73
A. Aldroubi
1 Introduction 73
1.1 An oblique wavelet based on the Haar mul¬
tiresolution 73
2 Multiscaling Functions and Multiwavelet Bases .... 78
2.1 Multiscaling functions 78
2.2 Multiwavelets 79
2.3 Classification of wavelet bases 80
2.4 Two scale equations 82
3 Construction of Oblique Wavelet and Multiwavelet
Bases 83
3.1 Oblique multiwavelet bases based on the
Hermite cubic splines MRA 85
4 Fast Filter Bank Algorithms 86
4.1 Initialization 89
5 References 90
Contents vii
5 Frames and Riesz bases: a short survey 93
S. J. Favier, R. A. Zalik
1 Introduction 93
2 Frames and Riesz bases in Hilbert Spaces 93
3 Frame and Basis Perturbations 100
4 Special Clases of Frames and The Projection Method . 103
5 Exponential Frames and Bases 107
6 Wavelet Frames, Bases, and Bessel Sequences 109
7 References 114
6 Fourier Analysis of Petrov Galerkin Methods Based
on Biorthogonal Multiresolution Analyses 119
5. M. Gomes, E. Cortina
1 Introduction 119
2 Notation and some definitions 122
3 A Petrov Galerkin method for the KdV equation . . . 123
4 The linear case: Fourier analysis 124
4.1 Convergence results 127
4.2 Conditions for stability 130
5 Biorthogonal framework 131
5.1 Spline biorthogonal scaling functions 132
5.2 Algorithms for the calculation of a(k),b(l,k)
and c(k) 133
6 Numerical results 136
7 Acknowledgements 137
8 References 137
viii Contents
II Applications to Biomedical Sciences 141
7 Fine Structure of ECG Signal using
Wavelet Transform 143
H. Rix, 0. Meste
1 Introduction 143
2 Localization of Late Potentials by Time Frequency
Representations 144
3 Signal Shape Differences 147
3.1 Shape classifications of 1 D signals 147
3.2 Shape classification of 2 D signals 148
4 Conclusion 150
5 References 151
8 Spectral Analysis of Cardiorespiratory Signals 155
M. Risk, J. Sobh, R. Armentano, A. Ramirez and P.Saul
1 Introduction 155
2 Short term variability 158
2.1 Spectral Analysis Methods 158
2.2 Spectral Analysis 160
2.3 Autoregressive and moving average modeling 160
2.4 Fast Fourier Transform method 161
2.5 Blackman Tukey method 162
2.6 Transfer Function 163
3 Long term variability 165
3.1 Time domain methods 167
3.2 Frequency domain methods 167
4 Discussion 169
5 References 171
Contents ix
9 Characterization of Epileptic EEG Time Series (I):
Gabor Transform and Nonlinear Dynamics
Methods 179
S. Blanco, S. Kochen, R. Quian Quiroga, L. Riquelme,
0. Rosso and P. Salgado
1 Introduction 179
2 Experimental Setup and Clinical Data 181
3 Armonic Analysis of EEG Data 184
4 Time Frequency Analysis Based on Gabor Transform . 185
4.1 Analysis of EEG Signal I 189
4.2 Analysis of EEG Signal II 194
4.3 Information Transfer Analysis 199
5 Nonlinear Dynamics Analysis 202
5.1 Stationarity 203
5.2 Dynamical Systems 204
5.3 Attractors 206
5.4 Attractor Reconstruction 207
5.5 Choosing the Optimal Time Delay 209
5.6 Choosing the Minimum Embedding Dimension 209
5.7 Correlation Dimension 211
5.8 Lyapunov Exponent 213
5.9 Analysis of Signal II 215
6 Final Remarks 220
7 Acknowledgements 221
8 References 221
10 Characterization of Epileptic EEG Time Series (II):
Wavelet Transform and Information Theory 227
C. D Attellis, L. Gamero, S. Isaacson, R. Sirne and
M. Torres
1 Introduction 227
2 Data Collection 229
3 Theoretical Background 229
3.1 Wavelet Analysis and Filters 229
3.2 Entropy 232
4 Method I: Energy Based Detection Algorithm 233
4.1 Results and Comparisons 235
x Contents
4.2 Discussion 243
5 Method II: Multiresolution Entropy 243
5.1 Results 245
5.2 Discussion 254
6 Conclusions 258
7 References 259
III Applications in Physical Sciences 263
11 Wavelet Networks for Modelling Nonlinear
Processes 265
N. Roqueiro, E. L. Lima
1 Introduction 265
2 Models for non linear system identification 266
2.1 Volterra s series 267
2.2 Block oriented models 268
2.3 Non linear models linear in the parameters . . 270
3 Wavelet networks 274
3.1 Multivariable wavelet networks 275
3.2 Parallel structure of single variable wavelets . . 276
3.3 Conclusions 279
4 Examples 280
4.1 The non linear identification problem 280
4.2 Identification of a chaotic attractor 282
4.3 Continuous stirred tank reactor identification. . 287
4.4 Conclusions 295
5 General conclusion 296
6 References 297
12 Higher order asymptotic boundary conditions for an
oxide region in a semiconductor device 301
/. Gamba
1 Introduction 301
2 The full problem 303
2.1 Regularity of the full problem 304
2.2 Equivalent problem formulated in terms of the
Fourier representation 306
Contents xi
2.3 Higher order asymptotic behavior of the Oxide
boundary condition 308
2.4 Conclusions 312
3 References 313
13 Estimation of the complex plain—wave modulus in
viscoelastic media 315
E. M. Fernandez Berdaguer, J. E. Santos
1 Introduction 315
1.1 Description of the Viscoelastic Model 318
1.2 Formulation of the Estimation Problem . . .320
1.3 The Gateaux Derivatives 321
1.4 The Algorithms 322
1.5 The Adjoint Problem 323
1.6 Numerical Experiments 324
2 References 325
14 Numerical Modelling of Maxwell s Equations with
Applications to Magnetotellurics 329
J. E. Santos, L. Guarracino
1 The Differential Model and the Iterative Hybrid Finite
Element Domain Decomposition Algorithm 329
1.1 The Differential Model 330
1.2 A Differential Domain Decomposition
Formulation 333
1.3 The Iterative Hybrid Finite Element Domain
Decomposition Procedure 336
1.4 Experimental Calculations 339
1.5 Some remarks on the implementation of the
algorithm 340
2 Conclusions 343
3 References 343
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| indexdate | 2024-07-09T18:10:55Z |
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| spelling | Wavelet theory and harmonic analysis in applied sciences C. E. D'Attellis ... eds. Boston [u.a.] Birkhäuser 1997 XVIII, 345 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied and numerical harmonic analysis Wavelets (Mathematics) Harmonic analysis Wavelet (DE-588)4215427-3 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s DE-604 Wavelet (DE-588)4215427-3 s D'Attellis, Carlos E. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007743541&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wavelet theory and harmonic analysis in applied sciences Wavelets (Mathematics) Harmonic analysis Wavelet (DE-588)4215427-3 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4215427-3 (DE-588)4023453-8 |
| title | Wavelet theory and harmonic analysis in applied sciences |
| title_auth | Wavelet theory and harmonic analysis in applied sciences |
| title_exact_search | Wavelet theory and harmonic analysis in applied sciences |
| title_full | Wavelet theory and harmonic analysis in applied sciences C. E. D'Attellis ... eds. |
| title_fullStr | Wavelet theory and harmonic analysis in applied sciences C. E. D'Attellis ... eds. |
| title_full_unstemmed | Wavelet theory and harmonic analysis in applied sciences C. E. D'Attellis ... eds. |
| title_short | Wavelet theory and harmonic analysis in applied sciences |
| title_sort | wavelet theory and harmonic analysis in applied sciences |
| topic | Wavelets (Mathematics) Harmonic analysis Wavelet (DE-588)4215427-3 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Wavelets (Mathematics) Harmonic analysis Wavelet Harmonische Analyse |
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