Mathematical signal analysis: wavelets, Wigner distributions and a seismic application
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
CWI
2000
|
| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract
130 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IV, 168 S. graph. Darst. |
| ISBN: | 9061964997 |
Internformat
MARC
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| 100 | 1 | |a Oonincx, Patrick J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematical signal analysis |b wavelets, Wigner distributions and a seismic application |c P. J. Oonincx |
| 264 | 1 | |a Amsterdam |b CWI |c 2000 | |
| 300 | |a IV, 168 S. |b graph. Darst. | ||
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| 490 | 1 | |a Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract |v 130 | |
| 650 | 7 | |a Seismologie |2 gtt | |
| 650 | 7 | |a Signaalonderscheid |2 gtt | |
| 650 | 7 | |a Wavelets |2 gtt | |
| 650 | 7 | |a Wigner-verdelingen |2 gtt | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Fourier transformations | |
| 650 | 4 | |a Signal processing |x Mathematics | |
| 650 | 4 | |a Time-series analysis | |
| 650 | 4 | |a Wavelets (Mathematics) | |
| 650 | 4 | |a Wigner distribution | |
| 650 | 0 | 7 | |a Wigner-Verteilung |0 (DE-588)4641021-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Wavelet |0 (DE-588)4215427-3 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-009357394 | ||
Datensatz im Suchindex
| _version_ | 1804128507892072448 |
|---|---|
| adam_text | Contents
1 Introduction 1
1.1 Time Frequency Methods 1
1.2 Applications of the Wavelet Transform 13
1.2.1 Denoising 13
1.2.2 Compression 14
1.2.3 Wavelet Galerkin methods . 14
1.3 Some Main Results 15
2 Time Frequency Analysis 19
2.1 The Fourier Transform 19
2.1.1 The Fourier Transform on L1 20
2.1.2 The Fourier Transform on L2 22
2.2 The Windowed Fourier Transform 25
2.3 The Wigner Distribution 33
2.4 Lie Group Theory and the Heisenberg Group 41
3 The Wavelet Transform 45
3.1 The Continuous Wavelet Transform 45
3.2 The Discrete Wavelet Transform 54
3.2.1 Multiresolution Analysis in L2(JR) 56
3.2.2 MRA and Filter Banks 58
3.2.3 Implementation oftheDWT and its Use for 12(TL) 61
4 A Framework for Multiresolution Analysis in Hilbert Spaces 67
4.1 Frames and Riesz Systems 67
4.2 Multiresolution Analysis in Hilbert Spaces 72
4.3 Riesz Systems Generated by Unitary Operators 76
4.4 Riesz Bases in l2(Zn) 78
4.5 MRA and Riesz Bases in Hilbert Spaces 84
5 The FRFT and Affine Transformations in the Wigner Plane 89
5.1 The Fractional Fourier Transform 89
iii
iv
5.1.1 Definition and Properties 90
5.1.2 The FRFT and the Wigner Plane 93
5.2 Affine Transformations in the Wigner Plane 95
5.2.1 A Group Theoretical Approach 99
5.2.2 The FRFT Generalized 106
5.3 A Representation Formula 109
6 Localization Problems in Phase Space 119
6.1 Slepian s Energy Problem 119
6.2 Energy Concentration on a Circle in the Wigner Plane 125
6.3 Localization Problems and the Generalized FRFT 130
6.3.1 The Rectangle/Parallelogram Case and the Rihaczek Distribu¬
tion 131
6.3.2 The Circle/Ellipse Case 134
7 A Seismic Problem: Automatic S Phase Detection with the DWT 137
7.1 Introduction and Approach of the Seismic Problem 137
7.2 Seismic methods for S Phase Picking 139
7.2.1 Characteristic functions based on a cross power matrix .... 139
7.2.2 Rotation and the Energy Ratio 141
7.3 On the Use of Characteristic Functions 141
7.3.1 Error Analysis of the Characteristic Functions 142
7.3.2 Problems in Analysing Seismic Data 146
7.4 The Wavelet Method 147
7.4.1 Characteristic Functions and the DWT 147
7.4.2 A Set Up for the DWT Analysis 151
7.5 Examples and Results 153
|
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| id | DE-604.BV013692861 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:50:21Z |
| institution | BVB |
| isbn | 9061964997 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009357394 |
| oclc_num | 46669568 |
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| owner_facet | DE-91G DE-BY-TUM |
| physical | IV, 168 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | CWI |
| record_format | marc |
| series | Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract |
| series2 | Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract |
| spelling | Oonincx, Patrick J. Verfasser aut Mathematical signal analysis wavelets, Wigner distributions and a seismic application P. J. Oonincx Amsterdam CWI 2000 IV, 168 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract 130 Seismologie gtt Signaalonderscheid gtt Wavelets gtt Wigner-verdelingen gtt Mathematik Fourier transformations Signal processing Mathematics Time-series analysis Wavelets (Mathematics) Wigner distribution Wigner-Verteilung (DE-588)4641021-1 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Signalverarbeitung (DE-588)4054947-1 gnd rswk-swf Signalverarbeitung (DE-588)4054947-1 s Wavelet (DE-588)4215427-3 s DE-604 Wigner-Verteilung (DE-588)4641021-1 s Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract 130 (DE-604)BV001902011 130 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009357394&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Oonincx, Patrick J. Mathematical signal analysis wavelets, Wigner distributions and a seismic application Centrum voor Wiskunde en Informatica <Amsterdam>: CWI Tract Seismologie gtt Signaalonderscheid gtt Wavelets gtt Wigner-verdelingen gtt Mathematik Fourier transformations Signal processing Mathematics Time-series analysis Wavelets (Mathematics) Wigner distribution Wigner-Verteilung (DE-588)4641021-1 gnd Wavelet (DE-588)4215427-3 gnd Signalverarbeitung (DE-588)4054947-1 gnd |
| subject_GND | (DE-588)4641021-1 (DE-588)4215427-3 (DE-588)4054947-1 |
| title | Mathematical signal analysis wavelets, Wigner distributions and a seismic application |
| title_auth | Mathematical signal analysis wavelets, Wigner distributions and a seismic application |
| title_exact_search | Mathematical signal analysis wavelets, Wigner distributions and a seismic application |
| title_full | Mathematical signal analysis wavelets, Wigner distributions and a seismic application P. J. Oonincx |
| title_fullStr | Mathematical signal analysis wavelets, Wigner distributions and a seismic application P. J. Oonincx |
| title_full_unstemmed | Mathematical signal analysis wavelets, Wigner distributions and a seismic application P. J. Oonincx |
| title_short | Mathematical signal analysis |
| title_sort | mathematical signal analysis wavelets wigner distributions and a seismic application |
| title_sub | wavelets, Wigner distributions and a seismic application |
| topic | Seismologie gtt Signaalonderscheid gtt Wavelets gtt Wigner-verdelingen gtt Mathematik Fourier transformations Signal processing Mathematics Time-series analysis Wavelets (Mathematics) Wigner distribution Wigner-Verteilung (DE-588)4641021-1 gnd Wavelet (DE-588)4215427-3 gnd Signalverarbeitung (DE-588)4054947-1 gnd |
| topic_facet | Seismologie Signaalonderscheid Wavelets Wigner-verdelingen Mathematik Fourier transformations Signal processing Mathematics Time-series analysis Wavelets (Mathematics) Wigner distribution Wigner-Verteilung Wavelet Signalverarbeitung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009357394&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001902011 |
| work_keys_str_mv | AT oonincxpatrickj mathematicalsignalanalysiswaveletswignerdistributionsandaseismicapplication |