Analysis and probability: wavelets, signals, fractals
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2006
|
| Schriftenreihe: | Graduate Texts in Mathematics
234 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XLIV, 276 S. Ill., graph. Darst. |
| ISBN: | 0387295194 9780387295190 |
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Datensatz im Suchindex
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| adam_text | Contents
Preface
Getting started
An apology
Glossary: function, random variable, signal, state, sequence (inch vector-
valued), random walk, time-series, measurement, nested subspaces,
refinement, multiresolution, scales of visual resolutions, operator,
process, black box, observable (if self adjoint), Fourier dual pair,
generating function, time/frequency, P/Q, convolution, filter, smearing,
decomposition (e.g., Fourier coefficients in a Fourier expansion), analysis,
frequency components, integrate (e.g., inverse Fourier transform),
reconstruct, synthesis, superposition, subspace, resolution, (signals in a)
frequency band, Cuntz relations, perfect reconstruction from subbands,
subband decomposition, inner product, correlation, transition probability,
probability of transition from one state to another, fova
input/output, transformation of states, fractal, conditional expectation,
martingale, data mining (A translation guide!)
Multiresolutions
Prerequisites and cross-audience
Aim and scope
Self-similarity
New issues, newtools
List of names and discoveries
General theory
A word about the graphics and the illustrations
Special features of the book
Exercises: Overview
Figures. Read Mel
x
Acknowledgments
1
Prerequisites
Prelude
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Exercises
History
References and remarks
2
Prerequisites
Prelude
2.1
22
2.3
2.4
2.5
2.6
2.7
2.8
Exercises
References and remarks
3
Prerequisites
Prelude
3.1
3.2
3.3
Exercises
References and remarks
4
Prerequisites
Prelude
Contents xi
4.1 Affine
4.2
4.3
4.4
Conclusions
Exercises
References and remarks
5
Prerequisites
Prelude
5.1
5.2
5.3
5.4
5.5
Exercises
References and remarks
6
Prerequisites
Prelude
6.1
6.2
Exercises
References and remarks
7
Prerequisites
Prelude
7.1
7.2
7.3
7.4
7.5
7.6
7.7
relations (CARs)
Exercises
References and remarks
xii Contents
8
Prerequisites
Prelude
8.1
8.2
8.3
8.4
Exercises
References and remarks
9
application to maltiresolntions
Prerequisites
Prelude
9.1
9.2
9.3
9.4
9.5
9.6
9.7
Exercises
References and remarks
Appendices: Polyphase matrices and the operator algebra On
Prerequisites
Prelude
Appendix A: Signals and filters
Appendix B: Hubert space and systems of operators
Appendix C: A tale of two Hubert spaces
Table C.I
principle
Appendix D: Signal processing, matrices, and programming diagrams
References and remarks: Systems theory
Afterword
Comments on signal/image processing terminology
Introduction
JPEG
JPEG
GIF
Grayscale
Contents xiii
Quadrature-mirror
What is a frame?
To the mathematics student
To an engineer
Alias (aliasing)
Engineering
Mathematics
Computational mathematics
Epigraphs
References
Symbols
Index
Drawing by the author, next page:
Wavelet algorithms are good for vast sets of numbers.
An engineering friend described the old approach to data mining as
Just drop a computer down onto a gigantic set of unstructured numbers!
fdata mining: see Section
|
| adam_txt |
Contents
Preface
Getting started
An apology
Glossary: function, random variable, signal, state, sequence (inch vector-
valued), random walk, time-series, measurement, nested subspaces,
refinement, multiresolution, scales of visual resolutions, operator,
process, black box, observable (if self adjoint), Fourier dual pair,
generating function, time/frequency, P/Q, convolution, filter, smearing,
decomposition (e.g., Fourier coefficients in a Fourier expansion), analysis,
frequency components, integrate (e.g., inverse Fourier transform),
reconstruct, synthesis, superposition, subspace, resolution, (signals in a)
frequency band, Cuntz relations, perfect reconstruction from subbands,
subband decomposition, inner product, correlation, transition probability,
probability of transition from one state to another, fova
input/output, transformation of states, fractal, conditional expectation,
martingale, data mining (A translation guide!)
Multiresolutions
Prerequisites and cross-audience
Aim and scope
Self-similarity
New issues, newtools
List of names and discoveries
General theory
A word about the graphics and the illustrations
Special features of the book
Exercises: Overview
Figures. Read Mel
x
Acknowledgments
1
Prerequisites
Prelude
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Exercises
History
References and remarks
2
Prerequisites
Prelude
2.1
22
2.3
2.4
2.5
2.6
2.7
2.8
Exercises
References and remarks
3
Prerequisites
Prelude
3.1
3.2
3.3
Exercises
References and remarks
4
Prerequisites
Prelude
Contents xi
4.1 Affine
4.2
4.3
4.4
Conclusions
Exercises
References and remarks
5
Prerequisites
Prelude
5.1
5.2
5.3
5.4
5.5
Exercises
References and remarks
6
Prerequisites
Prelude
6.1
6.2
Exercises
References and remarks
7
Prerequisites
Prelude
7.1
7.2
7.3
7.4
7.5
7.6
7.7
relations (CARs)
Exercises
References and remarks
xii Contents
8
Prerequisites
Prelude
8.1
8.2
8.3
8.4
Exercises
References and remarks
9
application to maltiresolntions
Prerequisites
Prelude
9.1
9.2
9.3
9.4
9.5
9.6
9.7
Exercises
References and remarks
Appendices: Polyphase matrices and the operator algebra On
Prerequisites
Prelude
Appendix A: Signals and filters
Appendix B: Hubert space and systems of operators
Appendix C: A tale of two Hubert spaces
Table C.I
principle
Appendix D: Signal processing, matrices, and programming diagrams
References and remarks: Systems theory
Afterword
Comments on signal/image processing terminology
Introduction
JPEG
JPEG
GIF
Grayscale
Contents xiii
Quadrature-mirror
What is a frame?
To the mathematics student
To an engineer
Alias (aliasing)
Engineering
Mathematics
Computational mathematics
Epigraphs
References
Symbols
Index
Drawing by the author, next page:
Wavelet algorithms are good for vast sets of numbers.
An engineering friend described the old approach to data mining as
"Just drop a computer down onto a gigantic set of unstructured numbers!
fdata mining: see Section |
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| index_date | 2024-07-02T13:39:37Z |
| indexdate | 2024-07-09T20:33:53Z |
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| language | English |
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| spelling | Jørgensen, Palle E. T. 1947- Verfasser (DE-588)124805515 aut Analysis and probability wavelets, signals, fractals Palle E. T. Jorgensen Berlin [u.a.] Springer 2006 XLIV, 276 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate Texts in Mathematics 234 Fractals Mathematical analysis Wavelets (Mathematics) Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Fraktal (DE-588)4123220-3 gnd rswk-swf Signalverarbeitung (DE-588)4054947-1 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Wavelet (DE-588)4215427-3 s Fraktal (DE-588)4123220-3 s Signalverarbeitung (DE-588)4054947-1 s Mathematische Methode (DE-588)4155620-3 s Graduate Texts in Mathematics 234 (DE-604)BV000000067 234 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2682753&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014573176&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jørgensen, Palle E. T. 1947- Analysis and probability wavelets, signals, fractals Graduate Texts in Mathematics Fractals Mathematical analysis Wavelets (Mathematics) Mathematische Methode (DE-588)4155620-3 gnd Fraktal (DE-588)4123220-3 gnd Signalverarbeitung (DE-588)4054947-1 gnd Wavelet (DE-588)4215427-3 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Analysis (DE-588)4001865-9 gnd |
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| title | Analysis and probability wavelets, signals, fractals |
| title_auth | Analysis and probability wavelets, signals, fractals |
| title_exact_search | Analysis and probability wavelets, signals, fractals |
| title_exact_search_txtP | Analysis and probability wavelets, signals, fractals |
| title_full | Analysis and probability wavelets, signals, fractals Palle E. T. Jorgensen |
| title_fullStr | Analysis and probability wavelets, signals, fractals Palle E. T. Jorgensen |
| title_full_unstemmed | Analysis and probability wavelets, signals, fractals Palle E. T. Jorgensen |
| title_short | Analysis and probability |
| title_sort | analysis and probability wavelets signals fractals |
| title_sub | wavelets, signals, fractals |
| topic | Fractals Mathematical analysis Wavelets (Mathematics) Mathematische Methode (DE-588)4155620-3 gnd Fraktal (DE-588)4123220-3 gnd Signalverarbeitung (DE-588)4054947-1 gnd Wavelet (DE-588)4215427-3 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Fractals Mathematical analysis Wavelets (Mathematics) Mathematische Methode Fraktal Signalverarbeitung Wavelet Wahrscheinlichkeitsrechnung Analysis |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2682753&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014573176&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT jørgensenpalleet analysisandprobabilitywaveletssignalsfractals |