An Introduction to Wavelet Analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2004
|
| Schriftenreihe: | Applied and Numerical Harmonic Analysis
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | An Introduction to Wavelet Analysis provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and application of wavelet bases. The book develops the basic theory of wavelet bases and transforms without assuming any knowledge of Lebesgue integration or the theory of abstract Hilbert spaces. The book motivates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, and then shows how a more abstract approach allows us to generalize and improve upon the Haar series. Once these ideas have been established and explored, variations and extensions of Haar construction are presented. The mathematical pre-requisites for the book are a course in advanced calculus, familiarity with the language of formal mathematical proofs, and basic linear algebra concepts. Features: *Rigorous proofs with consistent assumptions on the mathematical background of the reader; does not assume familiarity with Hilbert spaces or Lebesgue measure * Complete background material on (Fourier Analysis topics) Fourier Analysis * Wavelets are presented first on the continuous domain and later restricted to the discrete domain, for improved motivation and understanding of discrete wavelet transforms and applications. * Special appendix, "Excursions in Wavelet Theory " provides a guide to current literature on the topic * Over 170 exercises guide the reader through the text. The book is an ideal text/reference for a broad audience of advanced students and researchers in applied mathematics, electrical engineering, computational science, and physical sciences. It is also suitable as a self-study reference guide for professionals. All readers will find |
| Beschreibung: | 1 Online-Ressource (XX, 452 p) |
| ISBN: | 9781461200017 9781461265672 |
| ISSN: | 2296-5009 |
| DOI: | 10.1007/978-1-4612-0001-7 |
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| 500 | |a An Introduction to Wavelet Analysis provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and application of wavelet bases. The book develops the basic theory of wavelet bases and transforms without assuming any knowledge of Lebesgue integration or the theory of abstract Hilbert spaces. The book motivates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, and then shows how a more abstract approach allows us to generalize and improve upon the Haar series. Once these ideas have been established and explored, variations and extensions of Haar construction are presented. The mathematical pre-requisites for the book are a course in advanced calculus, familiarity with the language of formal mathematical proofs, and basic linear algebra concepts. Features: *Rigorous proofs with consistent assumptions on the mathematical background of the reader; does not assume familiarity with Hilbert spaces or Lebesgue measure * Complete background material on (Fourier Analysis topics) Fourier Analysis * Wavelets are presented first on the continuous domain and later restricted to the discrete domain, for improved motivation and understanding of discrete wavelet transforms and applications. * Special appendix, "Excursions in Wavelet Theory " provides a guide to current literature on the topic * Over 170 exercises guide the reader through the text. The book is an ideal text/reference for a broad audience of advanced students and researchers in applied mathematics, electrical engineering, computational science, and physical sciences. It is also suitable as a self-study reference guide for professionals. All readers will find | ||
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:04Z |
| institution | BVB |
| isbn | 9781461200017 9781461265672 |
| issn | 2296-5009 |
| language | English |
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| spelling | Walnut, David F. Verfasser aut An Introduction to Wavelet Analysis by David F. Walnut Boston, MA Birkhäuser Boston 2004 1 Online-Ressource (XX, 452 p) txt rdacontent c rdamedia cr rdacarrier Applied and Numerical Harmonic Analysis 2296-5009 An Introduction to Wavelet Analysis provides a comprehensive presentation of the conceptual basis of wavelet analysis, including the construction and application of wavelet bases. The book develops the basic theory of wavelet bases and transforms without assuming any knowledge of Lebesgue integration or the theory of abstract Hilbert spaces. The book motivates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, and then shows how a more abstract approach allows us to generalize and improve upon the Haar series. Once these ideas have been established and explored, variations and extensions of Haar construction are presented. The mathematical pre-requisites for the book are a course in advanced calculus, familiarity with the language of formal mathematical proofs, and basic linear algebra concepts. Features: *Rigorous proofs with consistent assumptions on the mathematical background of the reader; does not assume familiarity with Hilbert spaces or Lebesgue measure * Complete background material on (Fourier Analysis topics) Fourier Analysis * Wavelets are presented first on the continuous domain and later restricted to the discrete domain, for improved motivation and understanding of discrete wavelet transforms and applications. * Special appendix, "Excursions in Wavelet Theory " provides a guide to current literature on the topic * Over 170 exercises guide the reader through the text. The book is an ideal text/reference for a broad audience of advanced students and researchers in applied mathematics, electrical engineering, computational science, and physical sciences. It is also suitable as a self-study reference guide for professionals. All readers will find Mathematics Functional analysis Computer science / Mathematics Computer science Computational Science and Engineering Signal, Image and Speech Processing Computational Mathematics and Numerical Analysis Applications of Mathematics Functional Analysis Informatik Mathematik Wavelet (DE-588)4215427-3 gnd rswk-swf Wavelet (DE-588)4215427-3 s 1\p DE-604 https://doi.org/10.1007/978-1-4612-0001-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Walnut, David F. An Introduction to Wavelet Analysis Mathematics Functional analysis Computer science / Mathematics Computer science Computational Science and Engineering Signal, Image and Speech Processing Computational Mathematics and Numerical Analysis Applications of Mathematics Functional Analysis Informatik Mathematik Wavelet (DE-588)4215427-3 gnd |
| subject_GND | (DE-588)4215427-3 |
| title | An Introduction to Wavelet Analysis |
| title_auth | An Introduction to Wavelet Analysis |
| title_exact_search | An Introduction to Wavelet Analysis |
| title_full | An Introduction to Wavelet Analysis by David F. Walnut |
| title_fullStr | An Introduction to Wavelet Analysis by David F. Walnut |
| title_full_unstemmed | An Introduction to Wavelet Analysis by David F. Walnut |
| title_short | An Introduction to Wavelet Analysis |
| title_sort | an introduction to wavelet analysis |
| topic | Mathematics Functional analysis Computer science / Mathematics Computer science Computational Science and Engineering Signal, Image and Speech Processing Computational Mathematics and Numerical Analysis Applications of Mathematics Functional Analysis Informatik Mathematik Wavelet (DE-588)4215427-3 gnd |
| topic_facet | Mathematics Functional analysis Computer science / Mathematics Computer science Computational Science and Engineering Signal, Image and Speech Processing Computational Mathematics and Numerical Analysis Applications of Mathematics Functional Analysis Informatik Mathematik Wavelet |
| url | https://doi.org/10.1007/978-1-4612-0001-7 |
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