An Introduction to Wavelet Analysis

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Sprache: Englisch

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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

Zusammenfassung

A new text/reference offering a comprehensive and detailed
presentation of wavelet theory, principles and methods. It presents
basic theory of wavelet bases and transforms without assuming
knowledge of advanced mathematics.
The book motivates the central ideas of wavelets by discussing Haar
series in depth and then presenting a more generalized viewpoint. The
material is presented with many examples, exercises and thorough
references. An essential text/reference for applied mathematicians,
engineers and scientists.

Inhaltsverzeichnis

1. Preface, 2. Functions and Convergence, 3. Fourier Series, 4. The
Fourier Transform, 5. Signals and Systems, 6. The Haar System, 7. The
Discrete Haar Transform, 8. Mulitresolution Analysis, 9. The Discrete
Wavelet transform, 10. Smooth, Compactly Supported Wavelets, 11.
Biorthogonal Wavelets, 12. Wavelet Packets, 13. Image Compression, 14.
Integral Operations; Appendices

Erscheinungsjahr:	2013
Fachbereich:	EDV
Genre:	Informatik
Rubrik:	Naturwissenschaften & Technik
Thema:	Lexika
Medium:	Taschenbuch
Reihe:	Applied and Numerical Harmonic Analysis
Inhalt:	xx 452 S.
ISBN-13:	9781461265672
ISBN-10:	1461265673
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Walnut, David F.
Hersteller:	Birkhuser Boston Birkhäuser Boston Applied and Numerical Harmonic Analysis
Maße:	235 x 155 x 26 mm
Von/Mit:	David F. Walnut
Erscheinungsdatum:	11.12.2013
Gewicht:	0,709 kg

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