Cantitate/Preț
Produs
Total produse
Vezi coșul
An Introduction to Wavelet Analysis de David F. Walnut

An Introduction to Wavelet Analysis: Applied and Numerical Harmonic Analysis

Autor David F. Walnut
en Limba Engleză Paperback – 11 dec 2013

Observăm că literatura academică dedicată analizei wavelet tinde adesea să penduleze între manuale ultra-simplificate și tratate dense de analiză funcțională care descurajează studenții de la inginerie sau fizică. An Introduction to Wavelet Analysis completează exact această lacună, oferind o rigoare matematică autentică fără a impune bariera cunoștințelor de teoria măsurii sau a spațiilor Hilbert. Autorul, David F. Walnut, care anterior a cartografiat evoluția istorică a domeniului în Fundamental Papers in Wavelet Theory, propune aici un demers pedagogic progresiv, centrat pe demonstrații formale accesibile celor care stăpânesc calculul diferențial și algebra liniară.

Suntem de părere că structura logică a volumului este unul dintre punctele sale forte. Textul începe cu o fundamentare solidă în analiza Fourier (serii și transformate), trece prin studiul sistemului Haar pentru a ilustra conceptele de bază, și evoluează natural către Analiza Multirezoluție și transformata wavelet discretă. Capitolele dedicate compresiei de imagine și pachetelor wavelet aduc o dimensiune practică esențială, demonstrând relevanța teoriei în procesarea semnalelor. Această abordare completează perspectiva oferită de A Friendly Guide to Wavelets de Gerald Kaiser, adăugând o structură mult mai riguroasă de demonstrații matematice și o explorare detaliată a construcțiilor biortonormale, aspecte tratate mai succint în alte texte introductive.

Prin cele peste 170 de exerciții integrate, volumul nu este doar o resursă de referință, ci un instrument activ de învățare. Tranziția de la domeniul continuu la cel discret este realizată pentru a facilita înțelegerea intuitivă a transformărilor, transformând un subiect adesea opac într-un parcurs coerent și aplicabil în științele computaționale.

Citește tot Restrânge

Din seria Applied and Numerical Harmonic Analysis

  • Distributions in the Physical and Engineering Sciences, Volume 1
    Preț: 38272 lei
  • 15% Sampling Theory, a Renaissance
    Preț: 63501 lei
  • 15% Advances in Gabor Analysis
    Preț: 61760 lei
  • Distributions in the Physical and Engineering Sciences: Distributional and Fractal Calculus, Integral Transforms and Wavelets
    Preț: 38230 lei
  • Distributions in the Physical and Engineering Sciences, Volume 2
    Preț: 38746 lei
  • 15% Sampling, Wavelets, and Tomography
    Preț: 62270 lei
  • 15% Heat Kernels for Elliptic and Sub-elliptic Operators: Methods and Techniques
    Preț: 62948 lei
  • 17% Introduction to Partial Differential Equations with MATLAB
    Preț: 46685 lei
  • Wavelets Through a Looking Glass
    Preț: 39452 lei
  • 15% Computational Methods for Three-Dimensional Microscopy Reconstruction
    Preț: 61805 lei
  • 15% Time-Frequency Representations
    Preț: 61919 lei
  • 15% Computational Signal Processing with Wavelets
    Preț: 62370 lei
  • 15% Excursions in Harmonic Analysis, Volume 2
    Preț: 62794 lei
  • 15% Stochastic Models, Information Theory, and Lie Groups, Volume 2
    Preț: 64051 lei
  • 15% Groupoid Metrization Theory
    Preț: 62873 lei
  • 24% Modern Sampling Theory
    Preț: 64632 lei
  • 32% Duration and Bandwidth Limiting
    Preț: 56517 lei
  • Wavelet Theory and Harmonic Analysis in Applied Sciences
    Preț: 37697 lei
  • 15% Frames and Bases: An Introductory Course
    Preț: 48608 lei
  • 15% Realtime Data Mining
    Preț: 62108 lei
  • Analysis of Divergence
    Preț: 39025 lei
  • Multiscale Potential Theory
    Preț: 39317 lei
  • 21% The Evolution of Applied Harmonic Analysis
    Preț: 58302 lei
  • Geometry of Digital Spaces
    Preț: 38041 lei
  • 15% Lectures on Constructive Approximation
    Preț: 51345 lei
  • 24% Variable Lebesgue Spaces
    Preț: 57020 lei
  • Mathematics for Multimedia
    Preț: 38564 lei
  • Fourier Analysis and Convexity
    Preț: 37267 lei
  • 5% Discrete Tomography: Foundations, Algorithms, and Applications
    Preț: 112331 lei
  • 23% Shearlets
    Preț: 57334 lei
  • Wavelets and Signal Processing
    Preț: 38287 lei
  • 18% Foundations of Time-Frequency Analysis
    Preț: 102188 lei
  • 18% Wavelet Transforms and Time-Frequency Signal Analysis
    Preț: 91968 lei
  • 20% Selected Unsolved Problems in Coding Theory
    Preț: 32198 lei
  • 15% The Fourier Transform in Biomedical Engineering
    Preț: 60975 lei
  • Methods of Applied Fourier Analysis
    Preț: 37554 lei
  • 18% Finite Frames
    Preț: 108568 lei
  • 18% Gabor Analysis and Algorithms
    Preț: 96654 lei
  • 15% A Mathematical Introduction to Compressive Sensing
    Preț: 53365 lei
  • 15% Excursions in Harmonic Analysis, Volume 1
    Preț: 62914 lei
  • 24% Wavelet Analysis and Applications
    Preț: 89729 lei

Preț: 38313 lei

Puncte Express: 575

Carte tipărită la comandă

Livrare economică 27 mai-10 iunie

 Adaugă în coș

Wish list
Gift list
Am citit!
Adaugă în listă

Specificații

ISBN-13: 9781461265672
ISBN-10: 1461265673
Pagini: 472
Ilustrații: XX, 452 p.
Dimensiuni: 155 x 235 x 26 mm
Greutate: 0.71 kg
Ediția:2004
Editura: birkhäuser
Colecția Applied and Numerical Harmonic Analysis
Seria Applied and Numerical Harmonic Analysis

Locul publicării:Boston, MA, United States

Public țintă

Research

De ce să citești această carte

Recomandăm această carte studenților de la matematică aplicată și inginerie care au nevoie de o bază teoretică solidă, dar accesibilă, în analiza wavelet. Cititorul câștigă o înțelegere clară a modului în care funcționează compresia de date și procesarea semnalelor, fără a fi nevoit să parcurgă cursuri avansate de analiză reală. Este un text rar care reușește să mențină rigoarea demonstrației matematice într-un limbaj adaptat cercetătorilor din afara departamentelor de matematică pură.

Descriere scurtă

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

Cuprins

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

Recenzii

"[This text] is carefully prepared, well-organized, and covers a large part of the central theory . . . [there are] chapters on biorthogonal wavelets and wavelet packets, topics which are rare in wavelet books. Both are important, and this feature is an extra argument in favour of [this] book . . . the material is accessible [even] to less advanced readers . . . the book is a nice addition to the series."   —Zentralblatt Math
"This book can be recommended to everyone, especially to students looking for a detailed introduction to the subject."   —Mathematical Reviews
"This textbook is an introduction to the mathematical theory of wavelet analysis at the level of advanced calculus. Some applications are described, but the main purpose of the book is to develop—using only tools from a first course in advanced calculus—a solid foundation in wavelet theory. It succeeds admirably. . . . Part I of the book contains 112 pages of preliminary material, consisting of four chapters on ‘Functions and Convergence,’ ‘Fourier Series,’ ‘Fourier Transforms,’ and ‘Signals and Systems.’ . . . This preliminary material is so well written that it could serve as an excellent supplement to a first course in advanced calculus. . . . The heart of the book is Part III: ‘Orthonormal Wavelet bases.’ This material has become the canonical portion of wavelet theory. Walnut does a first-rate job explaining the ideas here. . . . Ample references are supplied to aid the reader. . . . There are exercises at the end of each section, 170 in all, and they seem to be consistent with the level of the text. . . . To cover the whole book would require a year. An excellent one-semester course could be based on a selection of chapters from Parts II, III, and V."   —SIAM Review
"D. Walnut's lovely book aims at the upper undergraduate level, and so it includesrelatively more preliminary material . . . than is typically the case in a graduate text. It goes from Haar systems to multiresolutions, and then the discrete wavelet transform . . . The applications to image compression are wonderful, and the best I have seen in books at this level. I also found the analysis of the best choice of basis, and wavelet packet, especially attractive. The later chapters include MATLAB codes. Highly recommended!"   —Bulletin of the AMS