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Product Identifiers

PublisherBirkhäuser Boston

ISBN-100817639624

ISBN-139780817639624

eBay Product ID (ePID)1597959

Product Key Features

Number of PagesXx, 452 Pages

Publication NameIntroduction to Wavelet Analysis

LanguageEnglish

Publication Year2001

SubjectSignals & Signal Processing, Computer Science, Applied, Mathematical Analysis

TypeTextbook

Subject AreaMathematics, Computers, Technology & Engineering

AuthorDavid F. Walnut

SeriesApplied and Numerical Harmonic Analysis Ser.

FormatHardcover

Dimensions

Item Weight64.9 Oz

Item Length9.2 in

Item Width6.1 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN2001-025367

TitleLeadingAn

Reviews"[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." a?Zentralblatt Math "This book can be recommended to everyone, especially to students looking for a detailed introduction to the subject." a?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 developa'using only tools from a first course in advanced calculusa'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 a?Functions and Convergence,a? a?Fourier Series,a? a?Fourier Transforms,a? and a?Signals and Systems.a? . . . 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: a?Orthonormal Wavelet bases.a? 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." a?SIAM Review "D. Walnut's lovely book aims at the upper undergraduate level, and so it includes relatively 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!" a?Bulletin of the AMS, "[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 includes relatively 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, "[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 includes relatively 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, "[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 includes relatively 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, "[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, "[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 includes relatively 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

Number of Volumes1 vol.

IllustratedYes

Table Of Content1. Preface, 2. Functions and Convergence, 3. Fourier Series, 4. TheFourier Transform, 5. Signals and Systems, 6. The Haar System, 7. TheDiscrete Haar Transform, 8. Mulitresolution Analysis, 9. The DiscreteWavelet transform, 10. Smooth, Compactly Supported Wavelets, 11.Biorthogonal Wavelets, 12. Wavelet Packets, 13. Image Compression, 14.Integral Operations; Appendices

SynopsisA 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., "D. Walnut's lovely book aims at the upper undergraduate level, and so it includes relatively 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 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 elucidates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, and then shows how a more abstract approach allows one 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 prerequisites 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 about the mathematical background of the reader (does not assume familiarity with Hilbert spaces or Lebesgue measure). * Complete background material on is offered on Fourier analysis topics. * 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. An Introduction to Wavelet Analysis 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., An Introduction to Wavelet Analysis provides a comprehensivepresentationof the conceptual basis of wavelet analysis, including theconstructionand application of wavelet bases. The book develops the basic theoryof wavelet bases and transforms without assuming any knowledge ofLebesgue integration or the theory of abstract Hilbert spaces. Thebook motivates the central ideas of wavelet theory by offering adetailed exposition of the Haar series, and then shows how a moreabstract approach allows us to generalize and improve upon the Haarseries. Once these ideas have been established and explored,variations and extensions of Haar construction are presented. Themathematical pre-requisites for the book are a course in advancedcalculus, familiarity with the language of formal mathematical proofs,and basic linear algebra concepts. Features: *Rigorous proofs withconsistent 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) FourierAnalysis * Wavelets are presented first on the continuous domain andlater restricted to the discrete domain, for improved motivation andunderstanding of discrete wavelet transforms and applications.* Special appendix, "Excursions in Wavelet Theory " provides a guidetocurrent literature on the topic* Over 170 exercises guide the reader through the text. The book isan ideal text/reference for a broad audience of advanced students andresearchers in applied mathematics, electrical engineering,computational science, and physical sciences. It is also suitable as aself-study reference guide for professionals. All readers will find, A new text/reference offering a comprehensive and detailedpresentation of wavelet theory, principles and methods. It presentsbasic theory of wavelet bases and transforms without assumingknowledge of advanced mathematics.The book motivates the central ideas of wavelets by discussing Haarseries in depth and then presenting a more generalized viewpoint. Thematerial is presented with many examples, exercises and thoroughreferences. An essential text/reference for applied mathematicians,engineers and scientists., "D. Walnut's lovely book aims at the upper undergraduate level, and so it includes relatively 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 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 elucidates the central ideas of wavelet theory by offering a detailed exposition of the Haar series, and then shows how a more abstract approach allows one 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 prerequisites 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 about the mathematical background of the reader (does not assume familiarity with Hilbert spaces or Lebesgue measure). * Complete background material on is offered on Fourier analysis topics. * 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. An Introduction to Wavelet Analysis 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.

LC Classification NumberQA71-90