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A Friendly Guide to Wavelets

A Friendly Guide to Wavelets This volume is designed as a textbook for an introductory course on wavelet analysis and time-frequency analysis aimed at graduate students or advanced undergraduates in science and engineering. It can also be used as a self-study or reference book by practicing researchers in signal analysis and related areas. Since the expected audience is not presumed to have a high level of mathematical background, much of the needed analytical machinery is developed from the beginning. The only prerequisites for the first eight chapters are matrix theory, Fourier series, and Fourier integral transforms. Each of these chapters ends with a set of straightforward exercises designed to drive home the concepts just covered, and the many graphics should further facilitate absorption. ; This volume is designed as a textbook for an introductory course on wavelet analysis and time-frequency analysis aimed at graduate students or advanced undergraduates in science and engineering. It can also be used as a self-study or reference book by practicing researchers in signal analysis and related areas. Since the expected audience is not presumed to have a high level of mathematical background, much of the needed analytical machinery is developed from the beginning. The only prerequisites for the first eight chapters are matrix theory, Fourier series, and Fourier integral transforms. Each of these chapters ends with a set of straightforward exercises designed to drive home the concepts just covered, and the many graphics should further facilitate absorption. Chapters 10 and 11 consist of original research and are written in a more advanced style. In Chapter 10 it is shown that the structure of Maxwell's equations implies the existence of a wavelet analysis specifically adopted to electromagnetic radiation. The associated "eletromagnetic wavelets" are pulses parameterized by their point of origin and their scale, and can be made arbitrarily short by choosing fine scales. Furthermore, it is shown that every electromagnetic wave can be composed of such localized wavelets. This is applied in Chapter 11 to give a new formulation of radar based on electromagnetic wavelets. Since this theory is fully relativistic, its description of the Doppler effect is exact. In particular, it is three-dimensional, and does not make the usual assumption that the outgoing signal has a narrow bandwidth. Thus it should be useful in the construction of ultra-wideband radar systems. ; Preface.- Suggestions to the Reader.- Symbols, Conventions, and Transforms.- Part I: Basic Wavelet Analysis. Preliminaries: Background and Notation.- Windowed Fourier Transforms.- Continuous Wavelet Transforms.- Generalized Frames: Key to Analysis and Synthesis.- Discrete Time-Frequency Analysis and Sampling.- Discrete Time-Scale Analysis.- Multiresolution Analysis.- Daubechies’ Orthonormal Wavelet Bases.- Part II: Physical Wavelets.- Introduction to Wavelet Electromagnetics.- Applications to Radar and Scattering.- Wavelet Acoustics.- References.- Index. ; From the reviews: "I wholeheartedly recommend this book for a solid and friendly introduction to wavelets, for anyone who is comfortable with the mathematics required of undergraduate electrical engineers. The book's appeal is that it covers all the fundamental concepts of wavelets in an elegant, straightforward way. It offers truly enjoyable (friendly!) mathematical exposition that is rich in intuitive explanations, as well as clean, direct, and clear in its theoretical developments. I found Kaiser's straightforward end-of-chapter exercises excellent...Kaiser has written an excellent introduction to the fundamental concepts of wavelets. For a book of its length and purpose, I think it should be essentially unbeatable for a long time." —Proceedings of the IEEE "It is well produced and certainly readable...This material should present no difficulty for fourth-year undergraduates...It also will be useful to advanced workers in that it presents a different approach to wavelet theory from the usual one." —Computing Reviews "I found this to be an excellent book. It is eminently more readable than the books...which might be considered the principal alternatives for textbooks on wavelets." —Physics Today "This volume is probably the most gentle introduction to wavelet theory on the market. As such, it responds to a significant need. The intended audience will profit from the motivation and common-sense explanations in the text. Ultimately, it may lead many readers, who may not otherwise have been able to do so, to go further into wavelet theory, Fourier analysis, and signal processing." —SIAM Review "The first half of the book is appropriately named. It is a well-written, nicely organized exposition...a welcome addition to the literature. The second part of the book introduces the concept of electromagnetic wavelets...This theory promises to have many other applications and could well lead to new ways of studying these topics. This book has a number of unique features which...makes it particularly valuable for newcomers to the field." —Mathematical Reviews "The book is indeed what its title promises: A friendly guide to wavelets...In short, Kaiser's book is excellently written and can be considered as one of the best textbooks on this topic presently available...it will enjoy wide distribution among mathematicians and physicists interested in wavelet analysis." —Internationale Mathematische Nachrichten "I loved 'A Friendly Guide to Wavelets'. I advised it to my graduate students." —Yves Meyer, Université Paris-Dauphine “Taking into account the importance of the wavelet theory in … physics and engineering, there was a need for writing a textbook that is more suitable for students and researchers with a limited knowledge of the functional analytic background. The book by Gerald Kaiser aims at this goal. … the friendly guide to wavelets is still an interesting literature, taking a very special view to the tools of Fourier and wavelet analysis for applications in signal processing. … this book is very unique.” (Gerlind Plonka-Hoch, Zentralblatt MATH, Vol. 1230, 2012) “This is a thorough introduction to most aspects of wavelets. It is an unaltered reprint of a 1994 book, but it is still reasonably up-to-date for the topics it covers. … The book is intended to be ‘friendly’ toward engineering and scientific readers by using the language of classical analysis … .” (Allen Stenger, The Mathematical Association of America, June, 2011) ; I wholeheartedly recommend this book for a solid and friendly introduction to wavelets, for anyone who is comfortable with the mathematics required of undergraduate electrical engineers. The book's appeal is that it covers all the fundamental concepts of wavelets in an elegant, straightforward way. It offers truly enjoyable (friendly!) mathematical exposition that is rich in intuitive explanations, as well as clean, direct, and clear in its theoretical developments. I found Kaiser's straightforward end-of-chapter exercises excellent...Kaiser has written an excellent introduction to the fundamental concepts of wavelets. For a book of its length and purpose, I think it should be essentially unbeatable for a long time. —Proceedings of the IEEE It is well produced and certainly readable...This material should present no difficulty for fourth-year undergraduates...It also will be useful to advanced workers in that it presents a different approach to wavelet theory from the usual one. —Computing Reviews I found this to be an excellent book. It is eminently more readable than the books...which might be considered the principal alternatives for textbooks on wavelets. —Physics Today This volume is probably the most gentle introduction to wavelet theory on the market. As such, it responds to a significant need. The intended audience will profit from the motivation and common-sense explanations in the text. Ultimately, it may lead many readers, who may not otherwise have been able to do so, to go further into wavelet theory, Fourier analysis, and signal processing. —SIAM Review The first half of the book is appropriately named. It is a well-written, nicely organized exposition...a welcome addition to the literature. The second part of the book introduces the concept of electromagnetic wavelets...This theory promises to have many other applications and could well lead to new ways of studying these topics. This book has a number of unique features which...makes it particularly valuable for newcomers to the field. —Mathematical Reviews The book is indeed what its title promises: A friendly guide to wavelets...In short, Kaiser's book is excellently written and can be considered as one of the best textbooks on this topic presently available...it will enjoy wide distribution among mathematicians and physicists interested in wavelet analysis. —Internationale Mathematische Nachrichten For additional review samples and related material, please visit the author's website at www.wavelets.com. ; Considered one of the best textbooks on this topic for mathematicians and physicists interested in wavelet analysis Covers all the fundamental concepts of wavelets in an elegant, straightforward way Has a number of unique features, which makes the book particularly valuable for newcomers to the field ; GB http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Friendly Guide to Wavelets

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Publisher
Birkhäuser Boston
Copyright
Copyright � Springer Basel AG
DOI
10.1007/978-0-8176-8111-1
Publisher site
See Book on Publisher Site

Abstract

This volume is designed as a textbook for an introductory course on wavelet analysis and time-frequency analysis aimed at graduate students or advanced undergraduates in science and engineering. It can also be used as a self-study or reference book by practicing researchers in signal analysis and related areas. Since the expected audience is not presumed to have a high level of mathematical background, much of the needed analytical machinery is developed from the beginning. The only prerequisites for the first eight chapters are matrix theory, Fourier series, and Fourier integral transforms. Each of these chapters ends with a set of straightforward exercises designed to drive home the concepts just covered, and the many graphics should further facilitate absorption. ; This volume is designed as a textbook for an introductory course on wavelet analysis and time-frequency analysis aimed at graduate students or advanced undergraduates in science and engineering. It can also be used as a self-study or reference book by practicing researchers in signal analysis and related areas. Since the expected audience is not presumed to have a high level of mathematical background, much of the needed analytical machinery is developed from the beginning. The only prerequisites for the first eight chapters are matrix theory, Fourier series, and Fourier integral transforms. Each of these chapters ends with a set of straightforward exercises designed to drive home the concepts just covered, and the many graphics should further facilitate absorption. Chapters 10 and 11 consist of original research and are written in a more advanced style. In Chapter 10 it is shown that the structure of Maxwell's equations implies the existence of a wavelet analysis specifically adopted to electromagnetic radiation. The associated "eletromagnetic wavelets" are pulses parameterized by their point of origin and their scale, and can be made arbitrarily short by choosing fine scales. Furthermore, it is shown that every electromagnetic wave can be composed of such localized wavelets. This is applied in Chapter 11 to give a new formulation of radar based on electromagnetic wavelets. Since this theory is fully relativistic, its description of the Doppler effect is exact. In particular, it is three-dimensional, and does not make the usual assumption that the outgoing signal has a narrow bandwidth. Thus it should be useful in the construction of ultra-wideband radar systems. ; Preface.- Suggestions to the Reader.- Symbols, Conventions, and Transforms.- Part I: Basic Wavelet Analysis. Preliminaries: Background and Notation.- Windowed Fourier Transforms.- Continuous Wavelet Transforms.- Generalized Frames: Key to Analysis and Synthesis.- Discrete Time-Frequency Analysis and Sampling.- Discrete Time-Scale Analysis.- Multiresolution Analysis.- Daubechies’ Orthonormal Wavelet Bases.- Part II: Physical Wavelets.- Introduction to Wavelet Electromagnetics.- Applications to Radar and Scattering.- Wavelet Acoustics.- References.- Index. ; From the reviews: "I wholeheartedly recommend this book for a solid and friendly introduction to wavelets, for anyone who is comfortable with the mathematics required of undergraduate electrical engineers. The book's appeal is that it covers all the fundamental concepts of wavelets in an elegant, straightforward way. It offers truly enjoyable (friendly!) mathematical exposition that is rich in intuitive explanations, as well as clean, direct, and clear in its theoretical developments. I found Kaiser's straightforward end-of-chapter exercises excellent...Kaiser has written an excellent introduction to the fundamental concepts of wavelets. For a book of its length and purpose, I think it should be essentially unbeatable for a long time." —Proceedings of the IEEE "It is well produced and certainly readable...This material should present no difficulty for fourth-year undergraduates...It also will be useful to advanced workers in that it presents a different approach to wavelet theory from the usual one." —Computing Reviews "I found this to be an excellent book. It is eminently more readable than the books...which might be considered the principal alternatives for textbooks on wavelets." —Physics Today "This volume is probably the most gentle introduction to wavelet theory on the market. As such, it responds to a significant need. The intended audience will profit from the motivation and common-sense explanations in the text. Ultimately, it may lead many readers, who may not otherwise have been able to do so, to go further into wavelet theory, Fourier analysis, and signal processing." —SIAM Review "The first half of the book is appropriately named. It is a well-written, nicely organized exposition...a welcome addition to the literature. The second part of the book introduces the concept of electromagnetic wavelets...This theory promises to have many other applications and could well lead to new ways of studying these topics. This book has a number of unique features which...makes it particularly valuable for newcomers to the field." —Mathematical Reviews "The book is indeed what its title promises: A friendly guide to wavelets...In short, Kaiser's book is excellently written and can be considered as one of the best textbooks on this topic presently available...it will enjoy wide distribution among mathematicians and physicists interested in wavelet analysis." —Internationale Mathematische Nachrichten "I loved 'A Friendly Guide to Wavelets'. I advised it to my graduate students." —Yves Meyer, Université Paris-Dauphine “Taking into account the importance of the wavelet theory in … physics and engineering, there was a need for writing a textbook that is more suitable for students and researchers with a limited knowledge of the functional analytic background. The book by Gerald Kaiser aims at this goal. … the friendly guide to wavelets is still an interesting literature, taking a very special view to the tools of Fourier and wavelet analysis for applications in signal processing. … this book is very unique.” (Gerlind Plonka-Hoch, Zentralblatt MATH, Vol. 1230, 2012) “This is a thorough introduction to most aspects of wavelets. It is an unaltered reprint of a 1994 book, but it is still reasonably up-to-date for the topics it covers. … The book is intended to be ‘friendly’ toward engineering and scientific readers by using the language of classical analysis … .” (Allen Stenger, The Mathematical Association of America, June, 2011) ; I wholeheartedly recommend this book for a solid and friendly introduction to wavelets, for anyone who is comfortable with the mathematics required of undergraduate electrical engineers. The book's appeal is that it covers all the fundamental concepts of wavelets in an elegant, straightforward way. It offers truly enjoyable (friendly!) mathematical exposition that is rich in intuitive explanations, as well as clean, direct, and clear in its theoretical developments. I found Kaiser's straightforward end-of-chapter exercises excellent...Kaiser has written an excellent introduction to the fundamental concepts of wavelets. For a book of its length and purpose, I think it should be essentially unbeatable for a long time. —Proceedings of the IEEE It is well produced and certainly readable...This material should present no difficulty for fourth-year undergraduates...It also will be useful to advanced workers in that it presents a different approach to wavelet theory from the usual one. —Computing Reviews I found this to be an excellent book. It is eminently more readable than the books...which might be considered the principal alternatives for textbooks on wavelets. —Physics Today This volume is probably the most gentle introduction to wavelet theory on the market. As such, it responds to a significant need. The intended audience will profit from the motivation and common-sense explanations in the text. Ultimately, it may lead many readers, who may not otherwise have been able to do so, to go further into wavelet theory, Fourier analysis, and signal processing. —SIAM Review The first half of the book is appropriately named. It is a well-written, nicely organized exposition...a welcome addition to the literature. The second part of the book introduces the concept of electromagnetic wavelets...This theory promises to have many other applications and could well lead to new ways of studying these topics. This book has a number of unique features which...makes it particularly valuable for newcomers to the field. —Mathematical Reviews The book is indeed what its title promises: A friendly guide to wavelets...In short, Kaiser's book is excellently written and can be considered as one of the best textbooks on this topic presently available...it will enjoy wide distribution among mathematicians and physicists interested in wavelet analysis. —Internationale Mathematische Nachrichten For additional review samples and related material, please visit the author's website at www.wavelets.com. ; Considered one of the best textbooks on this topic for mathematicians and physicists interested in wavelet analysis Covers all the fundamental concepts of wavelets in an elegant, straightforward way Has a number of unique features, which makes the book particularly valuable for newcomers to the field ; GB

Published: Nov 3, 2010

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