Mathematical Principles of Signal Processing: Fourier and Wavelet Analysis by Pi

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Fourier analysis and its modern extension of wavelet analysis provides one of the most useful tools in many applied sciences. This text provides a rigorously mathematical introduction to the subject, while emphasizing their uses in signal processing and other applications in communications engineering.

FORMATHardcover LANGUAGEEnglish CONDITIONBrand New Publisher Description

From the reviews: "[!] the interested reader will find in Bremaud's book an invaluable reference because of its coverage, scope and style, as well as of the unified treatment it offers of (signal processing oriented) Fourier and wavelet basics." Mathematical Reviews

Notes

Fourier analysis and its modern extension of wavelet analysis provides one of the most useful tools in many applied sciences. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction to the subject, while emphasizing their uses in signal processing and other applications in communications engineering. An appendix provides the necessary background on Lebesgue integrals.

Table of Contents

A1 Fourier Transforms of Stable Signals.- A2 Fourier Series of Locally Stable Periodic Signals.- A3 Pointwise Convergence of Fourier Series.- B1 Filtering.- B2 Sampling.- B3 Digital Signal Processing.- B4 Subband Coding.- C1 Hilbert Spaces.- C2 Complete Orthonormal Systems.- C3 Fourier Transforms of Finite-Energy Signals.- C4 Fourier Series of Finite-Power Periodic Signals.- D1 The Windowed Fourier Transform.- D2 The Wavelet Transform.- D3 Wavelet Orthonormal Expansions.- D4 Construction of an MRA.- D5 Smooth Multiresolution Analysis.- The Lebesgue Integral.- References.- Glossary of Symbols.

Review

From the reviews: MATHEMATICAL REVIEWS "While many books exits, dealing either with 'theory' or 'applications', the interplay between signal processing and mathematics makes it difficult to find in a single volume the essentials of modern signal processing presented in a way which would be both rigorous for mathematicians and accessible for engineers. This challenge is precisely the purpose of Bremaud's book, and the goal is clearly attained. The presentation is clear, concise and self-contained, all the necessary concepts are put on a firm ground and proofs are worked out in great detail…In summary, the interested reader will find in Bremaud's book an invaluable reference because of its coverage, scope and style, as well as of the unified treatment it offers of (signal processing oriented) Fourier and wavelet basics." "This book wants to bridge the gap between engineering and mathematics … . What I liked most is the part on subband coding and the fact that bioorthogonal bases are discussed … . A nice feature of the text is that it stimulates the reader to actively assimilate the material because the theorems (almost all the proofs are included) are interlaced with exercises challenging to immediately apply what has been explained." (Adhemar Bultheel, Belgian Mathematical Society Simon Stevin Bulletin, Vol. 11 (2), 2004) "Brémaud has prepared this graduate-level book to bridge the gap between the mathematical theory of Fourier analysis and the application of that theory to signal processing and other areas of communications engineering. … To be readable by an engineering audience, the book includes a self-contained appendix on Lebesgue integration. … Given the importance of the subject matter and the thoroughness of the treatment, this book is recommended for acquisition by any library that supports graduate programs in mathematics, physics or engineering." (D. Z. Spicer, CHOICE, December, 2002) "This volume is a treatise bringing together Fourier analysis and signal processing. … The book is attractive due to the quality of the presentation and its conciseness. It is likely that engineers will gain mostly from it, but it is also of interest to applied mathematicians who will see developments in the repercussions of their discipline in the applications area." (A. Akutowicz, Zentralblatt MATH, Vol. 1009, 2003) "The interplay between signal processing and mathematics makes it difficult to find in a single volume the essentials of modern signal processing presented in a way which would be both rigorous for mathematicians and accessible for engineers. This challenge is precisely the purpose of Brémaud's book and the goal is clearly attained. The presentation is clear, concise and self-contained … . In summary, the interested reader will find in Brémaud's book an invaluable reference … ." (Patrick Elandrin, Mathematical Reviews, Issue 2003 h) "This book discusses the Fourier and wavelet analysis froma mathematical point of view. … The book contains also a number of exercises which appear inline in the text. … This book is the only one, to my knowledge, which combines Fourier and wavelets analysis into a single mathematical formalism. This is a strong benefit which makes that I can highly recommend the book to readers with a strong mathematical background." (Jan De Kinder, Physicalia, Vol. 25 (2), 2003)

Long Description

Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicate that in spite of its long history and well-established applications, the field is still one of active research. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals. The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing

Review Text

From the reviews: MATHEMATICAL REVIEWS "While many books exits, dealing either with a'theorya? or a'applicationsa?, the interplay between signal processing and mathematics makes it difficult to find in a single volume the essentials of modern signal processing presented in a way which would be both rigorous for mathematicians and accessible for engineers. This challenge is precisely the purpose of Bremauda's book, and the goal is clearly attained. The presentation is clear, concise and self-contained, all the necessary concepts are put on a firm ground and proofs are worked out in great detaila? In summary, the interested reader will find in Bremauda's book an invaluable reference because of its coverage, scope and style, as well as of the unified treatment it offers of (signal processing oriented) Fourier and wavelet basics." "This book wants to bridge the gap between engineering and mathematics a? . What I liked most is the part on subband coding and the fact that bioorthogonal bases are discussed a? . A nice feature of the text is that it stimulates the reader to actively assimilate the material because the theorems (almost all the proofs are included) are interlaced with exercises challenging to immediately apply what has been explained." (Adhemar Bultheel, Belgian Mathematical Society Simon Stevin Bulletin, Vol. 11 (2), 2004) "Br'maud has prepared this graduate-level book to bridge the gap between the mathematical theory of Fourier analysis and the application of that theory to signal processing and other areas of communications engineering. a? To be readable by an engineering audience, the book includes a self-contained appendix on Lebesgue integration. a? Given the importance of the subject matter and the thoroughness of the treatment, this book is recommended for acquisition by any library that supports graduate programs in mathematics, physics or engineering." (D. Z. Spicer, CHOICE, December, 2002) "This volume is a treatise bringing together Fourier analysis and signal processing. a? The book is attractive due to the quality of the presentation and its conciseness. It is likely that engineers will gain mostly from it, but it is also of interest to applied mathematicians who will see developments in the repercussions of their discipline in the applications area." (A. Akutowicz, Zentralblatt MATH, Vol. 1009, 2003) "The interplay between signal processing and mathematics makes it difficult to find in a single volume the essentials of modern signal processing presented in a way which would be both rigorous for mathematicians and accessible for engineers. This challenge is precisely the purpose of Br'mauda's book and the goal is clearly attained. The presentation is clear, concise and self-contained a? . In summary, the interested reader will find in Br'mauda's book an invaluable reference a? ." (Patrick Elandrin, Mathematical Reviews, Issue 2003 h) "This book discusses the Fourier and wavelet analysis from a mathematical point of view. a? The book contains also a number of exercises which appear inline in the text. a? This book is the only one, to my knowledge, which combines Fourier and wavelets analysis into a single mathematical formalism. This is a strong benefit which makes that I can highly recommend the book to readers with a strong mathematical background." (Jan De Kinder, Physicalia, Vol. 25 (2), 2003)

Review Quote

From the reviews: MATHEMATICAL REVIEWS "While many books exits, dealing either with 'theory' or 'applications', the interplay between signal processing and mathematics makes it difficult to find in a single volume the essentials of modern signal processing presented in a way which would be both rigorous for mathematicians and accessible for engineers. This challenge is precisely the purpose of Bremaud's book, and the goal is clearly attained. The presentation is clear, concise and self-contained, all the necessary concepts are put on a firm ground and proofs are worked out in great detail...In summary, the interested reader will find in Bremaud's book an invaluable reference because of its coverage, scope and style, as well as of the unified treatment it offers of (signal processing oriented) Fourier and wavelet basics." "This book wants to bridge the gap between engineering and mathematics ... . What I liked most is the part on subband coding and the fact that bioorthogonal bases are discussed ... . A nice feature of the text is that it stimulates the reader to actively assimilate the material because the theorems (almost all the proofs are included) are interlaced with exercises challenging to immediately apply what has been explained." (Adhemar Bultheel, Belgian Mathematical Society Simon Stevin Bulletin, Vol. 11 (2), 2004) "Brmaud has prepared this graduate-level book to bridge the gap between the mathematical theory of Fourier analysis and the application of that theory to signal processing and other areas of communications engineering. ... To be readable by an engineering audience, the book includes a self-contained appendix on Lebesgue integration. ... Given the importance of the subject matter and the thoroughness of the treatment, this book is recommended for acquisition by any library that supports graduate programs in mathematics, physics or engineering." (D. Z. Spicer, CHOICE, December, 2002) "This volume is a treatise bringing together Fourier analysis and signal processing. ... The book is attractive due to the quality of the presentation and its conciseness. It is likely that engineers will gain mostly from it, but it is also of interest to applied mathematicians who will see developments in the repercussions of their discipline in the applications area." (A. Akutowicz, Zentralblatt MATH, Vol. 1009, 2003) "The interplay between signal processing and mathematics makes it difficult to find in a single volume the essentials of modern signal processing presented in a way which would be both rigorous for mathematicians and accessible for engineers. This challenge is precisely the purpose of Brmaud's book and the goal is clearly attained. The presentation is clear, concise and self-contained ... . In summary, the interested reader will find in Brmaud's book an invaluable reference ... ." (Patrick Elandrin, Mathematical Reviews, Issue 2003 h) "This book discusses the Fourier and wavelet analysis from a mathematical point of view. ... The book contains also a number of exercises which appear inline in the text. ... This book is the only one, to my knowledge, which combines Fourier and wavelets analysis into a single mathematical formalism. This is a strong benefit which makes that I can highly recommend the book to readers with a strong mathematical background." (Jan De Kinder, Physicalia, Vol. 25 (2), 2003)

Description for Sales People

Fourier analysis and its modern extension of wavelet analysis provides one of the most useful tools in many applied sciences. This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction to the subject, while emphasizing their uses in signal processing and other applications in communications engineering. An appendix provides the necessary background on Lebesgue integrals.

Details ISBN0387953388 Author Pierre Bremaud Short Title MATHEMATICAL PRINCIPLES OF SIG Language English ISBN-10 0387953388 ISBN-13 9780387953380 Media Book Format Hardcover Year 2002 Imprint Springer-Verlag New York Inc. Subtitle Fourier and Wavelet Analysis Place of Publication New York, NY Country of Publication United States Edition 1st Edition Description 2002 Pages 270 DOI 10.1007/b84556;10.1007/978-1-4757-3669-4 AU Release Date 2002-05-02 NZ Release Date 2002-05-02 US Release Date 2002-05-02 UK Release Date 2002-05-02 Publisher Springer-Verlag New York Inc. Publication Date 2002-05-02 Alternative 9781441929563 DEWEY 515.2433 Illustrations XII, 270 p. Audience Postgraduate, Research & Scholarly We've got this

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