Introduction to Wavelets and Wavelet Transforms: A Primer 1st Edition by C. Burrus (PDF)

Description

Advanced undergraduate and beginning graduate students, faculty, researchers and practitioners in signal processing, telecommunications, and computer science, and applied mathematics. It assumes a background of Fourier series and transforms and of linear algebra and matrix methods.This primer presents a well balanced blend of the mathematical theory underlying wavelet techniques and a discussion that gives insight into why wavelets are successful in signal analysis, compression, dection, numerical analysis, and a wide variety of other theoretical and practical applications. It fills a gap in the existing wavelet literature with its unified view of expansions of signals into bases and frames, as well as the use of filter banks as descriptions and algorithms.

User’s Reviews

Editorial Reviews: From the Publisher This text is the only source available that presents a unified view of the theory and applications of discrete and continuous- time signals. It also is the only text to present the mathematical point of view, as well as the discrete-time signal processing perspective. It brings together information previously available only in research papers, in engineering and applied mathematics. From the Back Cover This book is the only source available that presents a unified view of the theory and applications of discrete and continuous- time signals. This is the only book to present the mathematical point of view, as well as the discrete-time signal processing perspective. It brings together information previously available only in research papers, in engineering and applied mathematics. Appropriate for researchers and practitioners in signal processing and applied mathematics.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is an odd textbook. It’s rigorous in nature but doesn’t provide many proofs or intuition. It seems almost like a reference for people who understand wavelet theory and need something to refresh their memory. If you are not a graduate student using this textbook in a class I would recommend “A First Course in Wavelets with Fourier Analysis” by Boggess and Narcowich. It covers much of the same material while presenting more intuition and proofs for almost all of the claims.In summary, this book is a good second or third read but the term “Introduction” in the title could be replaced with “Mathematical Theory of.”

⭐The book seems to be written with an assumption that the reader has plenty of background in the relevant mathematics. I would NOT recommend this book for the novice; it’s more for those already familiar with the general area but want to get more ‘in depth’. It examples are sprinkled with math notations that may not be familiar to most. For the beginner, I would recommend other wavelet books that are written from an ENGINEERING viewpoint rather than a mathematician’s viewpoint.Overall, well-written (for its intended audience).

⭐I believe this a well-written and somewhat rigorous overview of wavelets. I must add that it still somewhat of a mystery of me how one chooses the wavelet basis for a particular physical application!

⭐I have examined most of the popluar books printed on the subject of Wavelet Analysis and this is the best book for those who want to understand what a wavelet is, where is comes from, and how is it is useful for performing Time Scale signal analysis. I strongly suggest starting with this book.

⭐The authors lay out the mathematical preliminaries needed for understanding wavelets and their role in signal processing in this 268-page book, and do this at a level that is appropriate for advanced undergraduates majoring in mathematics, the physical sciences, or engineering. This book also provides a fairly detailed explanation of the closure of function spaces spanned by wavelets and scaling functions. The authors engage the reader at an intuitive level, while leaving the more detailed derivations to the appendices at the end of the book.The main criticism that I would levy at this book is that many of its derivations and proofs are lacking in rigor–to the point where the reader may remain unconvinced of their validity! This lack of rigor is particularly evident in the cases involving the Fourier transform, which is treated in a manner that is shockingly cavalier! I would recommend reading this volume along a book that provides a good treatment of Fourier transforms, such as Bracewell’s

⭐. I would have also preferred for more of these derivations to have been embedded in the main part of the text instead of being relegated to the appendices at the back of the book. For me, these derivations would have been easier to follow if they appeared when the need for them first arose.Of the introductory books that I have read on wavelets thus far, however, I find this one to offer to best place to first learn about these concepts. This book is particularly valuable as an orientation for the reader who wishes to proceed to Ingrid Daubechies’ seminal work

⭐. One particularly useful section is where the coefficients of the Daubechies D4 wavelet are calculated (p.66).

⭐This is the best book on wavelet I have read so far. It is a very good “self study” book. It gives both the signal processing and functional basis views which is necessary to appreciate and understand the wavelet techniques. On of the best thing is the authors present mathematical preliminaries in an understandable manner, ideal for engineers. This should be the first place to start the wavelet tour.

⭐If you studied Mathematical Physics or if you like the mathematical approach that physicists used to write their papers and lectures, it ‘s a pleasant book to understand wavelets.

⭐Before reading this book, read the wavelet chapter fromDigital Image Processing (2nd Edition)by Rafael C. Gonzalez, Richard E. Woods

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