A First Course in Wavelets with Fourier Analysis 2nd Edition by Albert Boggess (PDF)

Description

A comprehensive, self-contained treatment of Fourier analysis and wavelets—now in a new editionThrough expansive coverage and easy-to-follow explanations, A First Course in Wavelets with Fourier Analysis, Second Edition provides a self-contained mathematical treatment of Fourier analysis and wavelets, while uniquely presenting signal analysis applications and problems. Essential and fundamental ideas are presented in an effort to make the book accessible to a broad audience, and, in addition, their applications to signal processing are kept at an elementary level.The book begins with an introduction to vector spaces, inner product spaces, and other preliminary topics in analysis. Subsequent chapters feature:The development of a Fourier series, Fourier transform, and discrete Fourier analysisImproved sections devoted to continuous wavelets and two-dimensional waveletsThe analysis of Haar, Shannon, and linear spline waveletsThe general theory of multi-resolution analysisUpdated MATLAB code and expanded applications to signal processingThe construction, smoothness, and computation of Daubechies’ waveletsAdvanced topics such as wavelets in higher dimensions, decomposition and reconstruction, and wavelet transformApplications to signal processing are provided throughout the book, most involving the filtering and compression of signals from audio or video. Some of these applications are presented first in the context of Fourier analysis and are later explored in the chapters on wavelets. New exercises introduce additional applications, and complete proofs accompany the discussion of each presented theory. Extensive appendices outline more advanced proofs and partial solutions to exercises as well as updated MATLAB routines that supplement the presented examples.A First Course in Wavelets with Fourier Analysis, Second Edition is an excellent book for courses in mathematics and engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for mathematicians, signal processing engineers, and scientists who wish to learn about wavelet theory and Fourier analysis on an elementary level.

User’s Reviews

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

⭐This is a great introduction to wavelet theory for someone that has a strong calculus background and a basic understanding of analysis. I only skimmed the first four chapters which cover Fourier because I already had a strong Fourier background so I can only attest to the second half of the book.The motivation for wavelets via Haar decomposition is easy to follow and enlightening. Chapter 5 covers the mathematical nitty gritty and takes a bit more to work through but the proofs are annotated quite nicely. My only grief is chapter 7. It’s written in a way that makes you think the author didn’t feel like writing it but one of the technical editors said they should include it last minute. Overall, a great first read on wavelets. I would highly recommend for beginning grad students / upperclass undergrads in STEM disciplines.

⭐I have had 5 students use this book to learn about wavelets in independent study courses. The students range from very good undergraduates to beginning graduate students. They were all able to make progress on their own and work all of the problems in the book with some help from me. I think the book is a great introduction to the subject of wavelets and MRA’s. I will continue to use this book for individual students who are interested in learning about wavelets and relationships to Fourier transform methods.

⭐The Kindle version of this book is horrible. Some characters are replaced with squares, some formulas are hard to read with some font sizes. This is due to the fact that formulas are mixed images and text. Also, no page numbers.The content itself is okay. However, in my class we had to use supplementary texts because some concepts aren’t explained properly.

⭐the condition of the textbook was excellent. As expected, the book the one i needed and ordered. A satisfied customer

⭐as described

⭐Good

⭐Best book to learn from. I’m disappointed about the lack of discussion of Haar and Gabor wavelets, both of which found considerable application in engineering.

⭐Have seen all 5 star reviews above, I picked up this book from school’s library.After skim through it, I don’t think I can finish it.well, maybe it is “well” written, but what I am looking for is easy-to-understand, hands-on book which can give me examples of how to attack real problems. This book doesn’t provide any of that for me.Maybe because it is written by two math professors? and I don’t know why it receive all 5 star reviews.

⭐Ho0 trovato iol libro ottimo per la parte fi analisi di Fourier mentre per la parte di analisi in L2 è un tantino scarso

⭐

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