Free Ebook Wavelets Made Easy, by Yves Nievergelt
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Wavelets Made Easy, by Yves Nievergelt
Free Ebook Wavelets Made Easy, by Yves Nievergelt
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This book explains the nature and computation of mathematical wavelets, which provide a framework and methods for the analysis and the synthesis of signals, images, and other arrays of data. The material presented here addresses the au dience of engineers, financiers, scientists, and students looking for explanations of wavelets at the undergraduate level. It requires only a working knowledge or memories of a first course in linear algebra and calculus. The first part of the book answers the following two questions: What are wavelets? Wavelets extend Fourier analysis. How are wavelets computed? Fast transforms compute them. To show the practical significance of wavelets, the book also provides transitions into several applications: analysis (detection of crashes, edges, or other events), compression (reduction of storage), smoothing (attenuation of noise), and syn thesis (reconstruction after compression or other modification). Such applications include one-dimensional signals (sounds or other time-series), two-dimensional arrays (pictures or maps), and three-dimensional data (spatial diffusion). The ap plications demonstrated here do not constitute recipes for real implementations, but aim only at clarifying and strengthening the understanding of the mathematics of wavelets.
- Sales Rank: #701408 in Books
- Brand: Brand: Birkhäuser
- Published on: 2000-11-29
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x .81" w x 6.14" l, 1.23 pounds
- Binding: Hardcover
- 297 pages
- Used Book in Good Condition
Review
"The book explains in a nice way the nature and computation of mathematical wavelets, which provide a framework and methods for the analysis and synthesis of signals, images, and other arrays of data. A useful text for engineers, financiers, scientists, and students looking for explanation of wavelets."
―Journal of Information and Optimization Sciences
"Giving practice first and theory later, the author avoids discouraging readers whose main subject is not mathematics. The book is written in a very comprehensible and lively style. The text is essentially self-contained since many of the facts employed from analysis, linear algebra and functional analysis are stated and partially proved in the book."
―ZAA
From the Back Cover
This book, written at the level of a first course in calculus and linear algebra, offers a lucid and concise explanation of mathematical wavelets. Evolving from ten years of classroom use, its accessible presentation is designed for undergraduates in a variety of disciplines (computer science, engineering, mathematics, mathematical sciences) as well as for practising professionals in these areas.
This unique text starts the first chapter with a description of the key features and applications of wavelets, focusing on Haar's wavelets but using only high school mathematics. The next two chapters introduce one-, two-, and three-dimensional wavelets, with only the occasional use of matrix algebra.
The second part of this book provides the foundations of least squares approximation, the discrete Fourier transform, and Fourier series. The third part explains the Fourier transform and then demonstrates how to apply basic Fourier analysis to designing and analyzing mathematical wavelets. Particular attention is paid to Daubechies wavelets.
Numerous exercises, a bibliography, and a comprehensive index
combine to make this book an excellent text for the classroom as well as a valuable resource for self-study.
Most helpful customer reviews
43 of 52 people found the following review helpful.
Disappointing! Not at all Wavelets made "easy".
By A Customer
This book was quite a disappointment. It was not, as titled, Wavelets Made Easy. Despite the author's claims to the contrary, the book was not easy to read, largely due to the strongly professional mathematician's approach with unnecessarily obscure and involved notation. Later in the book the author adopted the mathematical formalism of proposition, proof, and lemma which is out of place in an introductory text aimed at non-mathematicians. Though the book treats a variety of applications of wavelets, little attention is paid to the background for these applications. Again, mathematical formalism takes precedence. Not recommended except perhaps for mathematicians, and for these, better texts are available.
9 of 10 people found the following review helpful.
The complex cannot be made easy, but it can be made clear
By Ian Kaplan
When I first saw this book, which is heavy on equations, I thought "wow, if this is wavelets made easy, I'd hate to see the hard version". And indeed this book is not light reading. But it is clear and there are plenty of examples. This book is far and away the best book on wavelets that I've found.
Wavelets are a complex topic. It would be unfair to think that you can pick up a book like this an read it like a popular science book. Reading a book like this takes concentration and effort. Implementing wavelet software is even more work, since some of the "in-place" algorithms are difficult. "Wavelets Made Easy" is a great foundation for anyone who wants to apply Haar wavelets for data analysis and filtering.
...
Nievergelt's coverage of Daubechies wavelets is not as
good as his coverage of Haar. He clearly explains the matrix
(linear algebra) view of Daubechies wavelets. The
coverage of edge effect issues is also good. However, as the
chapter proceeds, it fell apart, at least for me. There
appear to be errors in some of the algorithms. For example,
Nievergelt uses an average of the input time series over the
Daubechies wavelet. As far as I can see, this average cannot
be inverted to yield the original time series. Nievergelt's
Daubechies algorithm also does not seem to match algorithms
like the one published in Numerical Recipies.
So in summary, I'd say that this is a book that started out
well in the first few chapters but became less useful as
I worked through it.
4 of 5 people found the following review helpful.
Excellent.
By A Customer
The book is excellent in the sense that it has the right mixture of both theoretic and practical aspects. The portions on Fourier transforms also are apt for a newcomer to understand the theory. Of course, the first impression formed by seeing the title is that the matter inside would be plain english without any mathematics. However, the mathematics in the book has been kept elementary and in places where that wasn't possible, a thorough introduction has been provided.
The applications are explicitly mentioned and algorithms are written down clearly, instead of simply providing the theory and leaving the implementation for the student to figure out for himself. For the less mathematically oriented, the exercises at the end of each chapter will provide a good intuition to what will be encountered in the consequent sections. Once this book is read, other books that concentrate on specific aspects of wavelets will appear to be more understandable.
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