Wavelets Made Easy [Hardcover]

Yves Nievergelt (Author)

Book Description

Publication Date: April 28, 1999 | ISBN-10: 0817640614 | ISBN-13: 978-0817640613 | Edition: Corrected

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.

Editorial Reviews

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.

Product Details

• Hardcover: 297 pages
• Publisher: Birkhäuser; Corrected edition (April 28, 1999)
• Language: English
• ISBN-10: 0817640614
• ISBN-13: 978-0817640613
• Product Dimensions: 9.5 x 6.4 x 0.8 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 3.6 out of 5 stars  See all reviews (9 customer reviews)
• Amazon Best Sellers Rank: #1,126,862 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

42 of 50 people found the following review helpful:

1.0 out of 5 stars Disappointing! Not at all Wavelets made "easy"., August 17, 1999

By A Customer

This review is from: Wavelets Made Easy (Hardcover)

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:

3.0 out of 5 stars The complex cannot be made easy, but it can be made clear, February 20, 2001

By 

Ian Kaplan (Santa Fe, New Mexico) - See all my reviews

This review is from: Wavelets Made Easy (Hardcover)

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:

5.0 out of 5 stars Finally, Wavelets are explained !!, February 7, 2005

By 

Michael Roper "fearsome coder" (North Little Rock, AR USA) - See all my reviews
(REAL NAME)   

Amazon Verified Purchase

This review is from: Wavelets Made Easy (Hardcover)

Thank Yves.

I enrolled in an online graduate course for wavelets and could not understand the book and the professor liked to give very few problems with very little help to ensure that he would not have to grade many problems and to ensure that we would not understand the material well. I searched the web and checked out about 10 wavelet book in the library and still I could not get a clue on wavelets in how they actually worked and the mathematics behind them.

But, ... with Yves' book, ... it does still take some mental effort, but his book is readable and the homework assignments are doable without an instructor leading you or mis-leading you as the case may be.

Wavelets applications fascinate me and without Yves book, I still wouldn't have a clue.