CHOICE Current Reviews For Academic Libraries
A publication of the Association of College and Research Libraries
A division of the American Library Association
October 2009 Vol. 47 No. 02, SCIENCE & TECHNOLOGY, Mathematics, 47-0918, QA403, MARC

"This book provides a gentle introduction to wavelets, a subject that is traditionally viewed as a very complex and highly mathematical research topic.

There are many works already published on wavelets, each highlighting different approaches to the subject matter and written with sophisticated mathematics. However, Fugal (founder and president, Space & Signals Technologies LLC) has chosen to provide readers with an intuitive approach to the subject with plenty of discussions and ample examples. The contents originally formed the bulk of materials the author used in a professional workshop introducing wavelets.

The book illustrates concepts of different wavelets, filtering operations, and practical usages with figures and simple MATLAB numerical examples to provide the reader with insight into the underlying behavior. Technical terms are often defined when first used. A special section at the end of the text shows a sampling of other wavelet tutorial materials available in books and articles and on the Web.

This work is ideal for readers who would like to have a high-level understanding of wavelets without getting bogged down by heavy mathematics.

Summing Up: Highly recommended. Two-year technical program students and practitioners."

--J. Y. Cheung, emeritus, University of Oklahoma

Richard Lyons: "Just What I've Been Looking For"
(5-star review on 9/2/09)

Note: Richard Lyons is the author of Amazon's best-selling book on Digital Signal Processing for the last 7 years. He is an associate editor of the IEEE Signal Processing Magazine and edits the magazine's "Tips and Tricks" column.

"Wanting to learn something about wavelets, I've searched the Internet for "wavelet tutorial" material. What I found was pretty much all the same thing---material written by (I presume) university professors consisting of page after page of equations. Such material is difficult for beginners to comprehend. My company library did have one textbook on wavelets, but that book was, sadly, similar to the Internet material. Lots of equations, but little explanation of why wavelet transforms are important, how do we use them, and when should we use them to analyze signals.

Then I encountered Fugal's "Conceptual Wavelets in Digital Signal Processing". Wow, what a relief. Mr. Fugal begins by explaining the complicated topic of wavelet transforms in a gentle, clear, and ultimately meaningful way. He doesn't overwhelm (suffocate) the reader with equations. In the first chapter he gives several straightforward signal analysis examples that show how wavelet transforms can be used to analyze certain signal characteristics in ways that are not possible with traditional digital signal processing (DSP). After reading those examples, I sat back for a moment and thought, "Ah ha. So that's what wavelets are, and how they can be used. Now I'm beginning to understand why people are interested in wavelets." That 'made my day'.

Fugal uses this neat technique called "Jargon Alert". That's where, when he introduces new terminology, he clearly defines the meanings of special terminology (new words) for the reader. What a great idea. I wish more technical authors would do the same.

Now to be honest, I've only read the first chapter of Fugal's book, but I just wanted to advertise how happy I am to finally begin to grasp the meaning, and value, of wavelet transforms. I look forward to learning more as I continue reading"

W. Kurt Dobson: "Finally, a book on wavelets that makes sense!"
(5-star review on 10/26/09)

Note: W. Kurt Dobson is the CEO of Sigma Technology Holdings and has created several startup companies. He has authored 52 patents and many articles in the high-technology field (primarily in the mathematics of signal processing for wireless communications). He has consulted for several prominent Venture Capital firms and was awarded the IEEE Engineer of the Year in 1998.

"I am a practicing signal processing engineer and have been working with wavelets since they were first invented. My applications have been in modulation (US Robotics), audio/image/video processing/compression/recognition, hybrid algorithms, predictive algorithms, flow prediction for a magnetically levitated artificial heart (spin-off from the University of Utah), x-ray florescence spectroscopy (XRF) detectors, and wavelet/neural network algorithms for gas chromatography.

The science of wavelets was invented by mathematicians -- so, all of the early books were written by mathematicians and extremely difficult to navigate. The power of these new wavelet methods beyond Fourier Transforms was obvious, but quite difficult to understand and use.

I have a significant collection of books on wavelets from most of the mathematicians. When I received Lee Fugal's book, I was very pleased to see something that was written from a practical point of view. I found the book easy to read and understand, and even with a pretty heavy background in wavelets, I learned a lot. Also as a MatLAB user, it was very nice to find useful code examples along with wavelet toolbox functions explained in detail.

Thank you Lee Fugal for taking all the time to write this book. Everything else on my bookshelf is gathering dust -- Lee's book, 'Conceptual Wavelets' is what I use every day in my work."

Behrouz Farhang-Boroujeny: "Wavelets made easy"
(5-star review on 8/14/09)

Note: Dr. Boroujeny is a full professor at the University of Utah. He is the author of 2 books: "Adaptive Filters: theory and applications", and "Signal Processing Techniques for Software Radios". He currently serves as associate editor of IEEE Transactions on Signal Processing.

"Lee Fugal has done a great job in presenting the often hard to understand (very mathematical) concepts of wavelet transforms. The book is understandable by any engineer with basic knowledge of signals and systems. The book provides an intuitive understanding of wavelets when applied to various applications, while keeping the mathematical derivations as little as possible. To mention a few examples, Lee has done great job in presenting the following concepts:

Superimposing wavelet filter points correctly on the "continuous" wavelet by using trailing zeros. For example, the Daubechies 4 wavelet filter is actually 6 points. (pp. 4, 114-117).

Showing the inter-relationships between the Discrete Fourier Transform (DFT/FFT), Continuous Wavelet Transform (CWT), the Undecimated Discrete Wavelet Transform (UDWT/RDWT), and the conventional (downsampled) DWT. Whether stretching the wavelet or shrinking the data they are all still basic comparisons of the data to the various analyzing waveforms. (pp. 121-140).

Demonstrating how highpass and lowpass Halfband Filters are the genesis of the Perfect Reconstruction Quadrature Mirror Filters and how they can be factored into orthogonal and bi-orthogonal wavelets filters (pp. 141-167).

Explaining the true power of wavelet properties by using "fake wavelets". Obtaining the "magic numbers" of the Daubechies filters using only these desired properties (pp. 169-184).

Demonstrating Alias Cancellation in both the time and frequency domains and then reconciling this process to the equations found in most other books (pp. 251-278).

Understanding the Wavelet Dilation Equation as a convolution that can build an approximation of the Wavelet Function. Showing why artifacts look like the chosen wavelet filter. (pp. 281-299)."

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