HOW (AND WHY) THIS BOOK IS DIFFERENT Wavelets are incredibly powerful, but if you can t understand them, you can t use them or worse, blissfully misuse them! CONCEPTUAL WAVELETS is unique as a complete, in-depth treatment of the subject but from an intuitive, conceptual point of view. In this book we stress informed use of wavelets and leave the mathematically rigorous proofs to other texts. We do look at some key equations (at a high-school algebra level)--but only after the concepts are demonstrated so you can see the wavelets (and their associated equations) in action. FEATURES --More than 400 illustrations, figures, graphics, tables, visual comparisons, etc. are provided to simplify and clarify the concepts. All of these visual aids are explained in detail using familiar language and terminology. --Specific properties and suggested applications of the various wavelets and wavelet transforms are clearly shown using step-by-step walk-throughs, demonstrations, case studies, examples, and short tutorials. --Numerous Jargon Alerts and other Plain English explanations bring you up to speed with the current wavelet nomenclature. --References to some of the best traditional (and non-traditional) texts, papers, and websites are given for further application-specific study. We also familiarize you with wavelet software and show you how to read the results of their various displays. --Both the strengths and the weaknesses of the various wavelet transforms are revealed to help you avoid common traps and pitfalls (such as loss of alias cancellation). --This book clearly explains how to add (literally) another dimension to your signal processing capability by using wavelets to simultaneously determine the frequency, the time, and even the general shape of events and/or anomalies in your data. The last acknowledgment is to you, the reader, for having the courage to embark on a journey that you probably have heard was difficult but that has the promise of rich rewards as you add the power of wavelet processing to your professional repertoire. John A. Shedd in 1928 wrote A ship in harbor is safe but that is not what ships are built for . As you leave the safe harbor of conventional Digital Signal Processing to sail upon the wavelets, may you find the treasures you seek. Welcome Aboard!
Author(s): D. Lee Fugal
Year: 2009
Language: English
Pages: 374
1 - Preview of Wavelets, Wavelet Filters, and Wavelet Transforms......Page 16
1.1 - What is a Wavelet?......Page 17
2 - The Continuous Wavelet Transform (CWT) Step-by-Step......Page 46
3 - The Undecimated Discrete Wavelet Transform (UDWT) Step-by-Step......Page 58
4 - The Conventional (Decimated) DWT Step-by-Step......Page 74
5 - Obtaining Discrete Wavelet Filters from "Crude" Wavelet Equations......Page 94
6 - Obtaining Variable Length Filters from Basis Fixed Length Filters......Page 116
7 - Comparison of the Major Types of Wavelet Transforms......Page 136
8 - PRQMF and Halfband Filters and How They Are Related......Page 156
9 - Highlighting Additional Properties by Using "Fake" Wavelets......Page 184
10 - Specific Properties and Applications of Wavelet Families......Page 202
11 - Case Studies of Wavelet Applications......Page 236
12 - Alias Cancellation in the Conventional (Decimated) DWT......Page 266
13 - Relating Key Equations to Conceptual Understanding......Page 296
Appendix A - Relating Wavelet Transforms to Fourier Transforms
......Page 318
Appendix B - Heisenberg Boxes and the Heisenberg Uncertainly Principle......Page 332
Appendix C - Reprint of Article "Wavelets: Beyond Comparison"......Page 338
Appendix D - Further Resources for the Study of Wavelets......Page 348
Index......Page 358