The World According to Wavelets: The Story of a Mathematical Technique in the Making, Second Edition

I was very happy reading this book. If you are familiar with the Fourier transform and don't know anything about wavelets, this is a book for you. Actually, the book has got two parts. In the first part you can learn basic things about Fourier transform (about its usage but also about its limits), what we need wavelets for and what the wavelets are. It is explained in very simple language without any formulas. The second part contains basic formulas related to the topics in the first part. I find that the link between these two parts is very good. Also, the author gives physical explanation whenever it's possible.If you are a specialist in the wavelets area, you probably know all these things but if you are new (like me!) you will find that this book is quite useful.

I am a math professor,-- and I often wondered if it wouldn't be possible to get some essential math ideas accross to almost anyone, --and with fewer equations. Ideas can be burried in symbolism;-- not always! But it does happen. Many of my colleagues tell me that if it were possible, then it would be done. The author of this lovely little book didn't take math courses (she says!). Professional mathematicians would most likely agree with me that she (the author) did in fact communicate the essential ideas behind wavelets (and did it well!);- and so she must have understood them!! Perhaps, anyone who really wants to, can penetrate a specialized math discipline;-- I would guess. Perhaps it is not even hard!? At least this book proves that it is not impossible to communicatethe beauty of math;--and its uses. Take a look at the book, and judge for yourself! It is fun too!

I thing this is a fabulous book. I would not have it as your only book on wavelets. I would read it first to get the big picture. Then get a more applicative or theoretical book as you detail reference. The author has a knack for explaining the basic ideas clearly and simply. Easy and entertaining to read but it isn't all fluff. You learn the sweeping and critical ideas and terminology. Has broad coverage. Get this book... and one other.

I have four books in my personal library (in addition to Hubbard's)that deal with wavelets: "Wavelet Analysis With Applications toImage Processing," by L. Prasad and S. S. Iyengar, "JointTime-Frequency Analysis," by Shie Qian and Dapang Chen,"AFriendly Guide to Wavelets," by Gerald Kaiser, and "Wavelets:an Analysis Tool," by M. Holschneider. While these are good"introductory" books for people already deeply familiar withorthogonal bases and mathematics in general, I think they areinadequate for someone wanting a truly fresh introduction to thesubject.Hubbard's book, though, was just what I'd been looking for.My wife bought it for me after dinner and a movie as we were browsingthe local bookstore in celebration of my 45th birthday. Hubbard wroteher book with the idea in mind that it is possible to describeaccurately and in principle many mathematical concepts that are oftenmade incomprehensible, or nearly so, through technical jargon. Thetechnical jargon is necessary, of course, among professionalmathematicians, but it need not, and should not, get in the way ofconveying the basic ideas and concepts in an introductory text. As ascience writer, Hubbard has done a masterful job of doing just that.This book gives me the intuitive, spatial understanding of waveletsthat I just could not find in the other books I listed above. Ithelps form the basis for understanding the more detailed books, and italso provides some interesting historical information. The book isdivided into two parts. Part 1, called "The World According toWavelets," is essentially devoid of any mathematical formulas.Instead of using mathematical symbols it uses imagery and verbalexplanation. This is likely to be somewhat frustrating for those whohave a mathematical background. Indeed, there were times when I foundmyself trying to figure out which of several possibilities Hubbard wastalking about. Mostly, part one introduces the reader to the idea ofseparating a signal into its Fourier components, and then it extendsthis basic idea - that signals can be expressed in different"languages" to the notion of the wavelet. Sprinkledthroughout part 1 are references to part 2, which is titled"Beyond Plain English." Unlike Part 1, Part 2 is full ofmathematical equations and terminology (though not at the same levelas the other books I mentioned above). The level of mathematics ismostly limited to what you'd expect to find in an undergraduate classin physics or mathematics. Even with the mathematical detail,Hubbard presents Part 2 with the same sensitivity toward theexplanation of new ideas as she uses in Part 1. The first chapter inpart 2 reviews the Fourier series and the Fourier transform. Thischapter is less than ten pages long, but it's one of the best shortsummaries I've seen. It does not skimp on the mathematical detailsbut it's clear and understandable to a fault.Chapter 2 talks aboutthe convergence of the Fourier series and has some nice (you've seenthem before, I suspect)

Mathematics texts, as a rule, tend to be organized along the lines of presenting postulates, theorems, proofs, and examples in a sequential order. There are symbols to decipher, equations to be analyzed, proofs to verify, etc. On the other hand, mathematics books written in plain prose tend to be too general (good enough to provide an overview but usually not enough detail to really learn the subject matter well). Ms. Hubbard's book is a rare one indeed-- one that provides the reader with an intuitively solid overview of wavelets followed by a more traditional and substantial mathematical presentation. A unique (and very effective) feature of Ms. Hubbard's book is the way she links the mathematical details relevant to her more general discussions (towards the beginning of the text) with boxed references. Also, another clever feature that the author employs is the use of underscore braces to nonintrusively insert comments to equations. For those readers who desire more mathematical rigor and detail, Ms. Hubbard provides a very comprehensive reference to other sources. Whether you're a student, mathematician, engineer, scientist, or just a beginner who wants to learn wavelets, this book is a definite must have! In the vast woodland of wavelets Ms. Hubbard provides you with a map of the forest as well as a description of the trees-- a very rare combination for a math book!