Wavelets are an incredibly powerful tool, but if you can’t understand them, you can’t use them. Up till now, wavelets have been generally presented as a form of Applied Mathematics. Most of the literature still uses equations to introduce the subject.
Recently, however, there have been some excellent tutorials that explain wavelets to the “rest of us” in understandable and usable methods. An excellent place to begin is with the book “Conceptual Wavelets in Digital Signal Processing – An In-Depth Practical Approach for the Non-Mathematician. Some chapters are downloadable for free at www.conceptualwavelets.com. Chapter One (free) gives a completely understandable overview of wavelets and wavelet transforms. The last couple of chapters in the book introduce some key equations but only after the concepts are demonstrated so you can see the wavelets (and their associated equations) in action. The book has also received great reviews on amazon.com and by the American Library Association “Choice” awards.
Conventional “time domain” discrete data shows a series of data points at specific times, but not the frequency. Taking the Fourier Transform of these data points (“frequency domain data”) gives us specific frequencies but not the associated times. Wavelets can give us the time, the frequency, and even the general shape of the data. Adding these extra dimensions requires some familiarization and books such as Conceptual Wavelets provide that.
After acquiring a solid, intuitive understanding, the learner is ready to move on to the more conventional (and more mathematically oriented) resources. One excellent tutorial is the book “Wavelets and Wavelet Transforms” by Sydney Burrus of Rice University. Another is “The Wavelet Tutorial” in several parts by Robi Poliker of Rowan University.
An excellent Meta Site is found at www.wavelet.org. Another option is a comprehensive short course, “Wavelets: A Conceptual, Practical Approach” found at www.aticourses.com.