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“Conceptual Wavelets in Digital Signal Processing”, however, is vastly different from
other books in that we use numerous examples, figures, and demonstrations to show
how to understand and use wavelets. This is a very complete and in-depth treatment of
the subject, but from an intuitive, conceptual point of view. We let you look at a few
key equations found in the more mathematically oriented texts—but only after the con-
cepts are demonstrated and understood.* Then if you desire further study from tradi-
tional texts, this allows you to recognize these equations and understand in advance
how they relate to the real world having actually seen them “in action”.
It has been gratifying to present the 3-day course “Wavelets: A Conceptual, Practical
Approach” at universities, corporations, and conference centers around the country for
the past few years. Much of this book is “built” on these slides and improved by the
comments and suggestions from the attendees. Those with little or no math back-
ground have expressed gratitude for being able to “see the elephant” enough to under-
stand it and use it’s power. Those with a strong mathematical background have ex-
pressed thanks for new insights and intuitive understanding that was not immediately
evident from the equations.
One of the principle contributions of wavelets has been to bring those academic fields
together to observe the “elephant” and to “satisfy the mind”. It is not surprising then
that you will find this particular pachyderm described in terms of wavelets, wavelet fil-
ters, wavelet transforms, filter banks, multirate systems, matched filtering, multiresolu-
tion analysis and so on.
This author’s background is in Digital Signal Processing (Fast Fourier Transforms, Digi-
tal Filtering, etc.). and the description of the elephant is no doubt biased toward time or
frequency representations of data. You will soon learn, however, that both the power
and the complexity of wavelets lies in the fact that they deal with (are localized in) both
time and frequency! It is especially important to understand that this dual
(time/frequency) nature adds literally another dimension to wavelets! Instead of the
data being shown as a function of time or as a function of frequency we now can look
at the data simultaneously in terms of time and frequency (or at least effective fre-
quency).
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