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   -> Volume 1, Issue 7

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Author Message
Lora G. Weiss, Penn State Univ.

PostPosted: Fri Nov 29, 2002 12:01 pm    
Reply with quote



Randy K. Young
Applied Research Lab
Penn State Univ.
(814) 863-4499

Kluwer Academic Publishers
ISBN: 0-7923-9271-X

ordering info:

call: (617) 871-6300, ask for Customer Service, give ISBN
(0-7923-9271-X) & VISA...

or write: Kluwer Academic Publishers, PO Box 358, Accord Station,
Hingham, MA 02018, with ISBN and check/money order/etc.

%%%%%%%%%%%%%%%% CHAPTERS %%%%%%%%%%%%%%%%%%%%%%%%%%%%

Chapter 1: Introduction/Background
Chapter 2: The Wavelet Transform
Chapter 3: Practical Resolution, Gain, and Processing Structures
Chapter 4: Wavelet Theory Extensions and Ambiguity Functions
Chapter 5: Linear Systems Modelling with Wavelet Theory
Chapter 6: Wideband Scattering and Environmental Imaging

This book reviews, extends, and applies wavelet theory. The book
concentrates on the practical applications of wavelet theory. Many
pictures (86 of them) provide visualizations of wavelet theory and its
new extensions, as well as relationships to established concepts.
Wavelet theory is integrated with other general theories, including
linear systems theory and template matching or matched filtering.
These relationships create analogies with related research and
connections to practical applications. In addition, by demonstrating
the effectiveness of wavelet theory in these general applications, many
other specific applications may be improved. Temporal and spatial
signals and systems are considered. The properties of the wavelet
transform representation are sensitive to the chosen mother wavelet
(the kernel of the wavelet transform, analogous to the exponential
function in a Fourier transform). These properties are examined and
techniques for analyzing these sensitivities are presented.

Wavelet theory is extended with the new mother mapper operator that
efficiently maps a wavelet transform with respect to one mother wavelet
to a new wavelet transform with respect to a different mother wavelet.
The mother mapper efficiently calculates concise wavelet
representations that utilize multiple mother wavelets. The mother
mapper operator is also employed to efficiently compute "cross" wavelet
transforms or wideband cross ambiguity functions; these "cross"
operators extract the "commonalities" between two signals or systems to
determine the existence or structure of these commonalities.

An original system model, the space-time-varying (STV) wavelet
operator, is constructed with wavelet theory. As a special case, the
STV model can represent linear time-invariant (LTI) systems. LTI
systems are represented by the one-dimensional (1D)impulse response.
This one-dimensional impulse response is the center slice of the
two-dimensional (2D) STV representation. Both the LTI and STV models
can be made to also vary with time (leading to 2D and 3D models,

Physically, the STV wavelet operator creates an output by summing
weighted, scaled and translated replicas of the input; these weights
are the new system model. This is analogous to the LTI system model in
which the output is a weighted sum of translated replicas of the input
signal; with the weights being the LTI system model, the impulse
response. Obviously, time scaling is the additional feature of the STV
wavelet representation and is also the key to efficient representations
of the wideband reflection or scattering process and improved
estimation gains. By including the scaling operation as part of the
STV system model (that is independent of time), the estimation process
for this new system model can account for the linear time variation of
the system and, thus, have a valid model over a longer interval of
time. By estimating over a longer interval of time, more robust and
higher gain and resolution estimates can be formed. Finally, the
advantages of the new STV model are exploited to characterize or image
an environment.

Note from the editor: this book is available and the price is 67.50 US$.
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