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Wavelet Theory and Its Applications (Paperback, Softcover reprint of the original 1st ed. 1993)
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Wavelet Theory and Its Applications (Paperback, Softcover reprint of the original 1st ed. 1993)
Series: The Springer International Series in Engineering and Computer Science, 189
Expected to ship within 10 - 15 working days
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This book reviews, extends, and applies wavelet theory,
concentrating on the practical applications. Many pictures provide
visualizations of wavelet theory and its new extentions, 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 also be made to vary with time (leading
to 2D and 3D models, respectively). The advantages of the new STV
model are expolited to characterize or image an environment.
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 weighed 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 long interval of time. By
estimating over a long interval of time, more robust and higher
gain and resolution estimates can be formed.
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