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Books > Science & Mathematics > Physics > Classical mechanics > Sound, vibration & waves (acoustics)
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A First Course on Wavelets (Hardcover, New)
Loot Price: R5,871
Discovery Miles 58 710
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A First Course on Wavelets (Hardcover, New)
Series: Studies in Advanced Mathematics
Expected to ship within 12 - 19 working days
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Wavelet theory had its origin in quantum field theory, signal
analysis, and function space theory. In these areas wavelet-like
algorithms replace the classical Fourier-type expansion of a
function. This unique new book is an excellent introduction to the
basic properties of wavelets, from background math to powerful
applications. The authors provide elementary methods for
constructing wavelets, and illustrate several new classes of
wavelets. The text begins with a description of local sine and
cosine bases that have been shown to be very effective in
applications. Very little mathematical background is needed to
follow this material. A complete treatment of band-limited wavelets
follows. These are characterized by some elementary equations,
allowing the authors to introduce many new wavelets. Next, the idea
of multiresolution analysis (MRA) is developed, and the authors
include simplified presentations of previous studies, particularly
for compactly supported wavelets. Some of the topics treated
include: Several bases generated by a single function via
translations and dilations Multiresolution analysis, compactly
supported wavelets, and spline wavelets Band-limited wavelets
Unconditionality of wavelet bases Characterizations of many of the
principal objects in the theory of wavelets, such as low-pass
filters and scaling functions The authors also present the basic
philosophy that all orthonormal wavelets are completely
characterized by two simple equations, and that most properties and
constructions of wavelets can be developed using these two
equations. Material related to applications is provided, and
constructions of splines wavelets are presented. Mathematicians,
engineers, physicists, and anyone with a mathematical background
will find this to be an important text for furthering their studies
on wavelets.
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