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## ‣ Construction of M - Band bandlimited wavelets for orthogonal decomposition

Fonte: Rochester Instituto de Tecnologia
Publicador: Rochester Instituto de Tecnologia

Tipo: Tese de Doutorado

Português

Relevância na Pesquisa

47.826187%

#Bandlimits#Electrical engineering#Wavelet#QA403.3 .T46 2003#Wavelets (Mathematics)#Signal processing--Mathematics

While bandlimited wavelets and associated IIR filters have shown serious potential in
areas of pattern recognition and communications, the dyadic Meyer wavelet is the only
known approach to construct bandlimited orthogonal decomposition. The sine scaling
function and wavelet are a special case of the Meyer. Previous works have proposed a M
- Band extension of the Meyer wavelet without solving the problem. One key
contribution of this thesis is the derivation of the correct bandlimits for the scaling
function and wavelets to guarantee an orthogonal basis. In addition, the actual
construction of the wavelets based upon these bandlimits is developed. A composite
wavelet will be derived based on the M scale relationships from which we will extract the
wavelet functions. A proper solution to this task is proposed which will generate
associated filters with the knowledge of the scaling function and the constraints for Mband
orthogonality.

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## ‣ Matched wavelet construction and its application to target detection

Fonte: Rochester Instituto de Tecnologia
Publicador: Rochester Instituto de Tecnologia

Tipo: Dissertação

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Relevância na Pesquisa

37.80936%

#Imaging science#TA1632 .C4625 1995#Signal detection--Digital techniques#Image processing--Digital techniques#Wavelets (Mathematics)

This dissertation develops a new wavelet design technique that produces a wavelet that matches a desired
signal in the least squares sense. The Wavelet Transform has become very popular in signal and image
processing over the last 6 years because it is a linear transform with an infinite number of possible basis
functions that provides localization in both time (space) and frequency (spatial frequency).
The Wavelet Transform is very similar to the matched filter problem, where the wavelet acts as a zero
mean matched filter. In pattern recognition applications where the output of the Wavelet Transform is
to be maximized, it is necessary to use wavelets that are specifically matched to the signal of interest.
Most current wavelet design techniques, however, do not design the wavelet directly, but rather, build a
composite wavelet from a library of previously designed wavelets, modify the bases in an existing multiresolution
analysis or design a multiresolution analysis that is generated by a scaling function which
has a specific corresponding wavelet. In this dissertation, an algorithm for finding both symmetric and
asymmetric matched wavelets is developed. It will be shown that under certain conditions, the matched
wavelets generate an orthonormal basis of the Hilbert space containing all finite energy signals. The
matched orthonormal wavelets give rise to a pair of Quadrature Mirror Filters (QMF) that can be used
in the fast Discrete Wavelet Transform. It will also be shown that as the conditions are relaxed...

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