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   -> Volume 6, Issue 7


Preprint: Preprints on the construction of multiwavelets
 
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Qingtang Jiang (qjiang@haar.math.nus.sg)
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PostPosted: Sun Jul 06, 1997 4:47 pm    
Subject: Preprint: Preprints on the construction of multiwavelets
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#3 Preprint: Preprints on the construction of multiwavelets

1) Title: Orthogonal multiwavelets with optimum time-frequency
resolution

Author: Qingtang Jiang
Department of Mathematics
National University of Singapore
Singapore 119260
E-mail:qjiang@haar.math.nus.sg

Abstract:
A procedure to design orthogonal multiwavelets with better
time-frequency resolution is introduced. Formulas to compute the
time-durations and the frequency-bandwidths of scaling functions and
multiwavelets are obtained. For $N$, $2le Nle 6$, parameter
expressions of the multifilter banks which generate
symmetric/antisymmetric scaling functions and multiwavelets supported
in $[0, N]$ are presented. The orthogonal multiwavelets with optimum
time-frequency resolution are constructed and the optimal multifilter
banks are provided.

2) Title: On the design of multifilter banks and
orthogonal multiwavelet bases

Author: Qingtang Jiang

Abstract:
Several forms of the parameter expressions for the orthogonal
multifilter banks are presented. The explicit expressions for a group
of the orthogonal multifilter banks which generate
symmetric/antisymmetric scaling functions and orthogonal multiwavelets
are obtained. The balanced multiwavelet, multiwavelet pairs which are
more suitable for image processing are discussed. Based on the
parameter expressions for the orthogonal multifilter banks, the
balanced multiwavelets, multiwavelet pairs with better time-frequency
localization property are constructed and some optimal multifilter
banks are provided.

3) Title: On the construction of biorthogonal multiwavelet bases

Author: Qingtang Jiang

Abstract:
Biorthogonality of a set of compactly supported vector-valued
functions is discussed. Several forms of the parameter expressions for
a group of the $M$-channel biorthogonal multifilter banks are
presented. The symmetry of the scaling functions and biorthogonal
multiwavelets of dilation factor $M$ is considered. The explicit
expressions for a group of the $M$-channel biorthogonal multifilter
banks which generate symmetric/antisymmetric scaling functions and
biorthogonal multiwavelets of dilation factor $M$ are obtained. Based
on the parameter expressions of the biorthogonal multifilter banks and
the formulas to compute the energy moments of the scaling functions
and biorthogonal multiwavelets, the balanced biorthogonal
multiwavelets with better time-frequency resolution are constructed
and some optimal multifilter banks are provided.
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