TY  - JOUR
Y1  - 2015/06/15/
AV  - public
EP  - 3203
TI  - Enhanced B-Wavelets via Mixed, Composite Packets
KW  - B-wavelets
KW  -  filter characteristic
KW  -  wavelet packets
N2  - A modified B-wavelet construction with enhanced
filter characteristics is considered. The design comprises a superposition
of tessellated, integer dilated, ?sister? wavelet functions.
We here propose a cascaded filter-bank realisation of this wavelet
family together with some notable extensions. We prove that
modifications of low-order members exist in the multiresolution
subspace spanned by the half-translates of the original wavelets
and hence that the resulting modified wavelet coefficients can be
computed as convolutions of the undecimated original wavelet
coefficients. Finite impulse response filters are thus designed and
incorporated into a B-wavelet packet architecture such that the
mainlobe-to-sidelobe ratio of the resulting wavelet filter characteristic
is improved. This is achieved by designing the filters so
that zeros are introduced near to the maxima of the harmonics.
It is shown that the numbers of zeros can be balanced with the
length of the corresponding filters by controlling the ?modification
order?. Several constructions are presented. We prove that two
such constructions satisfy the perfect reconstruction property for
all orders. The resulting modified wavelets preserve many of the
properties of the original B-wavelets such as differentiability,
number of vanishing moments, symmetry, anti-symmetry, finite
support, and the existence of a closed form expression.
ID  - discovery1477576
IS  - 12
N1  - © 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
SP  - 3191
VL  - 63
A1  - Nelson, JDB
JF  - IEEE Transactions on Signal Processing
UR  - http://dx.doi.org/10.1109/TSP.2015.2419185
SN  - 1053-587X
ER  -