CHARACTERIZATION OF ORTHONORMAL HIGH-ORDER BALANCED MULTIWAVELETS IN TERMS OF MOMENTS

Title & Authors
CHARACTERIZATION OF ORTHONORMAL HIGH-ORDER BALANCED MULTIWAVELETS IN TERMS OF MOMENTS
Kwon, Soon-Geol;

Abstract
In this paper, we derive a characterization of orthonormal balanced multiwavelets of order p in terms of the continuous moments of the multiscaling function $\small{\phi}$. As a result, the continuous moments satisfy the discrete polynomial preserving properties of order p (or degree p - 1) for orthonormal balanced multiwavelets. We derive polynomial reproduction formula of degree p - 1 in terms of continuous moments for orthonormal balanced multiwavelets of order p. Balancing of order p implies that the series of scaling functions with the discrete-time monomials as expansion coefficients is a polynomial of degree p - 1. We derive an algorithm for computing the polynomial of degree p - 1.
Keywords
multiwavelets;balanced multiwavelets;characterization of balancing condition;polynomial preservation/annihilation;moments;orthonormal bases;
Language
English
Cited by
1.
Point Values and Normalization of Two-Direction Multi-wavelets and their Derivatives,;;

Kyungpook mathematical journal, 2015. vol.55. 4, pp.1053-1067
1.
Two-direction multiwavelet moments, Applied Mathematics and Computation, 2012, 219, 8, 3530
2.
Intrinsic s-elementary Parseval frame multiwavelets in L2(Rd), Journal of Mathematical Analysis and Applications, 2010, 367, 2, 677
3.
Point Values and Normalization of Two-Direction Multi-wavelets and their Derivatives, Kyungpook mathematical journal, 2015, 55, 4, 1053
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