Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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CHARACTERIZATION OF ORTHONORMAL HIGH-ORDER BALANCED MULTIWAVELETS IN TERMS OF MOMENTS

  • Kwon, Soon-Geol (DEPARTMENT OF MATHEMATICS EDUCATION SUNCHON NATIONAL UNIVERSITY)
  • Published : 2009.01.31
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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 $\phi$. 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.

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References

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