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Point Values and Normalization of Two-Direction Multi-wavelets and their Derivatives

KEINERT, FRITZ;KWON, SOON-GEOL

  • Received : 2015.10.31
  • Accepted : 2015.11.23
  • Published : 2015.12.23

Abstract

A two-direction multiscaling function ${\phi}$ satisfies a recursion relation that uses scaled and translated versions of both itself and its reverse. This offers a more general and flexible setting than standard one-direction wavelet theory. In this paper, we investigate how to find and normalize point values and derivative values of two-direction multiscaling and multiwavelet functions. Determination of point values is based on the eigenvalue approach. Normalization is based on normalizing conditions for the continuous moments of ${\phi}$. Examples for illustrating the general theory are given.

Keywords

two-direction multiwavelets;point values;normalization;multi-wavelet derivatives

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Acknowledgement

Supported by : Sunchon National University