Totally interpolating biorthogonal multiwavelet systems with approximation order

Abstract

In this article, compactly supported totally interpolating biorthogonal multiwavelet systems are studied. Necessary and sufficient conditions for such systems to have given approximation orders are stated in simple equations. It is shown that the shorter nontrivial filter component that has the minimum possible length for a given approximation order is uniquely determined up to a discrete parameter. Among systems with such property, we provide all totally interpolating biorthogonal stable multiwavelet systems of approximation orders 2 and 3 with minimal total length whose scaling vectors have minimal lengths as well.

Keywords:

• multiscaling functions
• multiwavelets
• interpolating

AMS Subject Classifications::

• Primary 42C40
• Secondary 65T60

Acknowledgements

This article was completed with the Ajou University research fellowship of 2011.