Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2011; 48(6): 1157-1167

Printed November 1, 2011

https://doi.org/10.4134/BKMS.2011.48.6.1157

Copyright © The Korean Mathematical Society.

Approximation and balancing orders for totally interpolating biorthogonal multiwavelet systems

Youngwoo Choi and Jaewon Jung

Ajou University, Ajou University

Abstract

We consider totally interpolating biorthogonal multiwavelet systems with finite impulse response two-band multifilter banks, and study balancing order conditions of such systems. Based on FIR and interpolating properties, we show that approximation order condition is completely equivalent to balancing order condition. Consequently, a prefiltering can be avoided if a totally interpolating biorthogonal multiwavelet system satisfies suitable approximation order conditions. An example with approximation order $4$ is provided to illustrate the result.

Keywords: multiwavelets, interpolating, balancing order

MSC numbers: Primary 42C40; Secondary 65T60