Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 757039, 18 pages
doi:10.1155/2010/757039
Research Article

Regular and Irregular Sampling Theorem for Multiwavelet Subspaces

Liu Zhanwei,1 Hu Guoen,2 and Wu Guochang3

1School of Information Engineering, Zhengzhou University, Zhengzhou 450001, China
2Department of Applied Mathematics, Zhengzhou Information Science and Technology Institute, Zhengzhou 450002, China
3College of Information, Henan University of Finance and Economics, Zhengzhou 450002, China

Received 5 March 2010; Accepted 26 July 2010

Academic Editor: Victoria Vampa

Copyright © 2010 Liu Zhanwei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the sampling theorem for frames in multiwavelet subspaces. Firstly, a sufficient condition under which the regular sampling theorem holds is established. Then, notice that irregular sampling is also useful in practice; we consider the general cases of the irregular sampling and establish a general irregular sampling theorem for multiwavelet subspaces. Finally, using this generalized irregular sampling theorem, we obtain an estimate for the perturbations of regular sampling in shift-invariant spaces.