Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 640789, 37 pages
Research Article

Minimum-Energy Multiwavelet Frames with Arbitrary Integer Dilation Factor

1Institute of Information and System Science, Beifang University of Nationalities, Yinchuan 750021, China
2School of Information Science & Technology, East China Normal University, Shanghai 200241, China

Received 15 May 2012; Accepted 26 June 2012

Academic Editor: Carlo Cattani

Copyright © 2012 Yongdong Huang 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.


In order to organically combine the minimum-energy frame with the significant properties of multiwavelets, minimum-energy multiwavelet frames with arbitrary integer dilation factor are studied. Firstly, we define the concept of minimum-energy multiwavelet frame with arbitrary dilation factor and present its equivalent characterizations. Secondly, some necessary conditions and sufficient conditions for minimum-energy multiwavelet frame are given. Thirdly, the decomposition and reconstruction formulas of minimum-energy multiwavelet frame with arbitrary integer dilation factor are deduced. Finally, we give several numerical examples based on B-spline functions.