Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 128294, 26 pages
doi:10.1155/2010/128294
Research Article

Characterizations of Tight Frame Wavelets with Special Dilation Matrices

Huang Yongdong1 and Zhu Fengjuan2

1Institute of Information and System Science, Beifang University of Nationalities, Yinchuan 750021, China
2Department of Foundation, Beifang University of Nationalities, Yinchuan 750021, China

Received 22 May 2010; Revised 29 October 2010; Accepted 25 November 2010

Academic Editor: Angelo Luongo

Copyright © 2010 Huang Yongdong and Zhu Fengjuan. 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 all generalized low-pass filters and tight frame wavelets with special dilation matrix 𝑀 (M-TFW), where M satisfies 𝑀 𝑑 = 2 𝐼 𝑑 and generates the checkerboard lattice. Firstly, we study the pseudoscaling function, generalized low-pass filters and multiresolution analysis tight frame wavelets with dilation matrix 𝑀 (MRA M-TFW), and also give some important characterizations about them. Then, we characterize all M-TFW by showing precisely their corresponding dimension functions which are nonnegative integer valued. Finally, we also show that an M-TFW arises from our MRA construction if and only if the dimension of a particular linear space is either zero or one.