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.
We study all generalized low-pass filters and tight frame wavelets with special dilation
matrix (M-TFW), where M satisfies and generates the checkerboard lattice.
Firstly, we study the pseudoscaling function, generalized low-pass filters and multiresolution analysis
tight frame wavelets with dilation matrix (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.