Some properties and construction of multiwavelets related to different symmetric centers

In this paper we are interested in discuss the symmetry property and construction of an m-band compactly supported orthonormal multiwavelets related to the filters with different symmetric centers. With the development of the several equivalent conditions on this type of symmetry in terms of filter sequences and polyphase matrices, we derive several necessary constraints on the number of symmetric filters of the system, which is crucial for the construction of multiwavelets associated with given multiscaling functions with different symmetry centers. Then, we show how to construct multiwavelets with desired symmetric property by matrix extensions. Finally, to illustrate our proposed general scheme, we give two examples in this paper.