AN ALGORITHM FOR CONSTRUCTING ORTHOGONAL ARMLET MULTI-WAVELETS WITH MULTIPLICITY r AND DILATION FACTOR a

The purpose of this paper is to construct an orthogonal Armlet multi-wavelets with mul-tiplicity r and dilation factor a.Firstly,the definition of Armlets with dilation factor a is proposed in this paper.Based on the Two-scale Similar Transform（TST）,the notion of the Para-unitary A-scale Similar Transform（PAST） is introduced,and we also give the transform on the all two-scale matrix symbols of the multi-wavelets with dilation a.Then we show that the PAST and the transform on the matrix symbols of the multi-wavelets keep the orthogonality of the multi-wavelets system.We discuss the condition that multi-wavelets corresponding to the multi-scaling functions are all Armlets.After performing the PAST and the transform on the matrix symbols of the multi-wavelets,the multi-scaling function can be balanced and the corresponding multi-wavelets can be Armlets at the same time.The construction of Armlets with high order is also discussed.At last,by a given example,we can conclude that the algorithm is feasible and efficient.