r重a尺度正交平衡插值多小波的设计

The Study of The Orthogonal Balanced Interpolation Multi-wavelets with Multiplicity r and Dilation Factor a

研究了r重a尺度紧支撑正交平衡插值多小波,其中a≠r.所得的多尺度函数是正交平衡插值的,同时对应的多小波是正交插值的.首先,根据插值多小波的定义,利用取整函数这一技巧,得到关于r重a尺度插值条件的显式方程.其次,研究了a=2,r=3和a=2,r=4的紧支撑正交插值多小波,并构造了相应的实例.最后,利用Gram-Schmidt正交化方法讨论了a=3,r=4的正交插值多小波,并给出了算例.

The orthogonal balanced interpolation multi-wavelets with multiplicity r and dilation factor a axe discussed in this paper, where α≠ r. The obtained multi-scaling function is orthogonal, balanced, and interpolated. And the corresponding multi-wavelets is orthogonal and interpolated. Firstly, according to the definition of interpolation multi wavelets, the explicit equation of the interpolation condition of the multi-scaling function with multiplicity r and dilation factor a is obtained by using the round-off number function. Secondly, the orthogonal interpolation multi-wavelets with α=2, r = 3 and α = 2, r = 4 are studied, and the corresponding examples are constructed. Finally, the orthogonal interpolation multi-wavelets with α = 3, r = 4 is constructed by the Gram-Schmidt^s orthogonalization and the example is given.