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 are discussed in this paper, where a ≠ 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 a = 2, r = 3 and a = 2, r = 4 are studied, and the corresponding examples are constructed. Finally, the orthogonal interpolation multi-wavelets with a = 3, r = 4 is constructed by the Gram-Schmidt's orthogonalization and the example is given.
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