加细函数的卷积构造算法

Journal of Applied Sciences ›› 2005, Vol. 23 ›› Issue (3): 305-307.

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The Construction of Refinable Function Based on Convolution

XIE Chang-zhen

Department of Mathematics, Shantou University, Shantou 515063, China

Received:2004-02-25 Revised:2004-07-08 Online:2005-05-31 Published:2005-05-31

Abstract

Abstract: Let φ₁, φ₂ be two refinable functions with the dilation factor a.A new method for constructing the refinable function based on the convolution of functions φ₁, φ₂ is presented.The properties such as periodicity and symmetry of the refinable function generated by the convolution of functioins φ₁, φ₂ are discussed.The B-spline function N_{i +j}(x) can be constracted by the convolution (N_i *N_j) (x) of two B-spline functions N_i(x) and N_j(x).Finally, two examples are given to illustrate how to use the method to construct refinable function.

Key words: refinable function, mask, convolution, scaling function

CLC Number:

O174.2

XIE Chang-zhen. The Construction of Refinable Function Based on Convolution[J]. Journal of Applied Sciences, 2005, 23(3): 305-307.

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The Construction of Refinable Function Based on Convolution

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