有限区间内四阶样条小波的构造

4th Order Spline Wavelets on a Bounded Interval

1.
Department of Civil Engineering, Zhejiang University of Technology, Hangzhou 310014, P R China;
2.
Department of Civil Engineering, The University of Hong Kong, Hong Kong, P R China

摘要: 用有限区间上的截断4阶B样条,构造了有限区间上的4阶样条小波。这些小波由边界小波和内部小波组成,对某一尺度,它们组成了有限维的小波空间。于是,任何有限区间上的函数皆可表示为该区间上的尺度函数和小波函数的有限和,即小波级数,这克服了用无穷区间上的小波进行有限信号处理时,在边界上误差较大的不足,同时将该小波用于偏微分方程具有同样重要的意义。
- B样条 /
- 小波 /
- 有限区间
Abstract: The 4th order spline wavelets on a bounded interval are constructed by the 4th order truncated B-spline functions.These wavelets consist of inner and boundary wavelets.They are bases of wavelet space with finite dimensions.Any function on an interval will be expanded as the sum of finite items of the scaling functions and wavelets.It plays an important role for numerical analysis of partial differential equations,signal processes,and other similar problems.
- B-spline:wavelet /
- bounded interval /

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