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The V-system is a complete orthogonal system of functions defined on the interval [0, 1], generated by finite Legendre polynomials
and the dilation and translation of a function generator, which consists of a finite number of continuous and discontinuous
functions. The V-system has interesting properties, such as orthogonality, symmetry, completeness and short compact support.
It is shown in this paper that the V-system is essentially a special multi-wavelet basis. As a result, some basic properties
of the V-system are established through the well-developed theory of multi-wavelets. From this point of view, more other V-systems
are constructed. 相似文献
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三角域上一类正交函数系的构造 总被引:3,自引:0,他引:3
V系统是作者2005年构造的一类L2[0,1]空间上的正交完备函数系. κ次V系统由κ次分片多项式组成,具有多分辨特性,是Haar小波函数的推广.基于V系统的正交表达,可以对CAGD中常见的几何模型用有限项V-级数做到精确重构,完全消除Gibbs现象,这是有限项Fourier级数或连续小波级数不能做到的.针对多变量情形,给出了三角域上的κ次正交V系统的构造方法.三角域上的V系统的重要应用显现在对3D复杂几何图组的整体频谱分析上. 相似文献
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