Sampling bases for the signal space composed of spline functions
Sampling bases for the signal space composed of spline functions
复制标题
由样条函数组成的信号空间的采样基
DOI：
10.1002/ecjc.4430720609
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发表时间：
1989
期刊：
影响因子：
--
通讯作者：
R. Mori
中科院分区：
文献类型：
--
作者：
M. Kamada;K. Toraichi;R. Mori
样条函数是光滑的分段多项式，几乎无振荡，它所构成的信号空间在插值和信号逼近问题中引起了人们的关注。为了充分利用这样的信号空间，必须对其属性进行清楚的描述。作为解决这一问题的一般方法，在信号空间中推导采样基是有效的。在此之前，作者讨论了样条函数组成的信号空间，并导出了次数限制为2的情况下的采样基。本文将结果推广到任意阶。抽样基地的例子示出的第二和第三度的实际情况。本文导出的采样基提供了由任意次样条函数组成的信号空间的基本特征。
The signal space composed of spline functions, which are smooth piecewise polynomials and almost free from oscillation, has attracted attention in the problems of interpolation and signal approximation. to make full use of such a signal space, there must be available a clear description of its properties. As a general approach to this problem, it is effective to derive the sampling basis in the signal space. Previously, the authors discussed the signal space composed of spline functions, and derived the sampling basis for the case where the degree is restricted to two. This paper extends the result to the arbitrary degree. Exam ples of sampling bases are shown for the practical cases of the second and the third degrees. the sampling basis derived in this paper provides the basic characterization of the signal space composed of spline functions of arbitrary degree.