| 摘要: |
| 着重研究基于{0,1}码变量表示的函数描述问题.首先,举例说明在多尺度分析观点下，信号处理中某些函数定义的新方法；进而提出“坐标分量分离方法”，并由此发现了平面区域上点集坐标数值的自相似结构；在揭示了如此自相似结构的基础上，构造了高维单纯形上的正交完备的二值函数系统；丰富与推广了Rademacher函数及Walsh函数的理论及应用. |
| 关键词: 多尺度分析，正交变换，坐标分量分离. |
| DOI： |
| 分类号: |
| 基金项目:本文研究得到国家自然科学基金资助. |
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| Multi-scale Expression of Data and Construction of a Kind of Orthogonal Transformation |
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DING Wei,QI Dong-xu
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| Abstract: |
| In this paper, the authors mainly discuss about how to express functions based on {0,1} code. At first, the examples are given to explain a new method in signal processing, in which functions are defined from the viewpoint of multi-scale analysis. Then the authors present “coordinate heft separate” method, discover self-similar structure of points set on plain area; based on this self-similar structure, construct orthogonal complete 2-value function system of high-dimension simplicity; enrich and extend the theory and application of Rademacher function and Walsh function. |
| Key words: Multi-scale analysis, orthogonal transformation, coordinate heft separate. |
