数据的多尺度表达及一类正交变换的构造

Multi scale Expression of Data and Construction of a Kind of Orthogonal Transformation

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．

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.