一类小波基函数的构造及其在测量数据处理中的应用探讨

Constructing a type of new wavelet function and discussing its application in surveying and mapping data processing

Shannon函数有很好的滤波性能,但向两端衰减速度缓慢;Gauss“窗”函数有很好的控制小波衰减的特性,但其低通滤波效果较差。根据这两个函数各自的优点构造了一类新的小波基函数,分别为满足低通的父小波和带通的一阶、二阶母小波,讨论了它们的正交性、完备性和紧支集性等性质,以GPS资料为例,分析其信号平滑和压缩效应、边缘效应和奇异点检测,得出一些有益的结论,为大地测量数据处理提供一种小波分析方法。

Shannon function is a function with good filter but bad local character, while Gauss window function with a better local character and wavelet attenuation controlling but bad low-pass. Shannon and Gauss functions are used to construct a new type of wavelet function in this paper, which are father wavelet meeting the need of low-pass and first-order and second-order mother wavelets meeting the need of band-pass. What is more, their character of orthogonality, completeness and compactly supported ability are discussed. Taking GPS data for example, the authors analyze its smoothing and compress effect, marginal effect and detect funny point to get some useful conclusion. It is obvious that it will be a significant method for GPS data processing.