基于正交正弦函数基的数值拟合方法

基于谐波分析理论，提出了基于正交正弦函数基的数值拟合方法，程序设计方法以一组具有广泛匹配能力的正弦函数（sinα1，sinα2，…，sinαn）作为拟合函数基，根据待拟合离散数据y，运用最小二乘法，计算出所有谐波的振幅（a0,a1,a2,…,an），采用正交化正弦函数基（sinα，Sin2α，…，sinnα）进行计算，从而使得系数的计算大为简化；预先分离出由两端点构成的直线组成的线性成分，采用纯非线性项进行拟合；以拟合数据覆盖半周期假定为基础，采用中心对称延拓方法完成稿子另半周期延拓，在同样项数下，本方法比傅立叶分析精度高，无须了解待拟合数值的更多特性，避免了经常发生的端点处出错现象，同时，由于它是基于最小二乘原理的，可用来拟合带权数据，对拟合非等精度观测数据尤其有用。

Numerical Method for Matching the Graphical Results by Resolving the Data into Orthogonal Sine Wavelets

A numerical method was presented for matching the graphical results by resolving the data into orthogonal sine wavelets. By using sine functions and the least square method, any data can be expressed. Usually, the computation for solving the coefficient vector (a0,a1,a2,…,an) is not easy. In order to simplify the computation, the orthogonal sine wavelets (sin α,sin 2α,…,sin nα) were used. In order to avoid computation failure at the two ends and realize smooth extension, the following measure was adopted before matching. ① Separate the linear and nonlinear formations; ② Smoothly extend to the whole cycle (0～2π). In order to achieve smooth extension, the linear and nonlinear formations were computed respectively, and the final value is the combination of the two parts. Compared with Fourier analysis method, this method has higher precision under the same items. It can avoid computation failure at two ends and achieve smooth extension in certain range. Because the method is based on the theory of the least square, it can be used to match the data which have different weight values.