基于MATLAB的数字信号的代数插值

Algebraic interpolation of digital signals based on MATLAB

通过实验获得的测量信号往往是一系列离散的数据{xi,yi,i=1,2,3…,N,}它们反映了2个物理量之间的函数关系:y=f(x)。当要获知该函数关系中的未知测量值时,常要用到代数插值的方法。本文详细介绍了Lagrange插值,Newton插值和Hermite插值等插值方法的数学原理。通过在MATLAB操作平台上进行算法编程,对一组实验测量信号分别进行3种插值处理,最后比较这些插值方法的优劣。

A series of discrete experiment data {xi ,yi, i = 1,2,3,...N, } can be obtained through an experiment. They reflect a certain relationship in a form of function between a couple of physics parameters, y = f（x）. When some unknown values complying with this function are in need, interpolation will be frequently used. This paper exquisitely introduces three different interpolation methods： Lagrange Interpolation, Newton Interpolation, and Hermite Interpolation. An arithmetic program is realized on MATLAB, furthermore, some measurement signals are analyzed by means of three methods respectively, and the contrast of these methods is presented eventually.