一种有效的分段光滑信号逼近方法

传统的Fourier变换，连续小波变换等方法在逼近具有分段光滑特性的非连续信号时，因 Gibbs现象的干扰会产生比较大的误差。本文提出了一种有效的分段光滑信号逼近方法。首先根据给定信号的分段点位置，构造一组标准正交分段多项式系，该函数系具有正交性，收敛性及再生性。然后将信号在该函数系下进行正交分解及重构，即可得到该信号的最佳平方逼近结果。数值实验表明，本文方法比传统的正交基具有更好的逼近结果。

An Efficient Approximation Method for Piecewise Smooth SignaI

The truncating Fourier and continue wavelet representation of a discontinuous piecewise smooth signal will introduce an unneglectable error which was named as the Gibbs phenomenon.In this paper,we proposed an effective piece-wise smooth signal approximation method.Firstly,a set of normal orthogonal piecewise polynomials was constructed ac-cording to the given positions of breaking points,and it has the properties of orthogonality,convergence and reproduction. Then the signal was orthogonal decomposed under this basis and the best square approximation result could be obtained using reconstruction.The numerical experiments show that our method have the higher accuracy approximation results than the other basis.