小波变换中基于正交多项式拟合的边界延拓

A boundary prolongation method based on orthogonal polynomial fitting in wavelet transform

为消除小波分解过程中的边界效应,给出了一种基于多项式拟合的边界延拓的新方式。该延拓方式首先对信号边界处的N个点进行M阶正交多项式拟合,将信号在边界处的低频变化规律用正交多项式表示出来,再利用得到的边界处的低频变化规律对信号进行延拓,从而减少了边界处引入的突变量。研究表明,N取30～50、M取2-4较为合适。进一步的实验表明,利用小波变换在该延拓方式下对信号进行基线校正时,边界效应得到了明显的改善。

A new boundary prolongation method based on orthogonal polynomial fitting was developed to remove the signal-end effect. In the prolongation method M-order orthogonal polynomial was fitted with N points for both ends firstly, the low-frequency function of signal＇s both ends was expressed by orthogonal polynomial, and then the signal was extended with function, so the imported high-frequency parts were lowered. Results showed that choosing N from 30-50 and M from 2-4 was proper. Further experiment showed that the signal-end effect was cut down clearly when the method mentioned above was used in baseline correction with wavelet transformation.