基于有理逼近的圆度测量信号高斯滤波方法

Gaussian filtering method for roundness measurement signals based on rational approximation

为了消除圆度测量中振动噪声等信号的影响,采用高斯滤波器作为测量信号处理滤波器,提出了高斯滤波器的一种逼近实现方法。在有理插值逼近基础上,建立了高斯滤波器的有理分式逼近模型。通过矩阵运算计算相应参数,得出了高斯滤波器的逼近滤波器。其与理想高斯滤波器的最大幅度偏差小于1%,截止波数内最大幅度偏差小于2‰。通过前向、后向差分变换,得出了零相移的数字滤波器。数字滤波算法只需一级零相移滤波,计算效率高。通过圆度测量信号的周期延拓,解决了数字滤波的边界效应问题。

To eliminate the influences of signals such as vibration noises of roundness measurement,a Gaussian filter is taken as the measurement signal processing filter,and a new implement method for Gaussian filter is provided.A rational fraction approximation model is established based on the rational interpolation approximation.The corresponding parameters are calculated by matrix operation and an approximation filter of Gaussian filter is concluded.The maximum amplitude error of the ideal Gaussian filter and its approximation filter is less than 1% and the maximum amplitude error in the cutoff undulations is less than 2‰.A zero phase shift digital filter is concluded through the forward difference transform and backward difference transform.The corresponding digital filtering algorithm has the simple structure of one cascade zero phase shift filtering and high computing efficiency.The edge effect of digital filters is solved through the cycle continuation of roundness measurement signals.