圆度测量中高斯滤波的逼近实现方法

Approximation Implementation Approach for Gaussian Filtering in Roundness Measurement

以B样条函数为基础，将约束条件引入变分原则，并结合小尺度参数高斯滤波器卷积特性，建立高斯滤波器的逼近滤波器。该滤波器与理论滤波器的幅度最大偏差小于1％，并具有零相移特性。在数字滤波算法中，包含两次零相移滤波和加权滤波循环计算，整个算法具有结构形式简单和计算效率较高的特点。根据圆度信号的周期封闭性，采用周期延拓法，消除数字滤波算法存在的边界效应问题。为圆度测量中高斯滤波器的实现提供了一种高精度、高效率的实现方法。

Gaussian filter acts as the filter for roundness signal processing and a new implementation approach for it is presented. Based on B-spline function, the variations principle with the constraint condition and the convolution characteristic of Gaussian filter of small scale parameter, the approximation filter of Ganssian filter is established. The amplitude characteristic deviation from the theory filter is less than 1% and has zero-phase-shift characteristic. The digital filtering algorithm consists of the zero-phase-shift filtering and the weighing filtering which loop two times in processing and has simply structure and high efficiency. The method of cycle continuation solves the edge effects of digital filtering by the periodicity of the roundness measurement signal. The approximation filter is both efficiency and accurate for the implementation of Gaussian filter in the application of roundness measurement.