表面测量中高斯滤波中线的有理逼近实现

doi:10.7964/jdxbgxb201405020

吉林大学学报(工学版) ›› 2014, Vol. 44 ›› Issue (5): 1347-1352.doi: 10.7964/jdxbgxb201405020

表面测量中高斯滤波中线的有理逼近实现

许景波^{1, 2}, 袁怡宝³, 崔晓萌^{1, 2}, 郭欣^{1, 2}, 王升^{1, 2}

1.哈尔滨理工大学测控技术与通信工程学院, 哈尔滨 150080;
2.测控技术与仪器黑龙江省高校重点实验室,哈尔滨 150080;
3.哈尔滨工业大学自动化测试与控制系, 哈尔滨 150001

收稿日期:2013-02-15 出版日期:2014-09-01 发布日期:2014-09-01
作者简介:许景波(1973), 男, 副教授, 博士.研究方向:高斯滤波器理论与应用, 表面及圆度测量、滤波、评定技术.E-mail:hitxjb@126.com
基金资助:
黑龙江省教育厅科学技术研究项目(11541053).

Rational approximation implementation approach to determine Gaussian filtering mean line in surface roughness measurement

XU Jing-bo^1,2,YUAN Yi-bao³, CUI Xiao-meng^1,2, GUO Xin^1,2, WANG Sheng^1,2

1.College of Measure-control Technology & Communication Engineering, Harbin University of Science and Technology, Harbin 150080,China;
2. The Higher Educational Key Laboratory for Measuring & Control Technology and Instrumentations of Heilongjiang Province,Harbin 150080,China;
3. Department of Automation Measurement & Control,Harbin Institute of Technology, Harbin 150001,China

Received:2013-02-15 Online:2014-09-01 Published:2014-09-01

摘要/Abstract

摘要： 通过有理分式逼近提出了一种高斯滤波器实现方法。由有理分式模型,根据插值逼近方法确定相应系数,得出的有理逼近分式具有较高的逼近精度,与理论高斯滤波器最大幅度偏差为0.88%,截止频率内的幅度偏差小于2‰,是优化的逼近函数。由逼近分式S域左半平面极点建立逼近滤波器,由后向差分变换得出Z域模型,并应用零相移滤波技术得出了零相移数字滤波算法,满足了表面测量中对高斯滤波器实现方法的相位要求。应用这一方法,建立了表面轮廓中线,分离出表面粗糙度数据,整个算法只经一级零相移滤波就能完成,具有较高的计算效率,为表面测量高斯滤波的实现提供了一种新的方法。

关键词: 表面粗糙度测量, 高斯滤波器, 有理逼近, 零相移滤波

Abstract: Based on rational fraction approximation, an implementation approach for Gaussian filter is presented. The coefficients in the rational fraction are determined by interpolation approximation. The deduced rational fraction is an optimization approximation function with high approximation accuracy. The maximum amplitude deviation from theoretical Gaussian filter is 0.88% in the whole frequency domain, and is less than 2‰ in cutoff frequency. The approximation filter is designed by the poles in the left half plane of S domain, and the corresponding digital filter in Z domain is obtained by backward difference transformation. The corresponding zero-phase-shift digital filtering algorithm is achieved by zero-phase-shift technique that meets the requirements of surface measurement. This method is applied to surface roughness measurement to determine the mean line of surface profile and separate surface roughness. The algorithm has high computation efficiency because it can be implemented by only one stage zero-phase-shift filtering, and provides a new method for surface measurement.

Key words: surface roughness measurement, Gaussian filter, rational approximation, zero-phase-shift filtering

中图分类号:

TB92

许景波, 袁怡宝, 崔晓萌, 郭欣, 王升. 表面测量中高斯滤波中线的有理逼近实现[J]. 吉林大学学报(工学版), 2014, 44(5): 1347-1352.

XU Jing-bo,YUAN Yi-bao, CUI Xiao-meng, GUO Xin, WANG Sheng. Rational approximation implementation approach to determine Gaussian filtering mean line in surface roughness measurement[J]. 吉林大学学报(工学版), 2014, 44(5): 1347-1352.

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表面测量中高斯滤波中线的有理逼近实现

Rational approximation implementation approach to determine Gaussian filtering mean line in surface roughness measurement

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