表面计量中高斯滤波器的一种高精度实现算法  

An Accurate Algorithm of Gaussian Filter for Surface Metrology

作　　者：朴伟英[1] 袁怡宝[2] 孙涛[1] 许景波[3] 

机构地区：[1]哈尔滨工业大学机电工程学院,哈尔滨150001 [2]哈尔滨工业大学电气工程与自动化学院,哈尔滨150001 [3]哈尔滨理工大学测控技术与通信工程学院,哈尔滨150040

出　　处：《纳米技术与精密工程》2013年第6期546-550,共5页Nanotechnology and Precision Engineering

摘　　要：为了能高精度地实现表面计量中的高斯滤波,基于中心极限定理,提出了一个高斯滤波器的二阶巴特沃思滤波器逼近数学模型.用双线性变换法设计了IIR型数字高斯逼近滤波器.逼近精度可以通过调节逼近滤波器的级联阶数实现.在八阶级联的条件下,高斯逼近滤波器与高斯滤波器的幅度传输特性偏差大约只有0.25%.高斯逼近滤波器采用迭代算法实现,算法简便,易于实现.迭代算法通过合理选择初始值,可以有效抑制边缘效应.实验结果表明,在普通的双核计算机上提取11 200点数据的表面中线仅需约160 ms,在高精度地实现高斯滤波特性的同时,还有效地抑制了边缘效应.For the purpose of highly accurate implementation of Gaussian filter in surface metrology, an approximation model of Gaussian filter using twoorder Butterworth filter is proposed, which is based on the central limit theorem. An IIR type digital Gaussian approximation filter is designed by bilinear trans formation. The amplitude transmission characteristic of this filter can be controlled by adjusting the casca ding orders. The amplitude transmission deviation of approximation filter from Gaussian filter is about O. 25% under the condition of eight orders. The implementation of the digital Gaussian approximation fil ter is easy due to its simple iterative algorithm. By reasonably choosing the initial value, the iterative al gorithm can effectively suppress the end effect. Experimental results show that the extraction of 11 200 point data from a general dualcore computer only consumes 160 ms. Gaussian filtering is realized with high accuracy and the end effect is suppressed effectively as well.

关 键 词：表面计量 高斯滤波器 二阶巴特沃思滤波器 边缘效应 

分 类 号：TN713[电子电信—电路与系统]