【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.更多还原

【Abstract】 For the purpose of highly accurate implementation of Gaussian filter in surface metrology,an approximation model of Gaussian filter using two-order Butterworth filter is proposed,which is based on the central limit theorem.An ⅡR type digital Gaussian approximation filter is designed by bilinear transformation.The amplitude transmission characteristic of this filter can be controlled by adjusting the cascading orders.The amplitude transmission deviation of approximation filter from Gaussian filter is about 0.25%under the condition of eight orders.The implementation of the digital Gaussian approximation filter is easy due to its simple iterative algorithm.By reasonably choosing the initial value,the iterative algorithm can effectively suppress the end effect.Experimental results show that the extraction of 11 200 point data from a general dual-core computer only consumes 160 ms.Gaussian filtering is realized with high accuracy and the end effect is suppressed effectively as well.更多还原