Edge effect elimination in the recursive implementation of Gaussian filters

Abstract

► The general approach to the design of recursive Gaussian filters to be used for separating the form, waviness and roughness components of the surface texture is discussed. ► Two ways of filter implementation were considered: series and parallel. ► In order to improve the numerical stability of the filter and reduce the rounding errors, the filter equations were described using the delta operator instead of the usually applied z operator. ► The proposed novel method of elimination of the edge effect involved selecting the initial values of the filter so that the root mean square deviation of the profile from the mean line could be minimized. ► The experiments show that the mean line and the mean surface were correctly determined for the whole area of the measured profile. The paper discusses a general methodology to the design of recursive Gaussian filters to be used for separating the form, waviness and roughness components of the surface texture. By selecting appropriate initial values for the filter difference equations, it is possible to eliminate the so-called edge effect and evaluate the whole registered profile. Two ways of filter implementation were considered: series and parallel. The incremental difference operator is applied in place of the usual shift operator z to describe the filter transfer function. This increases the accuracy of the representation of filter parameters and decreases the number of rounding errors. The results of the analysis were illustrated using 2D and 3D roughness profiles of a ball bearing race. The data show that the mean line and the mean surface were correctly determined for the whole area of the measured profile.