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