Abstract: A new implementation approach for Gaussian filter is presented . Based on the theory of B-spline function, the variational principle with constraint condition and the cascade characteristic of small-scale Gaussian filter, the approximation filter of Gaussian filter is obtained, and its maximum amplitude deviation from Gaussian filter is less than 1%, and it also has the zero-phase-shift characteristic. The algorithm for the approximation filter consists of the zero-phase-shift filtering and the weighing filtering, and only carries out two times of cycle. The algorithm teatures simple structure and high calculation efficiency. The approximation filter is also efficient and accurate for the implementation of Gaussian filter in the application of surface roughness measurement.

Key words: B-spline function, Gaussian filter, Mean line, Surface roughness