Gaussian Filter

Gaussian filter is calculated by a direct convolution of the surface topography with a Gaussian weighting function [1][2][3].  The weighting function S(x,y) is given by

3 Dimensional Gaussian Weighting Function

Where

x and y are the positions from the center of the weighting function

 
Lambda x c and lambda y c is the cutoff wavelength at 50% attenuation ratio

beta=ln2/pi

 
The transmission characteristic is 50% for the Gaussian Filter.  So a single filter is customary to obtain both the roughness and waviness surfaces. 



The convolution is the most common approach for Guassian filter. For increasing the speed, the implementation by FFT was suggested by J. Raja and V. Radhakrishnan [4]. In the FFT approach, the spectrum of the original signal is computed by FFT algorithm. Then the calculated spectrum is modified in frequency domain by a weighting function according to the required filtering. The final filtered profile in time domain is calculated by the inverse FFT of the modified spectrum. The block diagram of this method for the Gaussian filter used in the system is illustrated in below.


Gaussian filter implemented using the FFT method



References

1. Surface Texture (Surface Roughness, Waviness, and Lay), an American National Standard, ASME B46.1-2002, New York, NY

2. K. J. Stout, P. J. Sullivan, W. P. Dong, E. Mainsah, N. Lou, T. Mathia and H. Zahouani, The Development of Methods for The Characterisation of Roughness in Three Dimensions, Report EUR 15178 EN. EC Brussels, 1993

3. L. Blunt and X. Jiang, Advanced Techniques for Assessment Surface Topography, 1st edition, London Penton Press, 2003, ISBN 1903996112  

4. J. Raja and V. Radhakrishnan, Filtering of Surface Profiles Using Fast Fourier Transform, Int. of J. mach. Tool. Des. Res., Vol. 19, 133-141, 1979