Gaussian Filter

A Gaussian filter is defined as a moving average of the surface profile with a Gaussian weighting function.  The weighting function S(x) is given by

Gaussian Weighting Function S(x)=exp(-pi*(x/alpha/lamda c)^2/alpha/lamda c

Where

x: position from the center of the weighting function

 Lamda c : nominal cutoff wavelength of the profile filter

 alpha = sqrt(ln2/pi) = 0.4697

The transmission characteristic at Lamda is 50% for a Gaussian Filter.  So the Gaussian filter enables one to use a single filter to obtain both the roughness and waviness. 

Reference

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