# gaussian filter

http://www.reproducibility.org/rsflog/index.php?/archives/280-Program-of-the-month-sfsmooth.html

Fomel says
$\sigma = \sqrt{\frac{\mathrm{rect}^{2}-1}{6}}$
, for consistency between sfgaussmooth and sfsmooth.

gaussian filter at scipy.ndimage
https://github.com/scipy/scipy/blob/master/scipy/ndimage/filters.py

Gaussian filter, or Gaussian blur
http://www.librow.com/articles/article-9

Gaussian Blur – Image processing for scientists and engineers, Part 4
http://www.patrick-fuller.com/gaussian-blur-image-processing-for-scientists-and-engineers-part-4/

The 2-D Gaussain Filter
http://note.sonots.com/SciSoftware/GaussianFilter.html

Characteristic functions

Since the characteristic function of a convolution is the product of the characteristic functions of the densities involved, the central limit theorem has yet another restatement: the product of the characteristic functions of a number of density functions becomes close to the characteristic function of the normal density as the number of density functions increases without bound, under the conditions stated above. However, to state this more precisely, an appropriate scaling factor needs to be applied to the argument of the characteristic function.
An equivalent statement can be made about Fourier transforms, since the characteristic function is essentially a Fourier transform.