Fast Recursive 1D Signal Smoothing - IIR / Auto Regressive Implementation of Gaussian Smoothing
Have a look at my Fast Gaussian Blur Project at GitHub.

You will find there implementation of IIR Approximation of Gaussian Blur which implements the following papaers:


Recursive Gabor Filtering.
Recursive Implementation of the Gaussian Filter.
Boundary Conditions for Young - van Vliet Recursive Filtering.


The idea is pretty straight forward.