implementing gaussian filter in C

HeroofCode

I know due to the central limit theorem the Gaussian filter can be simplified to a weighted moving average.

I'm still understanding signals, but I know a moving average is

Y [ i ] = [itex]\frac{1}{N}[/itex][itex]\sum ^{N-1}_{j=0}[/itex] X[ i + j ]


From Wiki on Gaussian filter, if I process through a moving average for 4 or more times, it is an approximate of the Gaussian.

How would I do this ? I figured it would be some recursion, but any explanation?