For a time discrete signal, the rect-filter (for 1D signal [1,1]) is a perfect low pass filter. I was wondering, what is the best gaussian approximation of this filter?
For a current problem, I cannot use binomial filters but have to use Gaussian filters for smoothing. Ths question is thus, what is the standard deviation of a Gaussian filter best approximating the [1,1] rect-filter. 'Best' could e.g. mean is has similar probperties in the frequency domain.