How to determine stopband of discrete Gaussian, stdev sigma, support N

Question

I would like to analyse a gaussian smoothing kernel with a set standard deviation and support (let's say, in MATLAB, fspecial('gaussian', [5 1], 1.3) so sigma is 1.3 and support is 5) in the DTFT domain to determine the stopband.

My understanding is that the stopband is when the magnitude of the impulse response is below -3 dB. However, I don't have a clue how to determine this given a sigma and support value.

I'm particularly interested to see if the DTFT quantifies the artifact due to the compact support as I would like to understand this a little better.

Answer 1

I found answer at https://courseware.ee.calpoly.edu/~fdepiero/curr/dsp/dsp11.htm . Converted to the present problem, in MATLAB:

kernel2 = fspecial('gaussian', [1 5], 1.3)
spike = [1 0 0 0 0];   
[h, w] = freqz(kernel2, spike, 1024);
m = abs(h)
m_db = 10*log10(m/max(m));
plot(w,m_db)

Because the compact support Gaussian had zero crossings, I used the first zero to define the stop band.