My question is: Suppose that we have low pass spatial domain filter that averages 4-connected neighbors of that pixel and it doesn't consider its pixel in averaging. Find its corresponding filter in frequency domain and show that it is a low pass filter.
I know that I must take forward Fourier transform from spatial domain filter and its output is frequency domain filter, but I don't have any idea what is spatial filter is? I think that it is $w(x,y)$ such that $-1 \le x \le 1 $ and $-1 \le y \le 1$ and $w(-1,0) = w(0,-1) = w(0,1) = w(1,0) = 1$ and $w(-1,-1) = w(0,0) = w(1,-1) = w(-1,1) = w(1,1) = 0$ but I don't know how to take Fourier transform from this?
How do I take the Fourier transform of my 3×3 filter kernel?