Simple equivalency problem:
I plot out a 2D Gaussian function with a certain resolution in Matlab. i.e.
Let's call the result g1FFT.
I am testing with mu = 0.0 (always), and variance or sigma = 1.0. I want to compare it to the result of FFT(Gaussian), which should result in another Gaussian with a variance of (1./sigma).
g1FFT = circshift(g1FFT, [rows/2, cols/2, 0]);
freq_G1 = fft2(g1FFT);
freq_G1 = circshift(freq_G1, [-rows/2, -cols/2, 0]);
Since I am testing with sigma = 1.0, I would think that I should get two equivalent, 2D kernels, because if sigma = 1.0, then 1.0/1.0 = 1.0. So, g1FFT would equal freq_G1.
However, I do not get equivalent kernels. They have different magnitudes, even after normalization. Is there something I am missing?
Attached are cross-sections of the two kernels that I am talking about. Original sigma = 1.0 so that, even in the frequency-domain, the resulting sigma is also 1.0.