# Matlab - FFT of Gaussian - Equivalency

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kdottiemo on 19 Jun 2015
Simple equivalency problem:
I plot out a 2D Gaussian function with a certain resolution in Matlab. i.e.
Y = normpdf(X,mu,sigma) % over some resolution with the peak in the center
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).
i.e.
g1FFT = circshift(g1FFT, [rows/2, cols/2, 0]); % fft2 expects center to be in corners
freq_G1 = fft2(g1FFT);
freq_G1 = circshift(freq_G1, [-rows/2, -cols/2, 0]); % shift back to center, for comparison sake
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.

Salaheddin Hosseinzadeh on 19 Jun 2015
Edited: Salaheddin Hosseinzadeh on 19 Jun 2015
I'm not sure what you're intending to do.
Do you know about fftshift() command?
To me it sounds like you're having problem comparing the frequency domain result with time domain result. If this is your problem then have a look at fftshift command in MATLAB documentation.
Salaheddin Hosseinzadeh on 24 Jun 2015
You're kind of right. I don't know about this! I tried with my own sample and it's the same for me. except I got a different magnitude for a gaussian of amplitude 1.
x = -100:0.01:100;
g = gaussmf(x,[1,0]); % this needs fuzzy toolbox
plot(x,g);
figure
plot(fftshift(abs(fft(g))./numel(g)));
Why don't you search about the magnitude of fft, maybe what we see is correct!
let me know about it as well please.
Tnx

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