Calculate Fourier transform of a gaussian using Matlab. Full article at: http://www.firsttimeprogrammer.blogspot.com/2015/05/calculate-fourier-transform-of-gaussian.html

fourier_transform.m

% Fourier transform calculation
%-------------------------------------------------------

% Declare symbols to use
syms x t;

% Parameters of the transform
a = 300;    %scaling
b = 0;      %shifting
c = 0;      %smoothing

% Function to transform
u = exp(-(a*t-b)^2) * exp(1i*c*t);

% Transform of u
uHat = fourier(u,t,x);

% Printing u and u hat
simplify(uHat);
pretty(u)
pretty(uHat)

% Plotting
x_axis = linspace(-15,15,500);
figure;
plot(x_axis,abs(subs(uHat,x_axis)),x_axis,abs(subs(u,x_axis)));
xlabel('x');ylabel('y');
title('Function and its Fourier Transform');
legend('Fourier transform','function');