# How to fourier transform a gaussian curve?

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Antonio Sarusic on 26 Feb 2020
Hello,
I have the following function:
x_fit_func(x) = a1*exp(-((x-b1)/c1).^2);
a1, b1 and c1 are all constants and the function represents a gaussian curve.
Now I want to fourier transform this function and in theory i should again get a gaussian curve.
I tried it like this
x_F = fft(x_fit_func(x));
or like this
x_F = fft(x_fit_func);
But it always calculates something that is not a gaussian curve.
Does anyone know what I do wrong?
Thanks
Antonio

Star Strider on 26 Feb 2020
The ‘x_fit_fcn’ is not syntax that MATLAB recognises (except in the Symbolic Math Toolbox), as a function.
x_fit_func = @(x) a1*exp(-((x-b1)/c1).^2);
I also calculated the fft of the result tthat produced. It works.
Antonio Sarusic on 27 Feb 2020
Thank you very much!
Star Strider on 27 Feb 2020
As always, my pleasure!

DISHANTKUMAR PATEL on 1 Dec 2022
% isotropic Gaussian parameters n = 65; % resolution s = 2; % width x = linspace(-5,5,n); [X,Y] = meshgrid(x); gaus2d = exp( -(X.^2 + Y.^2 )/(2*s^2)); figure(1), clf surf(x,x,gaus2d) rotate3d on hold on % adjusting the radius of sphere x1 = x1*s; y1 = y1*s; z1 = z1; % add a constant to sphere, so that it is on top of gauss addi = max(gaus2d(:)) - min(z1(:)); z1 = z1 + addi; surf(x1,y1,z1) realCenter = [8,15,25]; [X,Y,Z] = sphere; XYZ = bsxfun(@plus,r*[X(:),Y(:),Z(:)], realCenter) % Label axes. xlabel('X', 'FontSize', 8); ylabel('Y', 'FontSize', 8); zlabel('Z', 'FontSize', 8); title('3D Sphere'); axis equal;