How to fourier transform a gaussian curve?

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

Answer 1

[Star Strider]

The ‘x_fit_fcn’ is not syntax that MATLAB recognises (except in the Symbolic Math Toolbox), as a function.

Try this versiion instead:

x_fit_func = @(x)  a1*exp(-((x-b1)/c1).^2);

I also calculated the fft of the result tthat produced. It works.

[Antonio Sarusic]

Can you maybe share your whole code.

I'm realtivly new to matlab and still have some problems understanding all this myself.

[Star Strider]

Sure!

Here is the code I used to test it:

a1 = 2;
b1 = 5;
c1 = 3;
x_fit_func = @(x)  a1*exp(-((x-b1)/c1).^2);
x = linspace(-10, 10, 50);

x_F = fft(x_fit_func(x))/numel(x);
Fs = 1/mean(diff(x));
Fn = Fs/2;
Fv = linspace(-1, 1, numel(x_F))*Fn;
Iv = 1:numel(Fv);

figure
plot(Fv, fftshift(abs(x_F)))
grid

It first calculates the Gaussian with ‘x_fit_func’ inside the fft call, then plots the result.

[Antonio Sarusic]

Thank you very much!

[Star Strider]

As always, my pleasure!

Answer 2

[DISHANTKUMAR PATEL]

% 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;