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How to fourier transform a gaussian curve?

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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?

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Star Strider
Star Strider 26 Feb 2020
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.

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Star Strider
Star Strider 27 Feb 2020
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);
plot(Fv, fftshift(abs(x_F)))
It first calculates the Gaussian with ‘x_fit_func’ inside the fft call, then plots the result.
Antonio Sarusic
Antonio Sarusic 27 Feb 2020
Thank you very much!
Star Strider
Star Strider 27 Feb 2020
As always, my pleasure!

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