Assuming I have a function $f(x)$. I can use a Numerical Fourier transformation

 NFourierTransform[] 

to find some points of $F(\omega)$. How can I do the same when I have not $f(x)$ but some points of it, i.e. $f(x_i)$.

Best

For example:

PDF[NormalDistribution[0, 1], x] f[x_] := E^(-(x^2/2))/Sqrt[2 \[Pi]] Testdata = Array[f, 100, {-2, 2}]; 

Fourier[Testdata] gives a complex dataset back, but the Foriertransformation should be again a real Gaussian?

Assuming I have a function $f(x)$. I can use a numerical Fourier transformation:

NFourierTransform[] 

to find some points of $F(\omega)$. How can I do the same when I have not $f(x)$ but some points of it, i.e. $f(x_i)$.

For example:

PDF[NormalDistribution[0, 1], x] f[x_] := E^(-(x^2/2))/Sqrt[2 \[Pi]] Testdata = Array[f, 100, {-2, 2}]; 

Fourier[Testdata] gives a complex dataset back, but the Fourier transform should be again a real Gaussian?

Assuming I have a function $f(x)$. I can use a Numerical Fourier transformation

 NFourierTransform[] 

to find some points of $F(\omega)$. How can I do the same when I have not $f(x)$ but some points of it, i.e. $f(x_i)$.

Best

Assuming I have a function $f(x)$. I can use a Numerical Fourier transformation

 NFourierTransform[] 

to find some points of $F(\omega)$. How can I do the same when I have not $f(x)$ but some points of it, i.e. $f(x_i)$.

Best

For example:

PDF[NormalDistribution[0, 1], x] f[x_] := E^(-(x^2/2))/Sqrt[2 \[Pi]] Testdata = Array[f, 100, {-2, 2}]; 

Fourier[Testdata] gives a complex dataset back, but the Foriertransformation should be again a real Gaussian?