Fourier transform

[salvomic]

hi all,
a part of Fourier series coefficients (see here), there is a function in the Prime (or XCas) to get the Fourier Transform (not FFT) and its inverse?
See in Wolfram Alpha, for example...
If not, I need help to make a program.

We could calculate it via laplace() (Laplace transform), but we need the "bilateral laplace transform" and I don't know how to get it with the Prime...
F[f(t)] == bilateral-L[f(t)] where \( s=i\omega \)

Thank you
Salvo

EDIT:
the general equation should be
\[ \int_{-\infty }^{\infty }f(x) e^{-i\omega t}dt \]
but with Prime I get often "undef" and if I set "complex" in CAS I get "Limit: Max order reached or unable to make series expansion Error: Bad argument"