I have a question about the relation between Fourier and Laplace transforms.
I have seen in some places that the transfer functions in the Laplace space are represented as $G(s)$ where $s$ is the variable in the frequency domain (Laplace). In other places I have seen that the transfer functions are represented as $G(iw)$ where $w$ is the frequency in the Fourier space and $i$ the imaginary unit.
I wonder how this connection applies because in some places it is supposed that the relation between both frequencies is $s=\sigma+iw$. But what is $\sigma$ then and why is it sometimes ignored?
If the relationship $s=iw$ would hold to be true, that means that we can Laplace transform by multiplying data times $i$ and doing the FFT?