As title says, what is the relationship between DTFT and continuous fourier transform? Let's say there is continious signal $f(t)$. Continuous Fourier transform convert this into $F(\omega)$. Now let us create infinite number of uniformly-distanced samples following Nyquist-Shannon sampling criterion, and DTFT these samples into $F_d (\Omega)$. What exactly is the relationship between $F(\omega)$ and $F_d (\Omega)$?
If $T$ is the sampling period then the relationship can be written as
So in general $F_d(\Omega)$ is an aliased version of the original spectrum. If $F(\omega)$ is ideally band-limited and the sampling theorem is satisfied, then you have