The Fourier transform of an arbitrary funtion, where $\vec{t} \in \mathbb{R}^2$ is given by
$FT[f ( \vec{t} )]= \hat{f} ( \vec{\omega})$ .
I'm trying to figure out if there can be some statement about the FT of $f(t+t')$, since in an older calculation I made I somehow used (intuitively)
$FT[f(t+t')] = \hat{f}(\omega+\omega')$ .
But it's not clear to me whether or not this is true and how to (dis-)prove it.. help would be appreciated