Use Fourier transform to find Fourier series coeficcients I understand that the Fourier Transform can be seen as a generalisation of the Fourier Series, where the period $T_0 \to \infty$ . Now I have encountered this strange question (in an engineering course on signal analysis):

Given a periodic function $x(t)$, find the Fourier Series coefficients $X_n$ by using the Fourier Transform.

What does this mean? How can it be done? As I see it, FS and FT are similar concepts, but they are not the same operation.
For reference, $x(t) = rect(\frac{t-0.25}{0.25}) * \Delta _1 (t)$ but I am seeking an answer in terms of any periodic function $x(t)$ .

Strictly speaking, the fourier transform is not defined for non-zero periodic functions. Such functions aren't in $L_1$ nor in $L_2$, so the fourier transform does not exist. If you attempt to compute it, you run into trouble when doing the integration, since the integral won't converge.
To apply the fourier transform to such functions, you must first generalize it to distributions. Some engineering texts do that, although usually without formal proofs that this is actually sane. You can put this construction on a firm mathematical basis, but it's not trivial. (Though it isn't that hard either - Rudin's book "Functional Analysis" for example includes a quite accessible derivation of the main results)
