Relation between Fourier Series & Fourier transform So i was just revising some basic DSP concepts. Just wanted to verify this fact.

Fourier series represents a periodic signal $\hat{x}(t)$ with period P as a countably infinite sum of sinusoids of frequency $0$, $\frac{1}{P},\frac{2}{P},\frac{3}{P}...$. This converges to the signal in the interval, $-\frac{P}{2} &lt; t &lt; +\frac{P}{2}$, and if the time domain signal is periodic, then over the whole time domain.

Fourier Transform is sorta like a limit of the fourier series where P goes to $\infty$. 

So i know that the fourier transform of $\operatorname{rect}(t)$ is $\operatorname{sinc}(f)$ ( ignoring the scaling factors ) . And that the fourier series of a $\operatorname{rect}()$ is given by http://mathworld.wolfram.com/FourierSeriesSquareWave.html ( which is also a $\operatorname{sinc}()$ in the frequency domain ) . 

I just wanted to confirm the following

If I sample the $\operatorname{sinc}()$ i obtain from the fourier transform of a $\operatorname{rect}()$, and use those values to reconstruct a fourier series, will i end up getting a square wave ?
Regarding reciprocal domains, such as the "time" domain and "frequency" domain, that are related to each other by the Fourier Transform, whenever you uniformly sample in one domain, it causes periodic extension in the other domain.  It does that always.

So the Fourier Series is an example of sampling in the frequency domain causing periodicity in the time domain.  The corresponding example (using duality of the Fourier Transform) is the so-called DTFT (Discrete-Time Fourier Transform) $X(e^{j\omega})$ of a sampled sequence $x[n]$ which is naturally periodic with period $2 \pi$.  And normally we consider $X(e^{j\omega})$ with $-\pi &lt; \omega \le +\pi$ .