Fourier Series Special Case

In the very special case of truly periodic signals $x(t) = x(t+NT)$, for all $t\in(-\infty,\infty)$, the DFT may be regarded as computing the Fourier series coefficients of $x(t)$ from one period of its sampled representation $x(nT)$, $n=0,1,\dots,N-1$. The period of $x$ must be exactly $NT$ seconds for this to work. For the details, see §B.3.