# Sampling Frequency in a OFDM Technique

I am a new learner of OFDM. One source I refer explained OFDM in this way:

Consider 4 symbols $$X_0$$, $$X_1$$, $$X_2$$, $$X_3$$ $$\in \mathbb C$$. They are modulated using Multi-Carrier Modulation. The time domain equation is given as

$$c(t)=\sum_{n=0}^{3}X_ne^{j2\pi f_nt}$$

for the duration $$0\leq t > \leq 4T$$, and $$f_n=\dfrac{n}{4T}$$.

Now, he samples the signal at a sampling rate, $$F_s=\dfrac{1}{T}$$ so that

$$c(mT)=\sum_{n=0}^{3}X_ne^{j2\pi \dfrac{n}{4T}mT}=\sum_{n=0}^{3}X_ne^{j \dfrac{2\pi nm}{4}}$$

This means that the sampled version of $$c(t)$$ is the IDFT of the symbols $$X_i$$, $$i=0,1,2,3$$.

What I am thinking is, since the spectrum of $$c(t)$$ is the shifted version of sinc pulses, considering only the main lobe of each sinc pulse, the spectrum is band limited to $$\dfrac{-1}{4T}\leq f \leq \dfrac{4}{4T}$$. So the sampling frequency should be twice the maximum which is $$2*\dfrac{4}{4T}=\dfrac{2}{T}$$. This is not taking me to the IDFT equation. Can you please correct where I am doing wrong?