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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?

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What you're doing wrong is considering only the main lobe. Don't do that!

The sinc as spectral shape is elegant, because it has its zeros in all the other carriers' exact frequencies. So don't truncate; also, truncating a sinc after the main lobe ignores a lot of its energy.

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  • $\begingroup$ If I won't truncate the spectrum(the sinc pulse), then how to find the sampling frequency? $\endgroup$ – Narendra Deconda Dec 4 '18 at 11:01
  • $\begingroup$ The sampling frequency just needs to be a multiple of the subcarrier spacing for the spectral zeros to still get folded onto the carrier frequencies; assuming your receiver has a good rate match to the transmitter, you'd hence use just the bandwidth of your overall OFDM system (including guard carriers) as sampling rate and be done. $\endgroup$ – Marcus Müller Dec 4 '18 at 12:18

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