Shannon theorem and zero padding Sorry if I ask a basic question but I am a bit lost.

I have a data set in frequential domain, I need to go to time domain to perform time-gating and then going back to frequencies. In order to do this, I compute an inverse Discrete Fourier Transform. 

Shannon theorem tells us that two times the difference between the greatest and the least frequency, respectively noted as $f_N$ and $f_0 ( \ne 0)$, contained in the signal must be less then the sample-rate in time domain ($F_t$). Do I need to do some zero padding to avoid aliasing ?

Without zero padding on frequential domain, what is the relation between $F_t$ and $f_N, f_0$ ? My guess is that $F_t=f_N-f_0$. Is that correct ?

If I must do some zero padding, should I do it this way :

$$(0,\dots,0,f_0,\dots,f_N,0 \dots,0)$$

With enough zeros such that the first frequency contained in the padded signal is $0$ and the last is $2 f_N$ ?
If my guess above is correct, then the new sample rate is high enough to avoid aliasing, because it will be $F_t=2f_N&gt;2(f_N-f_0)$.

Thanks for your help.
You'll not experience aliasing – in the end, the IDFT result per definition only contains frequency components that can be represented by the original frequency domain.

If you will, just stop worrying about aliasing: the DFT and inverse DFT are just base change matrices in $\mathbb C^N$, and are invertible.

Aliasing can only happen when something is non-invertible. This is not the case here; so, no problem.

What you might see is leakage, but you're already taking care of that by windowing.