Treating the measured frequency response of a system as a DFT
So, after worrying about whether the frequency response is "low pass in nature" (i don't think it needs to be a LPF, it could be high pass in nature, but all of the interesting features of your frequency response should be below Nyquist and maybe well below Nyquist), you might also wonder about if you have the necessary phase information in your frequency response.  if it is magnitude-only data, then you might have to guess at the phase.

if you iFFT the magnitude-only data (mirroring it about $f=0$), you will come up with an impulse response that is also mirrored about $t=0$.  that's fine, give it a delay of half of the length of the impulse response, and you have a linear-phase FIR.  you get linear phase because you started not knowing anything of the phase.  you can also take that FIR, factor it with some nasty factorization program (maybe MATLAB has that), reflect (using the reciprocal function) all zeros outside the unit circle to inside the unit circle, the re-multiply all of the factors and you will have a minimum-phase FIR with the same magnitude frequency response.