# Treating the measured frequency response of a system as a DFT

I have frequency response data of an analog system that I would like to turn into a digital filter in Matlab. Is it kosher to think of my frequency samples as constituting a DFT of the system impulse response, even though there was never a time-domain signal in the first place? If I do an ifft on the frequency response data, can this be treated as the impulse response of the system? If so, what is the sample rate? Do I assume it is twice the highest measured frequency?

Is there a way to build a digital filter from impulse response data without knowing the sample rate?

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.