I am not expert in DSP, actually, I use it rarely. However, I have found a problem to face quite different than the usual.
The problem is very simple: given a complex signal (obtained experimentally) in the frequency domain that represents a impulse response function (IRF), calculate its representation in time domain. The IRF (magnitude and phase) is illustrated in the graph below.
The data are: frequency (w), magnitude and phase.
Firstly, it seemed as simple as apply IFFT, but it does not. My first surprise was the result of IFFT is a complex number. Unexpected once I expected to have a time domain signal. The other problem would be calculate the time axis, because I do not have any information. I must say that the only information known about the time domain is that the IRF is non-casual.
If someone could help me and give some direction I would be very grateful!