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Im new to communications so this may be a stupid question, but I am somewhat confused. I am trying to train an automatic modulation classification (AMC) algorithm on IQ data from the RadioML dataset. The data comes in IQ format (eg [1024, 2] matrix).

I am reading papers now which use feature based methods and talk about getting the hilbert transform / DFT of the received signal and extracting features from there (for example, the std deviation of the instantaneous amplitude, see Table 1 here).

My question is what do I take the hilbert transform/DFT of? Would it be the IQ signal (I+jQ) or is there something more else involved (multiplying by sin/cos)?

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    $\begingroup$ The Hilbert transformation leaves you with your signal, and a copy of your signal rotated 90 degrees. I and Q are the signal and the signal rotated by 90 degrees. In other words, if you have I and Q, then something has already done a Hilbert transform (or approximation) for you. $\endgroup$ – JRE Feb 21 at 23:35
  • $\begingroup$ also, maybe start with the papers of the authors of the RadioML dataset (that being Tim O'Shea et al, not researchers that do a survey paper). They're linked on the same web page as the dataset, when you click on "Publications". $\endgroup$ – Marcus Müller Feb 21 at 23:45
  • $\begingroup$ @JRE my goal is to go from the IQ signals back to the 'recieved signal' as discussed in those papers. So does that mean I need to do an 'inverse' hilbert transform? $\endgroup$ – DankMasterDan Feb 21 at 23:52
  • $\begingroup$ @MarcusMüller I read the original papers and looked at the data generation source code. I guess my question is more how the RadioML data relates to the 'received signal' discussed in the feature-based modulation classification literature (see linked paper above eq.3) $\endgroup$ – DankMasterDan Feb 21 at 23:53
  • $\begingroup$ it is the received signal, as the computer gets it from the receiver. $\endgroup$ – Marcus Müller Feb 22 at 0:08
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Usually an IQ signal is generated from a real (RF, AF, etc.) signal by a radio (by quadrature heterodyne, Tayloe demodulation, complex vector arithmetic, or otherwise). However, if you need IQ data, and the radio only generates I (or real) component samples, a Hilbert transform can be used to generate “fake” Q components (an approximation by making some assumptions about the original signal) to use in downstream IQ processing or analysis.

Thus, if you have an IQ signal, there is rarely any need to generate another fake similar Q signal component. Just use the Q component the radio provides instead of a Hilbert transform of the I component (which contains half the amount of information as contained by the full IQ signal).

And, to get a real signal back, just reverse whatever process (superhet, etc.) the radio used to generate IQ from RF.

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    $\begingroup$ note that the Q (=quadrature) component in a IQ signal is not just "the hilbert transform of the I"; it's an orthogonal part that contains just as much independent info as the I (=inphase) component. $\endgroup$ – Marcus Müller Feb 22 at 8:59
  • $\begingroup$ An IQ signal contains twice the information because it can contain info on both sidebands. One possible assumption for an I-only real signal from a SSB/superhet is that the other sideband has been filtered out, thus a Hilbert generated IQ should only contain half the possible information. Other assumptions are possible, such as aliasing/folding. $\endgroup$ – hotpaw2 Feb 22 at 16:20

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