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I would like to create a discriminator of an FSK signal in order to demodulate it.

I only have the real part of the signal and it is centered in zero frequency (baseband)

My main problem is that I am not able to make the arctan of this signal because it is real. I am in a symetry issue using cos-1 or sin-1.

Do you have any idea how to transform it to a complex representation?

I was wondering if it was possible to use Hilbert transform. I heard of it but I don't know if it is suitable for my problem.

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I only have the real part of the signal and it is centered in zero frequency (baseband)

Bad luck; with the real part of the signal you can't tell negative from positive frequencies.

Discarding the imaginary part discarded exactly that information. There's nothing you can do about that, the information is gone. Ignoring the imaginary part of a baseband signal literally ignores half of the signal content!

If your FSK was continuous-phase, you oversample sufficiently (i.e, especially not the MSK case), and the pulse shape applied before frequency-modulating is benign, and your SNR good enough, you might try to infer on whether you just saw a signal transition. You can't get the original bits that way, but you could maybe get the information of whether the last symbol is the same as the previous one. Good luck!

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  • $\begingroup$ Thanks. How is the imaginary part discarded? I shift a real signal with a real carrier to center it in zero. Maybe this is wrong? $\endgroup$ Jul 23, 2022 at 12:34
  • $\begingroup$ well, how did you shift, exactly? Because when I shift a passband signal to zero, I end up with a complex baseband. $\endgroup$ Jul 23, 2022 at 12:36
  • $\begingroup$ Multiply the real carrier with a sine and a cosine to create the complex baseband that would be needed as Marcus stated OR demodulate directly by multiplying the real signal with itself after a fixed delay at the carrier frequency that has a phase when centered at that carrier frequency of 90 degrees. (Or longer delays to have a higher gain but narrower bandwidth discriminator- some odd multiple of 90 degrees) $\endgroup$ Jul 23, 2022 at 12:49
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    $\begingroup$ This is straying off into a separate question, which you should ask separately (this is encouraged here). The short story is that when you shift a signal down to one channel of baseband you need to shift your signal such that the useful bandwidth of the signal is above DC, and such that any interference on either side of your signal isn't imaged into your signal. $\endgroup$
    – TimWescott
    Jul 23, 2022 at 14:28
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    $\begingroup$ Note that you can present the ADC with an IF of whatever frequency is necessary, then -- often with fairly low computational resources -- perform I/Q demodulation digitally, then downsample, then do the rest of your computation at the lower sample rate. $\endgroup$
    – TimWescott
    Jul 23, 2022 at 23:45

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