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We have an acquisition hardware in our lab that acquires and digitizes data from a source generating band-limited signal in the MHz range. It samples the signal at a rate of 4 times the center frequency $f_0$ of the signal. In the documentation, they say that this specific sample rate makes it easier to convert the RF samples to demodulated IQ samples.

How would $f_s=4f_0$ make the demodulation easier? I have been using Hilbert transform to achieve the demodulation (the old-fashioned way). But, if there is any shortcut offered by this specific sample rate, that would be really helpful.

Thanks.

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  • $\begingroup$ What is the bandwidth of your signal? $\endgroup$
    – Gillespie
    Jul 5, 2022 at 3:03

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To get IQ data from a bandlimited signal centered at f0, with a bandpass well inside f0-f0/2 to f0+f0/2, and using a sample rate of fs=4*f0, you can simply keep 2 successive samples out of every 4, and ignore the rest. Take every 4th sample, put them in the I channel, take the samples right after those and put them in the Q channel, and throw away the 3rd and 4th sample out of every 4 samples (I Q ignore ignore I Q ignore ignore I Q ignore ignore ... etc.). The result is an IQ signal at a sample rate of f0.

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    $\begingroup$ This is a very poor method since it is ignoring half the signal samples. Instead, the ignored samples should be used to enhance the SNR. $\endgroup$ Sep 20, 2019 at 17:54
  • $\begingroup$ @hotpaw2, you mind clarifying the notations in the first and last line regarding center frequency vs cut-off frequency? The $f_0$'s. $\endgroup$
    – Gilles
    Feb 10, 2021 at 12:42
  • $\begingroup$ If the signal is bandlimited to a bandwidth narrower than fs/8, then 3/4ths of the samples can be reconstructed from every 4th (according to Nyquist-Shannon-Kotelnikov), so there is no loss throwing away half the samples. $\endgroup$
    – hotpaw2
    Jul 8, 2022 at 15:12

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