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How can software-defined radios operate at high frequency?

The Nyquist rate dictates that you need to sample at twice the frequency to fully recover the signal. If my signal of interest is modulated at $2.5 \,\rm{GHz}$, doesn't my SDR need to sample at $5 \,\rm{GHz}$ to fully recover and demodulate the signal of interest?

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    $\begingroup$ Bandwidth and frequency are not the same thing in this case $\endgroup$ – Stanley Pawlukiewicz May 15 at 18:20
  • $\begingroup$ Nyquist does not dictate 5 GHz. Your bandwidth is not 2.5 GHz, it is much smaller. What is the bandwidth of your signal of interest? Read this article wescottdesign.com/articles/Sampling/sampling.pdf $\endgroup$ – Ben May 15 at 18:38
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The high-frequency (RF) section of an SDR is all analog. Typically, the analog receiver downconverts the RF signal to an intermediate frequency that is within the Nyquist range of the ADC. As Stanley points out, you can also do bandpass sampling, though that is less common, in my experience.

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    $\begingroup$ In fact, many (actually, most) of the SDR hardware that I can think of works with complex baseband, so we actually mix down to zero IF with two different, 90° phase offset mixers – and then we only need to sample at the bandwidth, but with two synchronous DACs. $\endgroup$ – Marcus Müller May 15 at 22:50
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    $\begingroup$ @MarcusMüller Personally I don't like to mix to zero IF; I prefer to do low IF, then carrier estimation and final downmix in discrete time. But it's a personal preference. $\endgroup$ – MBaz May 16 at 0:58
  • $\begingroup$ and it really depends on what you're doing! For example: A lot of OFDM-based systems are designed with zero-IF in mind: they have nulled out DC carriers, so that the LO leakage/DC cancellation doesn't affect the signal, and classical OFDM sync algorithms (Schmidl&Cox) do the frequency correction directly on the baseband. It's also a matter of how you "grow up" – I was raised into a complex baseband world (not even sure superhets were mentioned before I learned the quadrature demod), and the option that you could do low IF was a later realization. (Which I had while doing SDR tech support.) $\endgroup$ – Marcus Müller May 16 at 7:19
  • $\begingroup$ I did not know complex mixers were used in the front end! I thought they were just for Quadrature demodulation (after sampling in SDR). Can I think of the LO setting of the SDR as the frequency of the complex mixer? $\endgroup$ – nickhansenrf May 16 at 12:34
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    $\begingroup$ @MarcusMüller I agree with all you said. Of course I use the complex baseband all the time, but in my experience, some signals are easier to handle in low-IF. For example, I ask my students to capture and decode NOAA satellite weather images. If those are downmixed to a low IF first, then removing the Doppler followed by envelope detection is easy. Those two operations are not as simple (both conceptually and in their implementation) if we went straight to baseband. $\endgroup$ – MBaz May 16 at 14:24

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