When calculating the Nyquist frequency should carrier frequency be included

Question

This isn't my field, so please forgive any misnomers on my part.

I'm looking into buying a amateur radio receiver, and I'm thinking about what sampling rate I need. I'm most interested in satellite signals, which transmit on ~400MHz (for example). So that would imply I have a nyquist frequency of ~800MHz, or 800 million samples per second. This seems much higher than any hardware I can find.

My current thinking is that the frequency to be used in the nyquist calculation isn't the carrier frequency. Which frequency should I use?

Answer 1

You are correct: a 400 MHz signal needs to be sampled at least at 800 Msamples/s, and that is either impossible or extremely expensive. However, this is not the entire story:

• Under some conditions, you can do bandpass sampling, where the sampling frequency is lower than Nyquist. See more at https://en.wikipedia.org/wiki/Undersampling.

• You can do analog bandpass filtering and down-conversion to some intermediate frequency (IF), which can then be sampled at reasonable cost/complexity. See https://en.wikipedia.org/wiki/Intermediate_frequency.

Most amateur digital radio receivers I'm aware of use the IF approach, and some also do bandpass sampling. For example, the RTL2832 can only sample at 2.6 Msamples/s, but it can receive signals at up to 2.2 GHz or so. If you see the device's datasheet, you'll see that it supports several different IFs.

Answer 2

If you want a realizable anti-alias filter (with a finite non-zero transition band), if you want to analyze your data in any finite amount of time, if the signal is modulated in any manner, then the sample rate needs to be some amount higher than twice your signal frequency in order capture information about your signal.

(or some amount lower for bandpass undersampling...)