Is this assuming you have some analog hardware that's demodulating the signal in front of your ADC? How do you demodulate a signal from a 1GHz carrier with 200 MSPS?
As the sibling comment mentioned, you don’t need to demodulate first, because that is actually what the sampling process of your ADC does.
You can think of it as multiplying the original signal by a comb (in the time domain) of delta functions, which folds everything (in the frequency domain) back into the nyquist frequency of your ADC. Each delta function corresponds to one sample. If your original signal was truly band-limited to 100MHz, then what comes out is a replica of the band limited signal.
One catch (which is actually fairly easy to do in practice) is that the sampling window needs to correspond to around 1/f of the carrier frequency. This is what YakBizzaro is talking about (ADC analog bandwidth) in their sibling post.
Thanks for the explanation! Between your comment and the Undersampling wiki page diydsp linked to I think I am on the path to enlightenment.
> If your original signal was truly band-limited to 100MHz
In practice, this means you need to band pass before the ADC, right? i.e. "signal" in this case is the entire input to the ADC and not just the particular modulated signal you care about
> In practice, this means you need to band pass before the ADC, right? i.e. "signal" in this case is the entire input to the ADC and not just the particular modulated signal you care about
Right and right.
And, you’d normally want that to be a contiguous 100 MHz band of frequencies (you could in principle have multiple discontiguous bands that add up to 100 MHz if they are spaced right (they don’t fold down to the same base frequencies), but that would be quite an unusual application).
To quote a meme: “That’s the neat part. You don’t.” If you bandlimit your input, aliasing effectively strips out the carrier tone and leaves the modulated signal.
In a way, you’re relying on aliasing / frequency folding to do it for you.
You can even improve information transfer in these scenarios by using a synchronizer, which allows you to phase shift your sampling to be at the ideal transition point in your information stream.
No, this assumption is incorrect. You can ADC first and then demodulate afterwards. The spectrum of your high-frequency (near 1 GHz) signal will be aliased at frequencies below the Nyquist frequency, but it’s easy to calculate the original frequency, if you know that the signal is band-limited.
You can think of it as multiplying the original signal by a comb (in the time domain) of delta functions, which folds everything (in the frequency domain) back into the nyquist frequency of your ADC. Each delta function corresponds to one sample. If your original signal was truly band-limited to 100MHz, then what comes out is a replica of the band limited signal.
One catch (which is actually fairly easy to do in practice) is that the sampling window needs to correspond to around 1/f of the carrier frequency. This is what YakBizzaro is talking about (ADC analog bandwidth) in their sibling post.