Down sampling, bandpass sampling theorem, downconversion

[FrankJ777]

I'm trying to demodulate simple AM by using an ADC and the bandpass sampling theorem (as I understand it.) The way I understand the theorem is that by sampling a bandpass signal of frequency f$_{0}$ and bandwidth B, where f$_{0}$ >> B, as long as I use a sampling frequency of >2B I can reproduce the signal even though the sampling frequency is much less than f$_{0}$.
From what I've read, to accomplish the bandwidth of the ADC must be at least f$_{0}$. I'm not sure exactly what this means. Does it only mean the input to the ADC must not attenuate a signal of f$_{0}$? Or are they referring to the sampling aperture. I see the formula use to demonstrate the concept is m[n] = M(t)δ (t-nTs). But i realize that δ is instantaneous where as a ADC is not, so I'm wondering if the width of my sample needs to be around 1/f$_{0}$?

If anyone can lend some insight I'd appreciate the help.
Thanks

 

[marcusl]

I'm trying to demodulate simple AM by using an ADC and the bandpass sampling theorem (as I understand it.) The way I understand the theorem is that by sampling a bandpass signal of frequency f$_{0}$ and bandwidth B, where f$_{0}$ >> B, as long as I use a sampling frequency of >2B I can reproduce the signal even though the sampling frequency is much less than f$_{0}$.
From what I've read, to accomplish the bandwidth of the ADC must be at least f$_{0}$. I'm not sure exactly what this means. Does it only mean the input to the ADC must not attenuate a signal of f$_{0}$?

Yes, that is correct.

Or are they referring to the sampling aperture. I see the formula use to demonstrate the concept is m[n] = M(t)δ (t-nTs). But i realize that δ is instantaneous where as a ADC is not, so I'm wondering if the width of my sample needs to be around 1/f$_{0}$?

I don't understand your question.

Bandpass sampling is somewhat sophisticated, and requires different filtration than regular baseband sampling to achieve a good SNR. I fear that a couple of short answers on this forum won't give you a deep enough understanding of sampling, filtration and DSP. Have you had a course in DSP? Do you have a DSP text to read?