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In the digital domain a higher sampling will have a better SNR.

  • Similarly does a narrow filter give a better SNR in analog domain?
  • Once analog signal is converted into digital signal can SNR be increased? By using a digital filter?
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In the digital domain a higher sampling will have a better SNR

No, that's not the case.

In fact, if you oversample a bandlimited signal, you don't get overproportionally more signal power than you get more noise power, but as long as you don't use perfect filters which don't exist, you do see more noise, introduced at every step of the analog-to-digital conversion.

You can get an improved SNR from an oversampled signal. But it's not due to higher sampling, but due to processing gain of what you you do with the sampled signal.

Similarly does a narrow filter give a better SNR in analog domain?

If you assume your noise has a wider bandwidth than your signal, then quite directly follows that the less bandwidth that contains only noise you let through, the better your SNR gets.

Don't forget that SNR is usually just a "helper figure", not inherently something you care about without looking at what has happened to your signal. For example, inevitably, very narrow analog filters have very nonlinear phase, which leads to very strong distortion of the signal's phase. At the end you might have a very good SNR, which only compares powers of signal to noise, but your signal might still be very, very broken.

Once analog signal is converted into digital signal can SNR be increased? By using a digital filter?

That is one way of achieving processing gain as outlined above, yes. So, no, your higher-sampled signal doesn't have better SNR, your digitally postprocessed signal has.

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  • $\begingroup$ so even if my analog signal SNR is less after adc I can increase SNR by putting digital filter. can this also decrease number of bit errors in digital communication? SNR means it's signal to total noise in analog domain and -fs/2 to ga/2 in digital domain? $\endgroup$
    – mark
    Commented Jun 5, 2020 at 13:50
  • $\begingroup$ I'll go ahead and say: if you're not clear about the relationship of bit errors to SNR, you might want to review your basic knowledge of digital comms! $\endgroup$ Commented Jun 5, 2020 at 13:52
  • $\begingroup$ SNR means it's signal to total noise in analog domain and -fs/2 to ga/2 in digital domain? don't know what that means. $\endgroup$ Commented Jun 5, 2020 at 13:53
  • $\begingroup$ @ Marcus I do know the relationship of bit errors to snr. I will reframe the question. For any system with a given receiver sensitivity,noise figure we calculate SNR required at adc input to get error free comm. I was wondering for any weak signal I can improve SNR in the digital domain however weak it may be? $\endgroup$
    – mark
    Commented Jun 5, 2020 at 14:16
  • $\begingroup$ Sorry, here's my inner information theorist coming out: You can never get error free communication, as long as you have noise with an infinite support. However, what you meant is "sufficiently small error rate", and that is someting you can achieve, indeed! $\endgroup$ Commented Jun 5, 2020 at 14:22

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