# Conditions for representing (perfectly) an analog signal as a digital signal

Consider the following cases:

1. Sampling with a frequency of the "signal's central frequency"
2. Sampling a BP signal with twice the frequency of the signal BW.
3. Sampling an LP signal with the highest signal's frequency.
4. Sampling an LP signal with twice the highest signal's frequency
5. Sampling a BP signal with the frequency of the signal BW.

1. Since $f_{center} < f_{max} < 2f_{max}$, by the sampling theorem, it's not (always) possible.
2. This one is true, but I don't know why.
3. $f_{max} < 2f_{max}$ - the same as #1.
4. This is true by the sampling theorem (even though I think it should be $2f_{max} + \varepsilon$, isn't it)?
5. $BW < 2f_{max}$ so the answer is no, the same as #1.

Can you please validate my answers as well as help me with understanding 2 and 4?

Thanks!

• are we talking about complex or real sampling with your low-pass signal (i.e. is "LP" the same as "equivalent baseband")? is your signal for 1. a bandpass signal with the common $B\ll f_{center}$ assumption? – Marcus Müller Mar 13 '18 at 12:07
• – MBaz Mar 13 '18 at 14:08