Visualisation of bandwith of filter with sampling

Question

I'm having some trouble visualising (and understanding) the filtering of a sampled signal.

If I understand correctly, after sampling a signal, it is desired to have it go through a lowpass to retrieve the original signal again. The literature states the following below.

$\omega_0 < B < \omega_s - \omega_0$

Where $\omega_s$ is the sampling frequency and B is, what I assume, the bandwith of the filter.

I do not understand what is meant by the above expression and the literature is kind of crap at explaining it.

I was hoping someone can visualise this for me.

Answer 1

$B$ is the cut-off frequency of the anti-alias filter needed before sampling; $\omega_0$ is the signal bandwidth, and $\omega_s$ is the sampling frequency.

$B$ can also be the cut-off frequency of the (ideal) reconstruction filter (band-limited interpolator).

If this is the case, this suggests that the reconstruction filter is an ideal low-pass filter with cut-off frequency between the signal bandwidth and the next overlapped frequency component ($\omega_s - \omega_0$). The sampled signal contains repetitions of the original specturm every $\omega_s$, so when reconstructing, you want to get rid of all these repetitions and keep only the spectrum centered at 0.

I don't know what literature you are referring to, and why is it so crappy.