I was wondering why is it wrong to use a band-pass filter on a sampled signal?
If the signal we want to sample has frequencies up to fmax, we sample it with frequency fs = 2fmax (so that Nyquist theorem condition is fulfilled), and the spectrum of the sampled signal will have scaled "copies" of the original spectrum centered around frequencies k * fs (k = +-1, +-2 ...).
What would happen if we filtered that sampled signal with a band-pass filter [fs-fmax, fs+fmax], and why is it wrong? Wouldn't we end up with the signal we started with?