Passing a sampled signal through a filter 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?
Not sure what you mean by "wrong". 

The Nyquist criteria simply requires you to have "two samples per Hz of bandwidth". It doesn't have to be $[-f_{max},-f_{max}]$, it can be any frequency range that includes at least $2 \cdot f_{max}$ of bandwidth. However, for real signals you need to figure out what to do with the negative frequencies.

For more info google "bandpass sampling".