From what I thought I learned about sampling is that when you draw a sampled signal in the frequency domain, you can show copies or "images" of that signal at integer multiples of the sampling frequency. Is this true?
If so, I'm having a hard time understanding this conceptually. What does it really mean to make a copy at a different location on the frequency line?
For example, if I have a signal which when drawn in the frequency domain looks like a box centered at zero extending from $f_{low}$ to $f_{high}$, can I now say I can draw this box centered at integer multiples of the sampling frequency and so long as my box when redrawn does not touch another box I avoid aliasing? Why do I do this at integer multiples? For example if my sampling frequency is $20 \ \mathrm{Hz}$, what does the next integer multiple at $40 \ \mathrm{Hz}$ tell me? Does it mean I'll see something interesting if the signal were to run at $40 \ \mathrm{Hz}$?
I'm trying to get a better understanding of this so I can then understand bandpass sampling and what it means to select a location at $k$, $k-1$, etc.