Digital sampling of analog signals can produce surprising effects. It is tricky to explain and understand the frequency aliasing, which happens when undersampling. What is the aliased frequency? Why are there positive and negative frequencies in FFT, but only one Nyquist frequency?
Suppose you need to filter your noisy measurement a bit. Digital filter, oh, and those Z transforms... Most engineers I know would roll out a moving average filter (beware of overflow and aliasing!), few would pull their Mitra and Proakis from the bookshelves, looking up Butterworth again. But there...