The filtering ensures that the shape is known. A triangle wave above half the cutoff frequency becomes a sine wave as filtering removes the harmonics.
73
John KD6OZH
Hmm. That's not quite true. Consider a signal at 4kHz, being sampled at 8kHz. What you'd see is a triangle wave, if you were sampling at the peaks of the incoming signal (if you were sampling at the crossover points, you'd see no signal at all!). How do you tell what the waveform of the signal originally was? You can't...
If you sample your 4kHz signal at 16kHz, you've got four points across each cycle, so at least you can start to get an approximation. If the input signal was a sinewave you might see a sample at a crossing point, then a sample at a peak, then a sample at the next crossing point, then a sample at the next peak. You'd get a roughly sinewave-y signal, if you squint a bit.