Identifying / generating a waveform?

Question

I would like to code something that could take some sort of input and identify it as a square wave, triangle wave, or some sort of waveform. I also need some way of generating said waves.

I do have experience with C/C++, however, I'm not sure how I would approach simulating all of this. Eventually, I would like to translate it to a microcontroller program for reading its analog input to determine the waveform.

EDIT: Sorry; I should have mentioned it would be at a known frequency and the amplitude should be unknown.