Identifying common periodic waveforms (square, sine, sawtooth, …)

Question

Without any user interaction, how would a program identify what type of waveform is present in a recording from an ADC?

For the sake of this question: triangle, square

Answer 1

Do an FFT, find the odd and even harmonic peaks, and compare the rate at which they decrease to a library of common waveform.. peak... ratios.