Let's suppose I have a signal F(t) that is periodic, with two periodicities P1 and P2, with P1>P2. Suppose that I know the values of the two periodicities.
Using the Fast Fourier transform I can show the two values as peaks in a power spectrum. Now, let's suppose the second periodicity P2 (the faster one), has exactly the same value as the first harmonic of the fundamental value, or P2=2×P1. This means that I will be not able to distinguish it by using the power spectrum, at least not by looking at the frequency of the peak.
My question is: is there a way to separate the contributions in such a case? For example, is it possible to predict the power of the first harmonic, so that the difference between the predicted power and the observed power of the harmonic peak gives a result significant enough (i.e., greater than 3σ) to say that the first harmonic also "contains" the contribution from a periodicity?
Please, be plain I am not experienced in this (nonetheless some equations/numbers are ok).