Let's suppose I have a signal $F(t)$ that is periodic, with two periodicities $P_1$ and $P_2$, with $P_1 > P_2$. 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 $P_2$ (the faster one), has exactly the same value as the first harmonic of the fundamental value, or $P_2 = 2\times P_1$. 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 $3\sigma$) to say that the first harmonic also "contains" the contribution from a periodicity?