I am currently studying Fourier Series (on my own). I am using a few different references/sources. Some are more trying to give an intuition about Fourier Series and others are more rigorous.
Generally in references where explanation are not that rigorous, there is often an attempt at explaining the principle behind Fourier series, as making the signal resonate with an harmonic oscillator. Where if the signal "contains" that harmonic then the Fourier coefficient for this harmonic is different than 0 and 0 otherwise (I simplify).
My problem with this approach is that as I get deeper in the equations (again I am on my own so if I could ask a teacher probably he/she would answer this question), I really don't see the computation of the Fourier coefficient has something that has anything to do with the principle of an oscillator. The coefficients are an integral of the product of two functions. For me an oscillation is when you add up two waves together and get constructive or destructive interference.
I have seen the term "harmonic oscillator" being used in quite a few documents in which they were talking about Fourier series as well but:
1) I am not sure there's a direct connection. If there's one, could you please briefly tell me which one it is.
2) I don't think interpreting the principle by which a signal oscillates with a particular harmonic to explain the principle of Fourier series is a particularly accurate thing to say (at least it is misleading). I would like to know what experts think?