Eli Bendersky's website Today I was asked by a collegue at work about a Fourier series decomposition. It's been almost a year since I finished Uni, and about 2 years since I last saw Fourier series, the title of this journal entry is understandable.
It's funny to get back to remember these things, because I see how I still have grasp of the concepts, thought it's quite vague.
The actual question was whether some periodic signal, in its Fourier series decomposition, will have harmonics of frequencies lower than its own. My answer was "no", bar the "DC" harmonic. I'm not 100% sure, maybe these harmonics exist but are very small, but surely the main harmonic will be of the signal's frequency, otherwise the overall structure of the signal will be impossible to reproduce.