Why is the Fourier Series a special case of the Fourier Transform and not the other way around? I was reading a text book on the frequency domains in signal processing and my understanding is that the Fourier Transform considers signals that are a-periodic in time while the Fourier Series considers periodic signals in time (such as a sum of sinusoids).
But the book clearly mentions that the FS can be seen as a special case of the FT and that doesn't make sense to me.
My understanding is that the FT is a special case of FS where periodicity is just infinity. But the book says its the other way around without providing its own reasoning.
It makes no sense and I can't find answers online
That's more of a philosophical question. It makes no practical difference if you choose one answer over the other.
Personally, I would agree with the author. I find it  mathematically a lot easier to derive the Fourier Series from the Fourier Transform than the other way around. It also makes more sense to me to say &quot;periodic signals are a subset for all signals&quot; as compared to &quot;all signals are periodic, some just have a period of infinity&quot;. That kind of defeats the purpose of having periodicity as a specials case.