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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

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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 "periodic signals are a subset for all signals" as compared to "all signals are periodic, some just have a period of infinity". That kind of defeats the purpose of having periodicity as a specials case.

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  • $\begingroup$ Hi Hilmar, I just wanted to say thank you for your answer. It makes a bunch of sense to me, The author also said that the $1/2\pi$ term could be put in either side of the equation and it holds no meaning beyond convention and it seems like the same applies here. I hadn't realised it is a philosophical thing and nothing else $\endgroup$ – Mr. Johnny Doe Jan 23 at 13:34

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