the difference between DFT (discrete fourier transform) and DFS (discrete fourier series)

Question

To me they seem like the same thing, so I don’t get why they’re considered different.

To be clear, I’m not talking about Discrete-time Fourier Transform

In: 3

Answer 1

What’s considered the same in one context can be considered different in another context. Mathematically the concepts are close enough that they are basically the same, but in engineering context the specific implementation is important enough to distinguish them.

That’s like people distinguish between Fourier transform for periodic functions on the real line, versus Fourier transform on a circle. You don’t hear about Fourier transform on a circle in a signal processing context, because time isn’t a circle; but mathematically they are basically the same thing.