[analog31]

My only quibble is that the article is about the discrete Fourier transform.

[shash]

It’s usually easier to explain the dft. and easier to do a periodic function than a totally arbitrary sequence.

[krackers]

I've actually found the opposite, it's easier to conceptually understand the continuous FT, then analyze the DTFT, DFT, and Fourier Series as special cases of applying a {periodic summation, discrete sampling} operator before the FT.