Comment by cycomanic

Completely agree the transition between continuous and discrete domains is often glossed over and people use DFT, FT, DTFT and FFT almost interchangeably (I certainly have been guilty of that myself, and you are correct the FFT and DFT are equivalent for this discussion).

An interesting fact (somewhat related to your mentioning of the DTFT) is that one can consider the DFT as a filter with a sinc transfer function. That's essentially how you can understand the spectrum of an OFDM signal. You perform a block based FFT on your input bit/symbol stream, so you have waves at different carriers. However, because the stream is timevarying you essentially get sinc shaped spectra spaced at the symbol rate (excluding cycling prefixes etc.). So your OFDM spectrum is composed of many sincs spaced at fb, which is very squarish which is one of the reasons why OFDM is so advantageous.