A much less well known fact about the FFT (or the DFT) is that it is also exhibits a brickwall (rectangular) response. This can manifest itself when using zero padding in the frequency domain for upsampling, but is also the reason for artifacts when FFTing a nonperiodic window.

It's used in OFDM, where the subchannels are generated by an FFT and have a sinc shape (the Impulse response of the FFT) in the frequency domain.