You are “blurring” the samples because you know your function is NOT a step-function, essentially. So instead of trying to be “super precise” (you cannot), you

You are “blurring” the samples because you know your function is NOT a step-function, essentially. So instead of trying to be “super precise” (you cannot), you “blur” your Fourier transform. It is NOT that but my explanation is morally what you achieve.