For <math>\operatorname{rect} (x/a)</math>, its Fourier transform is<math display="block">\int_{-\infty}^\infty \operatorname{rect}\left(\frac{t}{a}\right)\cdot e^{-i 2\pi f t} \, dt
=a \frac{\sin(\pi af)}{\pi af} = a\ \operatorname{sinc}_\pi{(a f)}.</math>Note that as long as the definition of the pulse function is only motivated by its behavior in the time-___domain experience, there is no reason to believe that the oscillatory interpretation (i.e. the Fourier transform function) should be intuitive, or directly understood by humans. However, some aspects of the theoretical result may be understood intuitively, as finiteness in time ___domain corresponds to an infinite frequency response. (Vice versa, a finite Fourier transform will correspond to infinite time ___domain response.)
