$\Delta t$:区間幅
■sin波（正弦）
$$F(\omega)=\displaystyle\int^{\Delta t/2}_{-\Delta t/2} sin(\omega_0 t) \cdot e^{-j\omega t} dt=\displaystyle\int^{\Delta t/2}_{-\Delta t/2} sin(\omega_0 t) [cos(\omega t)-j sin(\omega t)]dt$$
$$=-2j\displaystyle\int^{\Delta t/2}_{0} sin(\omega t) sin(\omega_0 t) dt=j \displaystyle\int^{\Delta t/2}_{0} [cos(\omega+\omega_0)t-cos(\omega-\omega_0)t]dt$$
$$=j[\displaystyle\frac{sin{(\omega+\omega_0) \cdot\frac {\Delta t}{2}}}{\omega+\omega_0}-\displaystyle\frac{sin{(\omega-\omega_0) \cdot\frac {\Delta t}{2}}}{\omega-\omega_0}]$$
■cos波（余弦）
$$F(\omega)=\displaystyle\int^{\Delta t/2}_{-\Delta t/2} cos(\omega_0 t) \cdot e^{-j\omega t} dt=\displaystyle\int^{\Delta t/2}_{-\Delta t/2} cos(\omega_0 t) [cos(\omega t)-j sin(\omega t)]dt$$
$$=2\displaystyle\int^{\Delta t/2}_{0} cos(\omega t) cos(\omega_0 t) dt= \displaystyle\int^{\Delta t/2}_{0} [cos(\omega-\omega_0)t+cos(\omega+\omega_0)t]dt$$
$$=\displaystyle\frac{sin{(\omega-\omega_0) \cdot\frac {\Delta t}{2}}}{\omega-\omega_0}+\displaystyle\frac{sin{(\omega+\omega_0) \cdot\frac {\Delta t}{2}}}{\omega+\omega_0}$$