Ethan's Notes

    Unit Rectangle

    #Math

    $$

    \text{rect}(t)=\begin{cases}
    1, & \lvert t\rvert\leq \frac{1}{2} \\0, & \text{else}
    \end{cases}
    $$

    $$

    \text{rect}_{\Delta}(t)=\begin{cases}
    \frac{1}{\Delta}, & \lvert t\rvert\leq \frac{\Delta}{2} \\0, & \text{otherwise}
    \end{cases}
    $$

    • $\displaystyle \Delta$ is the rectangle width

    $\displaystyle \mathcal{F}[\text{rect}(t/T)]=T\text{ sinc}(\omega T /2\omega)$