We consider the function $\varphi$ defined on $\mathbb{R}$ by
$$\forall x \in \mathbb{R}, \quad \varphi(x) = \begin{cases} 1 & \text{if } x \in \left[-\frac{1}{2}, \frac{1}{2}\right] \\ 0 & \text{otherwise} \end{cases}$$
Justify that $\varphi$ belongs to $E_{\mathrm{cpm}}$ and calculate its Fourier transform $\mathcal{F}(\varphi)$.