The image you provided presents an example of finding the Fourier transform of a rectangular pulse. Let's break down the components of the solution shown in the image:

1. Definition of $x(t)$: The function is a rectangular pulse defined by:

   \begin{cases} 1 & \text{for } |t| < \frac{T_p}{2} \\ 0 & \text{for } |t| \geq \frac{T_p}{2} \end{cases}$$ This is equivalent to the **rectangular function** or **rect(t/Tp)**.

2. Fourier Transform: The solution shows the Fourier transform formula applied to this function: $X(j\omega) = \int_{-\infty}^{\infty} x(t)e^{-j\omega t} dt$ Here, the limits of integration are adjusted according to the function being non-zero only within the range $-\frac{T_p}{2} \leq t \leq \frac{T_p}{2}$. Hence the integral becomes: $X(j\omega) = \int_{-\frac{T_p}{2}}^{\frac{T_p}{2}} e^{-j\omega t} dt$

3. Solving the Integral: The Fourier transform of the rectangular pulse is solved through the integration, leading to a well-known result: $X(j\omega) = T_p \cdot \text{sinc} \left( \frac{\omega T_p}{2} \right)$ where $\text{sinc}(x)$ is the normalized sinc function defined as: $\text{sinc}(x) = \frac{\sin(\pi x)}{\pi x}$

The resulting Fourier transform shows the characteristic shape of the sinc function, which is often seen for pulse signals.

Would you like further details on any of these steps or the properties of the Fourier transform for this example?