\section{Question 1}
Find the Fourier transform of the following signal. (Hint: make good use of the function)
\begin{figure}[h]
\centering
\caption{Time-domain representation of the signal in Question 1.}
\end{figure}
\textbf{Answer: }
We commence our investigation by deriving the Fourier transform of the scaled function .
(1)
Leveraging the shift relation in Fourier transform,
we can extend the derivation to a generalized form for :
Thus, employing this generalized form, we deduce that (\Cref{fig:fourier_transform_2D})
\begin{figure}[h]
\centering
\hbox{
\hspace{1cm}
}
\caption{Fourier Transform of : Real and Imaginary Parts}
\label{fig:fourier_transform_2D}
\end{figure}