Question $2($ULO$4)$

A ground penetrating radar $($GPR$)$ is to be implemented to study to detect sink holes in the city. It emits radio waves of $300$ MHz and $800$ MHz $.$ The sampling frequency of $2\mathrm{.}4$ GHz will be used to sample signals before being supplied to this filter.

a$)$ Design a $7-$point FIR filter that accepts or passess signals of $300$ MHz so that the $300$ MHz echo. Provide the impulse response $\backslash (\backslash$mathrm$\{$h$\}[\backslash$mathrm$\{$n$\}]\backslash )$ and plot the magnitude response.

b$)$ Design an IIR filter that passes $800$ MHz so that the GPR can detect the $800$ MHz echo. Provide the transfer function and plot the magnitude response.