$4\mathrm{.}1$ A continuous$-$time signal $x(t)$ has a Fourier transform $x()$ described by the figure below:

$x(t)$ is sampled by a periodic impulse train $p(t)={\displaystyle \underset{n=-}{\overset{}{}}}(t-nT)$ to produce a discrete$-$time signal $x(nT),$ where $T$ is the sampling period $T=\frac{1}{f_s}=\frac{2}{{}_s}.$

a$)$ With its Fourier transform being denoted by $x_p(),$ find its expression. $(4)$

b$)$ If ${}_s=15,$ plot the Fourier transform $x_p()$ of the sampled signal $x(nT).$

c$)$ Is it possible to reconstruct $x(t)$ from the sampled signal $x(nT),$ using a lowpass filter? Explain. $(2)$