$(18$ points$)$ Sampling with alternating impulse train

The figure shown below gives a system in which the sampling signal is an impulse train with alternating sign. The Fourier transform of the input signal is as indicated in the figure.

Figure $1$: Sampling with alternating impulse train

$($a$)(6$ points$)$ For sketch the Fourier transform of $x_p(t)$ and $y(t).$

$($b$)(4$ points$)$ For determine a system that will recover $x(t)$ from $x_p(t).$

$($c$)(4$ points$)$ For determine a system that will recover $x(t)$ from $y(t).$

$($d$)(4$ points$)$ What is the maximum value of $$ in relation to ${}_m$ for which $x(t)$ can be recovered from either $x_p(t)$ or $y(t).$