Figure $1$: A continuous$-$time signal $x(t)$

Problem $1[$Continuous$-$Time Signal $-25$ points$]$: Consider the continuous$-$time signal $x(t)$ given in Figure $1.$

Give the formula that computes the even part of $x(t).$

Determine and sketch the even part of $x(t).$ Show your work.

Give the formula that computes the odd part of $x(t).$

Determine and sketch the odd part of $x(t).$ Show your work.

Provide a method for checking whether both computations above $($in $2.$ and $4.)$ are correct.

Figure $2$: A discrete$-$time signal $x[n]$

Problem $2[$Discrete$-$Time Signal $-25$ points$]$: Consider the discrete$-$time signal $x[n]$ given in Figure $2.$

Determine and sketch the even part of $x[n].$ Show your work.

Determine and sketch the odd part of $x[n].$ Show your work.

Would it be possible to reproduce the discrete$-$time signal $x[n]$ from its even and odd parts computed earlier? Show your work.

$1$