Question $1$:

Do the reflection and the time$-$shifting operations commute? That is$,$ do the two block diagrams in Figure $1$ provide

identical signals $($i$.$e$.,$ is $y(t)$ equal to $z(t)?$ To provide an answer to this consider the signal $x(t)$ shown in Figure $??.$

Reflect $x(t)$ to get $v(t)=x(-t)$ and then shift it to get $y(t)=v(t-2).$ Then consider delaying $x(t)$ to get $w(t)=x(t-2),$

and reflecting it to get $z(t)=w(-t).$ Perform each of these operations on $x(t)$ to get $y(t)$ and $z(t)$; plot them and

compare these plots. What is your conclusion? Explain

Figure $1$: Question $1$