Part $2$: Signal Construction

Question $3$: $(6$ marks$)$

Express each of the following signals using step and ramp functions. Verify your answer.

Question $4$: $(3$ marks$)$

Repeat Part $2$ Question $1$ above by expressing all signals by using step functions only.

Hint: The transformation $r(t-t_0)=(t-t_0)u(t-t_0)$ may be useful.

Part $3$: Signal Representation using Even and Odd Functions

Question $5$: $(6$ marks$)$

For each of the following signals, express the signal using its even function $x_c(t)$ and odd function ${?}^{x_o(t)}.$ Then, sketch the original signal $x^{(t)},x_e(t),$ and $x_o(t).$

$($a$)x_1(t)=u(t-1)-u(t-3).$

$($b$)x_2(t)=u(t+3)-u(t+1).$

$($c$)x_3(t)=2u(t+4)-2u(t+2).$