1) (30p) "x(t/3-2)" is given below in terms of u(t), \( \mathrm{r}(\mathrm{t}) \) and \( \delta(t) \),
\[
x(t / 3-2)=-3 r(t-2)+2 u(t-3)+\delta\left((6 t+9)+t^{2}\right)+2 \delta(t-5)-3 r(t-5)
\]
a. please PLOT " \( x(t) " \)
b. please PLOT " \( x(3 t+1)+2 " \)

Answer

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Answer

\( x(3t+1)+2= -3r(3t-1) + 2u(3t-2) + \delta(6(3t+1)+9 + (3t+1)^2) + 2\delta(3t-4) -3r(3t-4)+2 \)

Steps

Step 1 ：\( x(t) = -3r(t-2) + 2u(t-3) + \delta(6t+9 + t^2) + 2\delta(t-5) -3r(t-5) \)

Step 2 ：\( x(3t+1) = -3r((3t+1)-2) + 2u((3t+1)-3) + \delta(6(3t+1)+9 + (3t+1)^2) + 2\delta((3t+1)-5) -3r((3t+1)-5) \)

Step 3 ：\( x(3t+1)+2= -3r(3t-1) + 2u(3t-2) + \delta(6(3t+1)+9 + (3t+1)^2) + 2\delta(3t-4) -3r(3t-4)+2 \)