$9$:$14$

:: $4$G $75$

Part $1$: Signal Operations

Question $1$: $(10$ marks$)$

Signal operations may occur in time$-$domain or in amplitudedomain. Time$-$domain operations include time$-$shifting, timescaling, and time$-$reversing while amplitude$-$domain operations include amplitude$-$shifting, amplitude$-$scaling, and amplitudereversing. Consider the sional $x(t)$ helow

Sketch the following pairs side$-$by$-$side in rows and determine the operation$($s$)$ type$($s$)$ occurred:

$($a$)y_1(t)=x(t-2)$ and $y_2(t)=x(t)-2.$

$($b$)y_3(t)=x(2t)$ and $y_4(t)=2x(t).$

$($c$)y_5(t)=x(-t)$ and $y_6(t)=-x(t).$

$($d$)y_7(t)=x(2t-2)$ and $y_8(t)=2x(t)-2.$

$($e$)y_9(t)=x(-2t+2)$ and $y_{10}(t)=-2x(t)+2.$

Question $2$: $(6$ marks$)$

Consider the signal $x(t)$ ac chnown halnwu

Sketch the following signals and determine the signal operation$($s$)$ type$($s$)$:

$($a$)y_1(t)=0\mathrm{.}5x(2t-1).$

$($b$)y_2(t)=x(-t+1)+1.$

$($c$)y_3(t)=-3x(2t+1)+6.$