Question

A) Write the mathematical expressions using the switching function for the waveforms below. B) Test your expressions by plotting the waveforms from your expressions using mathematical software. (Include printouts with your homework.) X(t) 30+. 157 N 3 4 5 t[s] -30 1 2

Answer 1

Unit Step function  $u(t)=1$  for  $t\geqslant 0$ and  $u(t)=0$ for .

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Unit Ramp function  $r(t)=t$  for  $t\geqslant 0$ and  $r(t)=0$ for .

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For the given signal:

For  $0\leq t< 1$ , $x_{1}(t)=15(u(t)-u(t-1))$

For  $1\leq t<3$ , $x_{2}(t)=15r(-t+3).u(t-1)$

For  $3\leq t<5$ ,  $x_{3}(t)=-30u(t-3)+30u(t-5)$

$\therefore$ Finally, $x(t)=x_{1}(t)+x_{2}(t)+x_{3}(t)$

desmos E Unit Step Function Create Account or -60 O u(t) = {t<0 : 0, t 20 : 1} 50 O r(t) = {t<0: 0, t >0 : 1} 40 O m = 15(1(1) –u(:– 1)) 30 n= 15r(-t+ 3)u(t– 1)+m N y =n- 30u (t – 3)+30u(t- 5) 20- 10 10 -2 -1 6. -10 -20- -30- -40 powered by desmos