Question

Consider a signal x(t) as shown below,


x(t) can be represented as,

• A. $0.666r(t+2)-0.666r\left(t\right)+u(t-3)-4u(t-5)$
• B. $1.5r(t+2)-1.5r\left(t\right)+u(t-3)-4u(t-5)$
• C. $1.5r(t+2)-1.5r\left(t\right)+u(t-3)+4u(t-5)$
• D. $0.666r(t+2)-0.666r\left(t\right)+u(t-3)+4u(t-5)$

Answer 1

The correct option is B $1.5r(t+2)-1.5r\left(t\right)+u(t-3)-4u(t-5)$


When slope change occur, we get ramp function and when amplitude change occur, we get unit step function.

ramp function =(final slope -initial slope) . r (t - c.p)

step function =(final amplitude - initial amplitude) . u (t - c.p)

$\therefore x\left(t\right)=(\frac{3}{2}-0).r(t+2)+(0-\frac{3}{2})r\left(t\right)+(4-3).u(t-3)+(0-4).u(t-5)$

$x\left(t\right)=1.5r(t+2)-1.5r\left(t\right)+u(t-3)-4u(t-5)$