Question

The impulse response of a continous time system is given by $h\left(t\right)=\delta (t-1)+\delta (t-3)$. The value of the step response at t = 2 is

• A. 1
• B. 3
• C. 0
• D. 2

Answer 1

The correct option is A 1

Step response = Integration of impulse response

$\int \delta (t-1)=u(t-1)$

$\int \delta (t-3)=u(t-3)$

$\text{at t = 2}$
$\text{y(2) = 1}$

$\text{Alternate solution:}$
For step response, impulse response can be integrated.
$\Rightarrow \text{y(t) = u(t -1) + u(t - 3)}$

$\text{y(2) = u(1) + u(-1)}$

$\text{= 1 + 0 = 1}$