Question

If x(t) is signal applied as input to LTI system with impulse response h(t). The output of the system is y(t) then value of $y\left(t\right){|}_{t=5}$ is ______.

• A. 75

Answer 1

The correct option is A 75
We know that

y(t) = ${\int }_{-\infty }^{\infty }x(t-\tau )h\left(\tau \right)d\tau$

and
y(5) = ${\int }_{-\infty }^{\infty }x(5-\tau )h\left(\tau \right)d\tau$

x(t) is u(t) and x(5 - $\tau$ ) will be u(5 - $\tau$) that is

also $h\left(\tau \right)$ is same as given in question and x(5- $\tau )$ . h($\tau )$ will be

so, $y\left(5\right)={\int }_{-\infty }^{\infty }x(5-\tau )h\left(\tau \right)d\tau =75$