engineering recuitment GATE EE 2023-24 Test Series Signals and Systems Linear Time Invariant Systems Properties of LTI Systems
What is the convolution integral c(t) for a system with input x(t) and impulse response h(t), where x(t) = u(t - 1) - u(t - 3) and h(t) = u(t) - u(t - 2) ?
1
\(c(t) = \left\{\begin{matrix} 0& t < 1 \\\ t - 1, & 1 \le t < 3 \\\ 5 - t, &3 \le t < 5 \\\ 0, & t \ge 5 \end{matrix} \right.\)
2
\(c(t) = \left\{\begin{matrix} 0& t < 1 \\\ t - \dfrac{1}{2}, & 1 \le t < 2 \\\ \dfrac{3}{2} - t, &2 \le t < 5 \\\ 0, & t \ge 5 \end{matrix} \right.\)
3
\(c(t) = \left\{\begin{matrix} 0& t < 1 \\\ 5-t, & 1 \le t < 4 \\\ 0, & t \ge 4 \end{matrix} \right.\)
4
\(c(t) = \left\{\begin{matrix} 2& 1 \le t \le 2 \\\ 1, & 3 \le t < 5 \\\ 0, & \rm{otherwise} \end{matrix} \right.\)