TIFR ECE 2012 | Question: 6

Question

Let $u(t)$ be the unit step function that takes value $1$ for $t \geq 0$ and is zero otherwise. Let $f(t)=e^{-t} u(t)$ and $g(t)=u(t) u(1-t)$. Then the convolution of $f(t)$ and $g(t)$ is

• A. $(e-1) e^{-t} u(t)$
• B. $1-e^{-t}$ for $0 \leq t \leq 1,(e-1) e^{-t}$ for $t \geq 1$ and zero otherwise
• C. $t e^{-t} u(t)$
• D. The convolution integral is not well defined
• E. None of the above