0 0 votes Convolution between two functions $f(t)$ and $g(t)$ is defined as follows: $$f(t) * g(t)=\int_{-\infty}^{\infty} f(\tau) g(t-\tau) d \tau$$ Let $u(t)$ be the unit-step function, i.e., $u(t)=1$ for $t \geq 0$ and $u(t)=0$ for $t<0$. What is $f(t) * g(t)$ if $f(t)=\exp (-t) u(t)$ and $g(t)=\sin (t) u(t)$ ? $\frac{1}{2}(\exp (-t)-\sin (t)+\cos (t)) u(t)$ $\frac{1}{2}(\exp (-t)+\sin (t)-\cos (t)) u(t)$ $\frac{1}{2}(\exp (-t)+2 \sin (t)-\cos (t)) u(t)$ $\frac{1}{2}(\exp (-t)+\sin (t)-2 \cos (t)) u(t)$ $\frac{1}{2}(\exp (-t)-\sin (t)+2 \cos (t)) u(t)$ Calculus tifrece2023 engineering-mathematics calculus + – admin 550 views answer comment Share Follow Add Sync Questions Print 0 reply Please log in or register to add a comment.
