Given a continuous LTI system with transfer function $$H(s)= -\frac{2s}{(s+6)(s+2)}$$
- Plot the location of the pole(s) and zero(s)
- Find all possible regions of convergence
- From the problem above find the impulse response
Here's my attempt
- The poles are $s_1=-6$ and $s_2=-2$ and the zero is $s_3=0$
- The all possible roc-s are
- Using inverse laplace transform I found $h(t)=e^{-2t}-3e^{-6t}$. For the right-sided signal I multiply $h(t)$ with $u(t)$ and I got $h_{RS}(t)=(e^{-2t}-3e^{-6t})u(t)$ and for the left-sided signal I multiply $h(t)$ with $u(-t)$ and I got $h_{LS}(t)=(e^{-2t}-3e^{-6t})u(-t)$.
My confusion is at the two-sided signal. My solution is $h_{TS}(t)=e^{-2t}-3e^{-6t}$ and my friend's solution is $h_{TS}(t)=-e^{-2t}u(-t) - 3e^{-6t}u(t)$. When I plotted the signal both are a two-sided signal. Since my professor didn't submit the solution we didn't know who's right or wrong.
Thank you.