# Figuring out impulse response

I need a little help with figuring out this problem. I understand most of it but the main part I don't understand is:

The signal $h''(t)+2*h'(t)+2*h(t)$ is of finite duration.

In the problem we are supposed to be find $H(s)$, we know it is a rational, causal, stable LTI system. With hints from the teacher I've gotten $H(s)=A*s/p(s)$. Now he said that figuring out this part will allow us to find $p(s)$, but I'm not sure on how. I guess the real part I'm confused about is what it means to be of finite duration.

Tyler

EDIT1: The other hints to finding $H(s)$

$H(1)=0.2$ (Will allow me to find A)

When input is unit step $U(t)$ the output is absolutely integrable ($H(s)=(s^n)*q(s)/p(s):n>0$)

When input is ramp $t*U(t)$ the output is not absolutely integrable($n=1$)

$H(s)$ has exactly one zero at infinity.($q(s)=1$)

• Is it possibile that $p(s)=s^2+2s+2$ ? Is the input an impulse? Are the initial conditions zero? – FdT Feb 20 '14 at 10:41
• The problem says nothing about initial conditions. I'll add the rest of the problem maybe that'll help – TylerM Feb 20 '14 at 13:30