# Compute output of a LTI system

Is it possible to compute the output from one linear time invariant system which unit impulse sequence is:

$$h(n) = \left(\frac{1}{3}\right)^nu(n)$$

and the entry in the system is:

$$x(n)=u(n)-u(n-2)$$

where $u(n)$ is the unit step sequence?

• Yes, but you subtract two steps. The first one goes up and starts at $n=0$, and the second one goes down (because of the negative sign) and starts at $n=2$, so your input signal can be written as $x(n)=\delta(n)+\delta(n-1)$. – Matt L. Jun 27 '14 at 15:01
• Yes, and the same for $x(1)$. For all other values of $n$, $x(n)$ is zero. – Matt L. Jun 27 '14 at 16:07
$$x(n)=\delta(n)+\delta(n-1)\Longrightarrow y(n)=h(n)+h(n-1)$$