Topic: Signals and Systems
A discrete-time LTI system has impulse response $h[n]=\delta[n]+\delta[n-1]$. What is its output $y[n]$ for an input $x[n]=u[n]$?
- A. $u[n]+u[n-1]$
- B. $2u[n]$
- C. $\delta[n]+\delta[n-1]$
- D. $u[n]$
Answer: A. $u[n]+u[n-1]$
Explanation: The output of an LTI system is the convolution of its input and impulse response: $y[n] = x[n] * h[n]$.
$y[n] = x[n] * (\delta[n] + \delta[n-1])$
By the shifting property of the delta function, $x[n] * \delta[n-k] = x[n-k]$.
$y[n] = x[n] + x[n-1]$. Since $x[n] = u[n]$, we have $y[n] = u[n] + u[n-1]$.