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Consider a discrete-time linear time-invariant (LTI) system $\boldsymbol{S}$, where
$$ y[n]=\boldsymbol{S}\{x[n]\} $$

Let
$$ \boldsymbol{S}\{\delta[n]\}=\left\{\begin{array}{cc} 1, & n \in\{0,1,2\} \\ 0, & \text { otherwise } \end{array}\right.$$

where $\delta[n]$ is the discrete-time unit impulse function. For an input signal $x[n]$, the output $y[n]$ is

  1. $x[n]+x[n-1]+x[n-2]$
  2. $x[n-1]+x[n]+x[n+1]$
  3. $x[n]+x[n+1]+x[n+2]$
  4. $x[n+1]+x[n+2]+x[n+3]$

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