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A real-valued signal $x(t)$ limited to the frequency band $\mid f \mid \leq \frac{W}{2}$ is passed through a linear time invariant system whose frequency response is $$H(f)  = \begin{cases} e^{-j 4 \pi f}, & \mid f \mid \leq \frac{W}{2} \\ 0, & \mid f \mid > \frac{W}{2} \end{cases}.$$ The output of the system is

  1. $x(t+4)$
  2. $x(t-4)$
  3. $x(t+2)$
  4. $x(t-2)$
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