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A wide sense stationary random process $X(t)$ passes through the LTI system shown in the figure. If the autocorrelation function of $X(t)$ is $R_X(\tau)$, then the autocorrelation function $R_Y(\tau)$ of the output $Y(t)$ is equal to

  1. $2R_X(\tau)+R_X(\tau-T_0)+R_X(\tau+T_0)$
  2. $2R_X(\tau)-R_X(\tau-T_0)-R_X(\tau+T_0)$
  3. $2R_X(\tau)+2R_X(\tau- 2T_0)$
  4. $2R_X(\tau)-2R_X(\tau- 2T_0)$
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