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$\mathrm{X(t)}$ is a stationary random process with autocorrelation function $R_X(\tau)=\exp \left(-\pi \tau^2\right)$. This process is passed through the system shown below. The power spectral density of the output process $\mathrm{Y}(\mathrm{t})$ is

- $(4 \pi^2 f^2+1) \exp (\pi f^2)$
- $(4 \pi^2 f^2-1) \exp(\pi f^2)$
- $(4 \pi^2 f^2+1) \exp (-\pi f)$
- $(4 \pi^2 f^2-1) \exp (-\pi f)$