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$\text{X}(t)$ is a stationary process with the power spectral density $\text{S}_{\text{X}}(f)>0$ for all $f$. The process is passed through a system shown below.

Let $\text{S}_\text{Y}(f)$ be the power spectral density of $\text{Y}(t)$. Which one of the following statements is correct?

  1. $\text{S}_\text{Y}(f)>0$ for all $f$
  2. $\text{S}_\text{Y}(f)=0$ for $|f|>1 \; \mathrm{kHz}$
  3. $\text{S}_\text{Y}(f)=0$ for $f=n f_{0}, f_{0}=2 \; \mathrm{kHz}, n$ any integer
  4. $\text{S}_\text{Y}(f)=0$ for $f=(2 n+1) f_{0} , f_{0}=1 \; \mathrm{kHz}, n$ any integer

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