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

Let $S_{y}(f)$ be the power spectral density of $Y(t)$. Which one of the following statements is correct?

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