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