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The frequency response $H(f)$ of a linear time-invariant system has magnitude as shown in the figure.

Statement $\text{I}:$ The system is necessarily a pure delay system for inputs which are bandlimited to $- \alpha \leq f \leq \alpha.$

Statement $\text{II}:$ For any wide-sense stationary input process with power spectral density $S_{x}(f),$ the output power spectral density $S_{y}(f)$ obeys $S_{y}(f) = S_{x}(f)$ for $- \alpha \leq f \leq \alpha.$

Which one of the following combinations is true?

1. Statement $\text{I}$ is correct, Statement $\text{II}$ is correct
2. Statement $\text{I}$ is correct, Statement $\text{II}$ is incorrect
3. Statement $\text{I}$ is incorrect, Statement $\text{II}$ is correct
4. Statement $\text{I}$ is incorrect, Statement $\text{II}$ is incorrect