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

 

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

 Statement I: The system is necessarily a pure delay system for inputs which are bandlimited to −𝛼≤𝑓≤𝛼.

Statement II: For any wide-sense stationary input process with power spectral density 𝑆H(𝑓), the output power spectral density 𝑆x(𝑓) obeys 𝑆y(𝑓)=𝑆x(𝑓) for −𝛼≤𝑓≤𝛼. Which one of the following combinations is true? 


Answer: Option 1. Both Statements are correct


Solution:

System has magnitude 1 and bandlimited, so statement 1 is true.

𝑆y(𝑓)=𝑆x(𝑓) is true as System has magnitude 1

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