GATE EC 2022 Set 1 — Question 23
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Question
The frequency response 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 .Statement II: For any wide-sense stationary input process with power spectral density , the output power spectral density obeys for .Which one of the following combinations is true?
Correct answer
(C) Statement I is incorrect, Statement II is correct
Solution
Statement I is incorrect because the figure only provides the magnitude response . A pure delay system requires a specific linear phase response (), which is not specified here. Magnitude alone does not define a pure delay system.Statement II is correct because for an LTI system, the relationship between input and output power spectral densities is . Since the figure shows for the range , it follows that in that range.
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