GATE EC 2022 Set 1 — Question 46
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Question
The outputs of four systems ( and ) corresponding to the input signal , for all time , are shown in the figure.
Based on the given information, which of the four systems is/are definitely NOT LTI (linear and time-invariant)?
Correct answer
(C) S₃; (D) S₄
Solution
An LTI (Linear Time-Invariant) system cannot produce frequencies at the output that are not present in the input signal.
1.For system , the input is (frequency ) and the output is (frequency ). Since a new frequency is generated, is definitely NOT LTI.
2.For system , the input is and the output is . This output contains a DC component () and a second harmonic (), neither of which were in the input. Thus, is definitely NOT LTI.
3.Systems and could potentially be LTI (e.g., could be a gain of and could be a phase shift of radian).
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