GATE EC 2025 Set 1 — Question 17
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Question
Consider the discrete-time system below with input and output . In the figure, and denote the impulse responses of LTI Subsystems 1 and 2, respectively. Also, is the unit impulse, and .Assuming , the overall system (denoted by the dashed box) is _______.
Correct answer
(D) nonlinear and time variant
Solution
Let the signal after the first adder be . The output of Subsystem 2 is . The final output is .
1.Linearity: For , . Since and , for zero input. A linear system must have zero output for zero input. Thus, the system is nonlinear.
2.Time-Invariance: If the input is shifted to , the output becomes . However, the shifted output is . Since the additive term is a fixed signal that does not shift with the input, . Thus, the system is time-variant.
Therefore, the system is nonlinear and time variant (D).Continue learning with Success Tracker
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