GATE EC 2023 Set 1 — Question 26
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Signals & Systems → LTI Systems → Causality & Stability
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Question
Consider a system with input and output . The system is
Correct answer
(B) Non-causal and time varying.
Solution
To determine the properties of the system :
Since , the output at depends on a future value of the input. Therefore, the system is non-causal.
Now, let's look at the shifted output:
Since (because for all ), the system is time-varying.Conclusion: The system is non-causal and time varying. Thus, option (B) is correct.
1.Causality: A system is causal if the output at any time depends only on the input for .
For the given system , let's test a value, say :Since , the output at depends on a future value of the input. Therefore, the system is non-causal.
2.Time Invariance: A system is time-invariant if a time shift in the input results in an identical time shift in the output.
Let the input be . The corresponding output is:Now, let's look at the shifted output:
Since (because for all ), the system is time-varying.Conclusion: The system is non-causal and time varying. Thus, option (B) is correct.
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