GATE EE 2024 Set 1 — Question 37
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Signals & Systems → LTI Systems → LTI, Causal & Stable Systems
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Question
The input and the output of a system are related as The system is
Correct answer
(B) linear and time-invariant.
Solution
The system equation can be rewritten as a convolution integral:where the impulse response is .
1.Linearity: Convolution is a linear operation, so the system is linear.
2.Time-Invariance: Since the impulse response is independent of the time at which the input is applied, the system is time-invariant.
3.Causality: Since for , the output at any time depends only on the input for . Thus, the system is causal.
Therefore, the system is linear and time-invariant.Continue learning with Success Tracker
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