GATE EE 2025 Set 1 — Question 42
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Signals & Systems → LTI Systems → Impulse Response & Convolution
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Question
The continuous-time unit impulse signal is applied as an input to a continuous-time linear time-invariant system 𝑺. The output is observed to be the continuous-time unit step signal . Which one of the following statements is true?
Correct answer
(B) It is possible to find a bounded input signal which when applied to 𝑺 results in an unbounded output signal.
Solution
The impulse response of the system is .
A system is BIBO (Bounded-Input Bounded-Output) stable if and only if its impulse response is absolutely integrable: .
For this system, . Thus, the system is unstable.
An unstable system means there exists at least one bounded input that produces an unbounded output. For example, if (which is bounded), the output is , which is unbounded as . Therefore, statement (B) is true.
A system is BIBO (Bounded-Input Bounded-Output) stable if and only if its impulse response is absolutely integrable: .
For this system, . Thus, the system is unstable.
An unstable system means there exists at least one bounded input that produces an unbounded output. For example, if (which is bounded), the output is , which is unbounded as . Therefore, statement (B) is true.
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