GATE EE 2015 Set 2 — Question 44
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumLTI, Causal & Stable SystemsLTI SystemsSignals & Systems
Signals & Systems → LTI Systems → LTI, Causal & Stable Systems
Last updated
Question
For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the following statements is TRUE?
Correct answer
(D) The unit step response will be bounded.
Solution
A linear time-invariant (LTI) system is Bounded-Input Bounded-Output (BIBO) stable if and only if its impulse response is absolutely integrable: .
- (A) is incorrect because the condition is absolute integrability, not just integrability.
- (B) is incorrect because a stable system can have an infinite duration impulse response (e.g., ).
- (C) is incorrect because the step response of a stable system is bounded but not necessarily absolutely integrable. For example, if , , which is bounded but its integral from 0 to diverges.
- (D) is correct because by the definition of BIBO stability, every bounded input (such as a unit step) must produce a bounded output.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE EE question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
Also appeared in
More questions on LTI Systems
2026 Set 1 Q11Consider the infinite-length, discrete-time sequence , where is an integer.…2026 Set 1 Q12Let be any continuous-time periodic signal with period . It is sampled uniformly with a…2026 Set 1 Q14Consider the following differential equation:…2026 Set 1 Q36A time-limited waveform is specified as follows:…2025 Set 1 Q20Consider a discrete-time linear time-invariant (LTI) system , where…