GATE EC 2016 Set 3 — Question 41
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumRegion of ConvergenceDiscrete-Time SignalsSignals & Systems
Signals & Systems → Discrete-Time Signals → Region of Convergence
Last updated
Question
The ROC (region of convergence) of the -transform of a discrete-time signal is represented by the shaded region in the -plane. If the signal , then the ROC of its -transform is represented by
Correct answer
(D) [figure]
Solution
The given discrete-time signal is for .
We can decompose this signal into its causal and anti-causal parts:
We can decompose this signal into its causal and anti-causal parts:
1.For the causal part , the -transform is and its ROC is .
2.For the anti-causal part , the -transform is and its ROC is .
The ROC of the total signal is the intersection of the individual ROCs:Since there is no region in the -plane that satisfies both and , the intersection is an empty set. Therefore, the -transform of does not converge for any value of , and the ROC does not exist.Hence, option (D) is the correct representation.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 EC 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.
More questions on Discrete-Time Signals
2026 Set 1 Q13The Laplace Transform of the signal is given by which of the following…2026 Set 1 Q15Two analog signals and ( in second), are sampled at a rate Hz,…2026 Set 1 Q16The response of a discrete time system obeys the following relation:…2026 Set 1 Q37The continuous time signal is real, periodic with period and satisfies the Dirichlet…2026 Set 1 Q43Consider a real signal , , such that for , …