GATE EE 2017 Set 1 — Question 7
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumMemory & InvertibilityLTI SystemsSignals & SystemsLTI, Causal & Stable Systems
Signals & Systems → LTI Systems → LTI, Causal & Stable Systems
Last updated
Question
Consider the system with following input-output relationwhere, is the input and is the output. The system is
Correct answer
(D) non-invertible and time varying
Solution
To determine the properties of the system :
The delayed output is:
Since for all (specifically when is odd), the system is time-varying.
Since for all odd regardless of the value of , we cannot uniquely recover from . Thus, the system is non-invertible.Therefore, the system is non-invertible and time varying.
1.Time-Invariance: A system is time-invariant if a delay in the input results in an identical delay in the output. Let be the response to :
The delayed output is:
Since for all (specifically when is odd), the system is time-varying.
2.Invertibility: A system is invertible if distinct inputs produce distinct outputs. For odd, , so:
Since for all odd regardless of the value of , we cannot uniquely recover from . Thus, the system is non-invertible.Therefore, the system is non-invertible and time varying.
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.
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…