GATE EC 2022 Set 1 — Question 56
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.NAT+2 / -0MediumLTI System PropertiesLTI SystemsSignals & Systems
Signals & Systems → LTI Systems → LTI System Properties
Last updated
Question
The outputs of four systems (, and ) corresponding to the input signal , for all time , are shown in the figure.
Based on the given information, which of the four systems is/are definitely NOT LTI (linear and time-invariant)?
Based on the given information, which of the four systems is/are definitely NOT LTI (linear and time-invariant)?
Correct answer
0.57 to 0.61
Solution
An LTI (Linear Time-Invariant) system has two fundamental properties:
1.Linearity: If input produces output and produces , then produces .
2.Time-invariance: If input produces output , then produces .
For a sinusoidal input , an LTI system can only change its amplitude and phase, but not its frequency. The output must be of the form .Let's analyze each system with input (frequency rad/s):- System : Output is . This is an amplitude scaling by -1 (or a phase shift of ). The frequency remains rad/s. An LTI system can produce this. So, could be LTI.
- System : Output is . This is a time-shifted version of the input. The frequency remains rad/s. An LTI system can produce this (e.g., a system with a phase shift). So, could be LTI.
- System : Output is . The frequency of the output is rad/s, which is different from the input frequency. An LTI system cannot change the frequency of a sinusoidal input. Therefore, is definitely NOT LTI.
- System : Output is . Using the trigonometric identity , we see that the output contains a DC component () and a component at frequency rad/s. An LTI system cannot introduce a DC component from a zero-mean sinusoidal input, nor can it change the frequency of the input sinusoid. Therefore, is definitely NOT LTI.
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 LTI Systems
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 , …