GATE EC 2016 Set 3 — Question 59
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumAutocorrelation & PSDRandom ProcessesCommunicationsFiltering Through LTI Systems
Communications → Random Processes → Autocorrelation & PSD
Last updated
Question
A wide sense stationary random process passes through the LTI system shown in the figure. If the autocorrelation function of is , then the autocorrelation function of the output is equal to
Correct answer
(B) 2R_X(τ) - R_X(τ - T₀) - R_X(τ + T₀)
Solution
From the block diagram, the output is given by:
The autocorrelation function of the output is defined as:
Expanding the product:
Using the linearity of expectation and the definition of for a WSS process:
Thus, option (B) is correct.
The autocorrelation function of the output is defined as:
Expanding the product:
Using the linearity of expectation and the definition of for a WSS process:
Thus, option (B) is correct.
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 Random Processes
2026 Set 1 Q22Consider a discrete memoryless source with an alphabet of four source symbols. is a…2026 Set 1 Q32A wireless digital transmission scheme is using -QAM over an additive white Gaussian noise…2026 Set 1 Q44A QPSK modulated signal from an additive white Gaussian noise (AWGN) channel is received with an…2026 Set 1 Q55Let the relevant bandwidth () of a digital communication system be and…2026 Set 1 Q57Consider a real, narrowband signal where the maximum…