GATE EC 2015 Set 2 — Question 61
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 ProcessesCommunications
Communications → Random Processes → Autocorrelation & PSD
Last updated
Question
is an independent and identically distributed (i.i.d.) random process with equally likely to be or . is another random process obtained as . The autocorrelation function of , denoted by , is
Correct answer
(B) [figure] width=80% align=center showing impulses at k=-1, 0, 1 with heights 0.5, 1.25, 0.5 respectively]
Solution
Given is an i.i.d. process with . Thus, and . The autocorrelation of is .The process is defined as . The autocorrelation function is:Substituting :This corresponds to impulses at with height , and at with height . This matches the plot in option (B).
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…