GATE EC 2015 Set 2 — Question 60
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Communications → Random Processes → Autocorrelation & PSD
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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 with impulses at k=-1, 0, 1 with heights 0.5, 1.25, 0.5 respectively]
Solution
Given that is an i.i.d. random process with .
The mean is .
The autocorrelation of is because it is zero-mean and i.i.d. with unit variance ().The process is defined as .
The autocorrelation function is:Expanding the terms:Substituting :Evaluating for different values of :
The mean is .
The autocorrelation of is because it is zero-mean and i.i.d. with unit variance ().The process is defined as .
The autocorrelation function is:Expanding the terms:Substituting :Evaluating for different values of :
- For :
- For :
- For :
- For :
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