GATE EC 2015 Set 3 — Question 62
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Communications → Random Processes → Autocorrelation & PSD
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Question
A random binary wave is given bywhere , is the unit step function and is an independent random variable with uniform distribution in . The sequence consists of independent and identically distributed binary valued random variables with for each . The value of the autocorrelation equals ________.
Correct answer
0.24 to 0.26
Solution
For a random binary wave with pulse and independent bits , the autocorrelation function is given by:
Since are i.i.d. with mean 0 and variance 1 (, ), if and otherwise.
The pulse is for and otherwise.
for .
This results in a triangular function: for .
We need to find :
.
Since are i.i.d. with mean 0 and variance 1 (, ), if and otherwise.
The pulse is for and otherwise.
for .
This results in a triangular function: for .
We need to find :
.
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