GATE EC 2020 Set 1 — Question 34
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Communications → Random Processes → Filtering Through LTI Systems
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Question
The random variable and is a real white Gaussian noise process with two-sided power spectral density , for all . The variance of is ______.
Correct answer
6 to 6
Solution
The random variable is defined as:Since is a zero-mean white Gaussian noise process, . The variance of is:For white noise, the autocorrelation function is .The inner integral is for .Thus, the variance of is .
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