GATE EC 2018 Set 1 — Question 38
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Communications → Random Processes → Filtering Through LTI Systems
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Question
Consider a white Gaussian noise process with two-sided power spectral density W/Hz as input to a filter with impulse response (where is in seconds) resulting in output . The power in in watts is
Correct answer
(B) 0.22
Solution
Given:
Input Power Spectral Density (PSD) of white Gaussian noise is W/Hz.
Impulse response of the filter is .The output power of an LTI system with input white noise is given by:Since is constant (white noise), we can apply Parseval's theorem to relate the integral of the squared magnitude of the frequency response to the integral of the squared impulse response:Substituting the given values:Using the standard Gaussian integral identity with :Therefore,The value closest to the calculated result is 0.22. Hence, option (B) is correct.
Input Power Spectral Density (PSD) of white Gaussian noise is W/Hz.
Impulse response of the filter is .The output power of an LTI system with input white noise is given by:Since is constant (white noise), we can apply Parseval's theorem to relate the integral of the squared magnitude of the frequency response to the integral of the squared impulse response:Substituting the given values:Using the standard Gaussian integral identity with :Therefore,The value closest to the calculated result is 0.22. Hence, option (B) is correct.
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