Consider a white Gaussian noise process 𝑁(𝑡) with two-sided power spectral density 𝑆𝑁

September 28, 2023

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Q. Consider a white Gaussian noise process 𝑁(𝑡) with two-sided power spectral density 𝑆_𝑁 (𝑓) = 0.5 W/Hz as input to a filter with impulse response 0.5𝑒^−𝑡2/2 (where 𝑡 is in seconds) resulting in output 𝑌(𝑡). The power in 𝑌(𝑡) in watts is

(A) 0.11 (B) 0.22 (C) 0.33 (D) 0.44

Ans: 0.22

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Consider a white Gaussian noise process 𝑁(𝑡) with two-sided power spectral density 𝑆𝑁

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Determine the correctness (or otherwise) of the following Assertion [A] and the Reason [R]

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