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

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