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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

1. 0.11
2. 0.22
3. 0.33
4. 0.44

Correct answer: 0.22

Solution

The power in the output Y(t) can be calculated using the formula that relates the power spectral density of the input noise and the filter's impulse response. The filter's impulse response has a corresponding frequency response that modifies the input noise's power spectral density, resulting in an output power of 0.22 watts.

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