Problem 2: A zero-mean Gaussian white noise process X(t) is passed through an RC low pass filter as shown below. The power spectral density of the input noise is flat with value of NJ2 for all frequencies. R X(t) Y(t) Evaluate the frequency response of the filter H(f) = Y(f)/X(f) in terms of R and С. Derive an expression for the power spectral density of the output process SAf). Find the mean and variance of the output process Y(t). i. %3D ii.

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Problem 2: A zero-mean Gaussian white noise process X(t) is passed through an
RC low pass filter as shown below. The power spectral density of the input noise
is flat with value of NJ2 for all frequencies.
X(t)
Y(t)
i.
Evaluate the frequency response of the filter H(f) = Y(f)/X(f) in terms of R and
С.
ii.
Derive an expression for the power spectral density of the output process
SKf).
Find the mean and variance of the output process Y(t).
iii.
Transcribed Image Text:Problem 2: A zero-mean Gaussian white noise process X(t) is passed through an RC low pass filter as shown below. The power spectral density of the input noise is flat with value of NJ2 for all frequencies. X(t) Y(t) i. Evaluate the frequency response of the filter H(f) = Y(f)/X(f) in terms of R and С. ii. Derive an expression for the power spectral density of the output process SKf). Find the mean and variance of the output process Y(t). iii.
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