White Gaussian noise of double-sided power spectral density 1 W/Hz is passed through a filter with frequency response function H(f) = (1 +j2πf)-1.
(a) What is the power spectral density, SY(f), of the output process?
(b) What is the auto correlation function, RY (τ), of the output process?
(c) What is the mean of the output process?
(d) What is the variance of the output process?
(e) Is the output process stationary?
(f) What is the first-order pdf of the output process?
(g) Comment on the similarities and dissimilarities of the output process and the random process considered in Example 7.2.
