Question: A filter with frequency response function H(f) = (1 + j2f) -1 is driven by a white-noise process with double-sided power spectral density of 1

A filter with frequency response function H(f) = (1 + j2πf)^-1 is driven by a white-noise process with double-sided power spectral density of 1 W/Hz.

(a) What is the cross-power spectral density of input with output?
(b) What is the cross-correlation function of input with output?
(c) What is the power spectral density of the output?
(d) What is the auto correlation function of the output?

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