Consider the linear system described by the difference equation

y(n) = 0.8y(n – 1) + x(n) + x(n – 1)

Where x(n) is a wide-sense stationary random process with zero mean and autocorrelation

γ_xx(m) = (1/2)^|m|

(a) Determine the power density spectrum of the output y(n).

(b) Determine the autocorrelation γ_yy(m) of the output.

(c) Determine the variance σ²_y of the output.