Question: 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

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

γxx(m) = (1/2)|m|

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

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

(c) Determine the variance σ2y of the output. 

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