Consider an AR (2) process which is described by the recursion
Y [n] = a1Y [n€“ 1] + a2Y [n€“ 2] + X [n]
Where is an IID random process with zero- mean and variance σ2X.
(a) Show that the autocorrelation function of the AR (2) process satisfies the difference equation,
RYY [k] a1R YY [k €“ 1] a2R YY = + [k €“ 2] k = 2, 3, 4 €¦
(b) Show that the first two terms in the autocorrelation function satisfy

From these two equations, solve for RYY [0] RYY [1] and in terms of a1 a2, and σ2X.
(c) Using the difference equation in part (a) together with the initial conditions in part (b), find a general expression for the autocorrelation function of an AR (2) process.
(d) Use your result in part (c) to find the PSD of an AR (2) process.

and (1-a2)Rrr[1] = a1Rr10] .