An MA(2) process is described by the difference equation x(n) = (n) + 0.81(n 2) where (n) is a white noise process with variance

An MA(2) process is described by the difference equation

x(n) = ω(n) + 0.81ω(n – 2)

where ω(n) is a white noise process with variance σ2u.

(a) Determine the parameters of the AR(2), AR(4), and AR(8) models that provide a minimum mean-square error fit to the data x(n).

(b) Plot the true spectra m and those of the AR(p), p = 2, 4, 8, and compare the results. Comment on how well the AR(p) models approximate the MA(2) process.