An AR(2) process is described by the difference equation x(n) = 0.81x (n - 2) + w(n)...

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

x(n) = 0.81x (n - 2) + w(n)

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

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

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