Consider the signal x(n) = (n + l)u(n) for n = 0, 1, ... , N.
(a) Find the first-order model and the minimum error using the covariance method, the forward and backward covariance methods, the Burg algorithm, and the modified covariance method. Comment on the differences in the models and compare x(n) to the model, x(n).
(b) Repeat part (a) using a second-order model. What behavior do you observe for the forward and backward covariance methods?
(c) Examine what happens using the Burg algorithm for model orders p > 2. Can you suggest a way to estimate the model order by looking at the sequence of errors Ef?
(d) Repeat parts (a) and (b) for the signal x(n) = n(0.9t. Add noise to x(n) and discuss the sensitivity of your model to the noise.