Consider an AR(2) process which is described by the recursion
![](https://test.transtutors.com/qimg/edd9f9da-454c-47d8-b116-fb968625ea94.png)
Where
is an IID random process with zero-mean and variance ![](https://test.transtutors.com/qimg/eb455614-874a-4e4e-b8bc-3b29d5ad8a37.png)
(a) Show that the autocorrelation function of the AR(2) process satisfies the difference equation
![](https://test.transtutors.com/qimg/e74d9c7f-5716-441f-b772-5ba57bc278bb.png)
(b) Show that the first two terms in the autocorrelation function satisfy
![](https://test.transtutors.com/qimg/8ab20df6-369e-4541-b43a-1d88c1b771cd.png)
(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.