Suppose that we are given a linear system characterized by the difference equation The system is excited by (1) White gaussian noise, x ∼ N (0, 3) and (2) exponentially correlated noise, Ree(k) =...

Suppose that we are given a linear system characterized by the difference equation

The system is excited by (1) White gaussian noise, x ∼ N (0, 3) and (2) exponentially correlated noise, Ree(k) = (1/2)^|k|. In both cases find:

(a) Output PSD, Syy (z)

(b) Output covariance, Ryy (k)

(c) Cross-spectrum, Sye(k)

(d) Cross covariance, Rye(k)