Consider the causal system y(n) = y(n 1) 1/8y(n 2) + x(n) + 1/3x(n 1) (a) Determine its system function. (b)

Consider the causal system
y(n) = ¾y(n – 1) – 1/8y(n – 2) + x(n) + 1/3x(n – 1)
(a) Determine its system function.
(b) Determine the type 1 state-space model.
(c) Determine the state transition matrix Φ{n} = Fn, for any n, using z-transform techniques.
(d) Determine the system function using the formula
H(z) = gt(zI – F) –1 q + d
Compute the answer with that in part (a)
(e) Compute the characteristic polynomial det(zI – F) and check if the system is stable.