Suppose that we have a scalar process given by x(t) = 1/2 x(t − 1) + w(t − 1), w ∼ N (0, Rww ) y(t) = cx(t) + v(t), v ∼ N (0, Rvv) (a) What is the steady-state gain for this systems? (b) What is the...

Suppose that we have a scalar process given by

x(t) = 1/2 x(t − 1) + w(t − 1), w ∼ N (0, Rww )

y(t) = cx(t) + v(t), v ∼ N (0, Rvv)

(a) What is the steady-state gain for this systems?

(b) What is the effect of increasing Rww on Kss for fixed Rvv?

(c) What is the effect of decreasing Rvv on Kss for fixed Rww ?

(d) Suppose Rvv = 0; what is the effect of increasing Rww on Kss?

(e) Suppose Rww = 0; what is the effect of decreasing Rvv on Kss?