A causal and stable LTI system S has its input x[n] and output y[n] related by the linea...

A causal and stable LTI system S has its input x[n] and output y[n] related by the linear constant-coefficient difference equation

Let the impulse response of S be the sequence h[n]. (a) Show that h[0] must be nonzero.

(b) Show that α₁ can be determined from knowledge of β, h[0], and h[1].

(c) If h[n] = (0.9)ⁿcos(πn/4) for 0 ≤ n ≤ 10, sketch the pole–zero plot for the system function of S, and indicate the ROC.