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 ?₁ can be determined from the knowledge of h[0] and h[1].

(c) If h[n] = (0.9)ⁿcos(?n/4) for 0 ? n ? 10, sketch the pole-zero plot for the system function of S, and indicate the region of convergence.

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10 y[n] + aky[n - k] = x[n] + Bx[n - 1]. k=1