The transfer function of a causal LTI discrete-time system is H(z) = (1 + z⁻¹)/(1 − .5z⁻¹).

(a) Find the poles and zeros of H(z). Choose the correct region of con-vergence corresponding to H(z)from the following and explain why

(i) |z| < 0.5,        (ii) 0.5 < |z| < 1,                (iii) |z| > 0.5.

(b) Write the difference equation characterizing this system

(c) Find the impulse response h[n] of this system.

(d) From the pole and zero information determine what type of filter is this system.