(a) Find the conditions on a transfer function G(z) such that its dc gain is zero. Prove your result.

(b) For

find the conditions of Gp (s) such that the de gain of G(z) is zero. Prove your result.

(c) Normally, a pole at the origin in the s-plane transforms into a pole at z = 1 in the z-plane. The function in the brackets in part (b) has a pole at the origin in the s-plane. Why does this pole not transform into a pole at z = 1?

(d) Find the conditions on G(z) such that its dc gain is unbounded. Prove your result.

(e) For G(z) as given in part (b), find the conditions of Gp (s) such that the dc gain of G(z) is unbounded. Prove your result.

-Ts G(z) = $ 1-6-6, (6) -G (0)| S