Question

The pole-zero plot of a transfer function H(z) for a discrete-time LTI system is shown in Fig. 3. Im(z) |z| = 1 Re(z) (0.5, 0) (2, 0) Fig. 3 i. Write the system transfer function H(z) that is associated with the poles-zero plot to within a scaling constant. ii. Can a system with this pole-zero plot be both stable and casual? iii. If the system is stable, can the impulse response h[n] be single-sided?

          The pole-zero plot of a transfer function H(z) for a discrete-time LTI system is shown in
Fig. 3.
Im(z)
|z| = 1
Re(z)
(0.5, 0)
(2, 0)
Fig. 3
i. Write the system transfer function H(z) that is associated with the poles-zero
plot to within a scaling constant.
ii. Can a system with this pole-zero plot be both stable and casual?
iii. If the system is stable, can the impulse response h[n] be single-sided?