(a) Transf01m G _ (z + 0.3)(z- 0.3)

(z)- (z- 0.1)(z- 0.5

+ 0.5i)(z- 0.5- 0.5i)

into a continuous-time equivalent system by means of ZOH method of sampling intervals ranging fr-om T8 = 0.01sec toTs = 1sec.

{b) Determine the poles and zeros of the resulting continuous-time systems.

(c) Plot the root locus for each of the continuous-time systems.

Problem 8. 9 The z-tmnsform of a discrete-time filter h(k) at a 1Hz sample rate is H z = 1 + (1/2)z-1

( ) [1- (1/2)z-1][1 + (1/2)z-1]'

(a) Letu(k) andy(k) be the discrete input and output ofthisfilter. Find a difference equation relating u( k) and y( k).

(b) Find the naturalfTequency and the damping coefficient of the filter's poles.

(c) Is the filter stable?

Problem