Page 415 - Schaum's Outline of Theory and Problems of Signals and Systems

402 STATE SPACE ANALYSIS [CHAP. 7

Thus,

which is the same result obtained in Prob. 4.32(c).
(6) By Eq. (7.44) the system function H(z) is given by

-I 1 2-Ti
3
Now (I ) = [ z112] [ -i :]
A
=
8 ( ) (
Thus,

which is the same result obtained in Prob. 4.32(a).

7.30. Consider the discrete-time LTI system described by

q[n + 11 = Aq[n] + bx[n]
Y [n] = cq[n] + h[n]

(a) Show that the unit impulse response h[n] of the system is given by

(6) Using Eq. (7. ]IT), find the unit impulse response hlnl of the system in Prob.
7.29.

(a> By setting q[O] = 0, x[k] = 6[k], and x[n] = 6[n] in Eq. (7.25), we obtain