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This question was created from Exam1_2012.pdf https://www.coursehero.com/file/26518299/Exam1-2012pdf/

Could you explain how to find the coefficients b1(k) as listed in this problem.

5. Stabilization of a Spatem Transfer Function: (20 Pla) The system transfer function for
an unstable discrete-time system is given by
HOE
A(E)
(5)
where
B(2) = 6(0)2 + 6(1)2 + 6(2)2 + 6(3)27 + b(4)23 + 6(5)2 + 6(6)
(6)
and
A(2) = 2 + 0(1)2 +0(2)2 + 0(3)2 + 0(4)2 + 0(5)= + 0(6)
The zeros of M(2), along with their magnitudes, are given by
= -1.0100, q1/ = 1.0
42
= -0.8018 +0.59767, |92 = 1.0
43 = -0.8018 - 0.59767, |41) = 1.0
0.9072 + 0.42061, q1) = 1.0
45 =
0.9072 - 0.42061, |q=] = 1.0
1.0000, 14x1 = 1.0
(7)
The poles of //(2), along with their magnitudes, are given by
= -0.4031 - 1.04457, [p)| =1.1196
P2
-0.4031 + 1.0445), \p2) = 1.1196
Pa
0.5994 + 0.68827, [py| = 0.9126
= 0.5994 - 0.68827, [py) = 0.9126
0.2954 - 1.3595), [px) = 1.3912
PE =
0.2954 + 1.35957, Ips) = 1.3912
(8)
. Determine the system transfer function for a stable discrete-time system that has
the same magnitude response as the one given above in Equation (5). Specify the
modified system transfer function as follows:
by (0)2 + 61 (1)2 + 61 (2)2' + by (3)2 + by (4)2 + 61 (5)= + by (6)
(2 -m)(=-m)(z-m)(z-m)(=-r)(=-re)
(9)
Determine the coellicients by(k) in terms of b(k) VO &lt; k &lt; 6. Determine the
poles fe in terms of p. V 1 &lt; &lt; &lt; 6. NOTE: You do not need to calculate the
actual decimal values of by (k) or re-

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