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

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someone explain how to find the coefficients fir b(k) and r(k) as stated in this problem

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5. Stabilization of a System Transfer Function: (20 Pis) The system transfer function for
an unstable discrete-time system is given by
H()=
B(=)
(5)
where
B(=) = 6(0)2 + 6(1)2 + 6(2)2 + 6(3)23 + (4)23 + 0(5)2 + 6(6)
(6)
and
A(2) = 2 + 0(1)2 +0(2)2 + 0(3)2 + 0(4)23 + 0(5)= + 0(6)
The zeros of M(z), along with their magnitudes, are given by
41 = -1.0100, q1| =1.0
12 =
-0.8018 + 0.59767, 192 = 1.0
43 =
-D.8018 - 0.59767, |41) = 1.0
41
0.9072 + 0.42067, 41) =1.0
=
0.9072 - 0.42061, |qs| = 120
1 0000, 1451 = 1.0
(7)
The poles of #(2), along with their magnitudes, are given by
PI = -0.4031 - 1.04457, Pil =1.1196
P2 = -0.4031 + 1.04457, [pz) = 1.1196
Pa
= 0.5994 + 0.68827, [pal = 0.9126
P = 0.5994 -0.68827, pi] = 0.9126
D = 0.2954 - 1.35957, [ps) = 1.3912
pa = 0.2954 + 1.35957, \p) = 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 + bi (1)2 + 61(2)2 + bi (3)2 + bi (4)23 + 6 (5)= + b (6)
(=-m)(=-m)(z-m)(z-m)(=-m)(=-re)
(9)
Determine the coefficients by(k) in terms of b() VO < < < 6. Determine the
poles re in terms of p, V 1 < < < 6. NOTE: You do not need to calculate the
actual decimal values of b (k) or re-

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