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Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition
book

Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition

by Harold Klee, Randal Allen
April 2016
Intermediate to advanced content levelIntermediate to advanced
815 pages
31h 29m
English
CRC Press
Content preview from Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition
where
~
g
k,1
¼
0, k ¼ 0
(2)
k1
, k ¼ 1, 2, 3, ...
(4:396)
~
g
k,2
¼
0, k ¼ 0, 1
(2)
k2
, k ¼ 2, 3, 4, ...
(4:397)
Combining Equations 4.395 and 4.396, the inverse z-transform is
f
k
¼
0, k ¼ 0
1, k ¼ 1
(2)
k1
þ (2)
k2
, k ¼ 2, 3, 4, ...
8
<
:
(4:398)
Simplifying the expression in Equation 4.398 when k ¼2, 3, 4, . . . gives
f
k
¼
0, k ¼ 0
1, k ¼ 1
( 2)
k2
, k ¼ 2, 3, 4, ...
8
<
:
(4:399)
(b) Long division of the denominator in Equation 4.392 into the numerator results in an innite
series. The rst few terms are
z þ 1
z
2
þ 2z
¼ z
1
z
2
þ 2z
3
4z
4
þ 8z
5
 (4:400)
Looking at Equation 4.400, it is possible to recognize a pattern in the coefcients starting with the
z
2
term. This ...
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Publisher Resources

ISBN: 9781439836736