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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
4.6.1 DISCRETE-TIME IMPULSE FUNCTION
We now introduce a discrete-time function, which plays a prominent role in analyzing the behavior
of linear discrete-time systems. The unit strength discrete-time impulse occurring at discrete-time
k ¼0isdened by
d
k
¼
1, k ¼ 0
0, k ¼ 1, 2, 3, ...
(4:369)
Delaying the discr ete-time impulse by n units of discrete-time produces
d
kn
¼
1, k ¼ n
0, k ¼ 0, 1, 2, ..., n 1, n þ 1, ...
(4:370)
It follows directly from the denition of the z-transform that
z{d
k
} ¼ 1 and z{d
kn
} ¼ z
n
(4:371)
An arbitrary discrete-time signal f
k
, k ¼0, 1, 2, . . . can be expressed as a weighted sum of unit
discrete-time impulses, that is,
f
k
¼
X
1
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Publisher Resources

ISBN: 9781439836736