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Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
Z-Transforms and Solution of Difference Equations 13-11
9. Evaluate z ( na
n
) using the definition of Z-transform.
Ans:
2
()
a
z
za
Recurrence Formula
10. Using the recurrence formula
Z ( n
p
) =
(/ )
z
ddz
1
[( )]
p
Zn
〈〉
, fi nd Z ( n
3
) and Z ( n
4
) given that
Z ( n
2
) =
2
3
2
(1)
z
z
+
.
Ans:
32
3
4
432
4
5
4
() ;
(1)
11 11
()
(1)
zzz
Zn
z
zzzz
Zn
z
++
〈〉=
+++
〈〉=
13.6 INVERSE Z-TRANSFORM
We have already defined the inverse Z-transforms of
u
(z), a function of a complex variable
z, by
Z
1
(
u
(z)) = u
n
(13.61)
which exists provided the series,
0
n
n
n
uz
=
con-
verges and u
n
is the sequence generating the series.
We will now consider methods for finding the
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Publisher Resources

ISBN: 9781299446557Publisher Website