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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
13-2 Mathematical Methods
Unit Step Sequence
The unit step sequence H ( n) or H
n
, n = 0, ±1,
±2, … is defined by
10
()
00
n
n
n
n
HH
=
<
for
or
for
(13.8)
1
1
1
11
–1–2 0
n
23
H (n)
The relation between the unit impulse sequence and
the unit step sequence
We have
1
()
0
nk
nk
nk
nk
dd
=
−=
for
or
for
(13.9)
and
1
()
0
nk
nk
nk
nk
HH
−=
<
for
or
for
(13.10)
() ()
n
k
nH kHd
=−∞
=
or
and
() () ( 1)nHnHnd =−−
Also,
()
()( )
k
fn fk n kd
=−∞
=−
(13.11)
13.2.2 Z-Transforms of Unit Step
and Unit Impulse Sequences
Example 13.1
Find the Z-transform of discrete unit step sequence
H
n
where
Convergence of the series. An infinite series of the
form
01
0
2
2
() ()
()
n
n
n
aza a az a
az a
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Publisher Resources

ISBN: 9781299446557Publisher Website