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
nHkHd
∞
=−∞
=
∑
or
and
()()(1)nHnHnd=−−
Also,
()
()()
k
fnfknkd
∞
=−∞
=−
∑
(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
azaaaza
aza
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