The z-Transform - Digital Signal Processing: Fundamentals and Applications - page 139

Table 5.1 Table of z-Transform Pairs

Region of
Convergence Line No. xðnÞ; n ‡ 0 z-Transform XðzÞ

P n¼0 xðnÞz n

1

xðnÞ

2

dðnÞ 1 jzj > 0

az
z

3

auðnÞ jzj > 1

1

z
ðz

4

nuðnÞ jzj > 1

2

1 Þ

zðz þ 1 Þ

5

2

n uðnÞ jzj > 1

3

ðz 1 Þ

z
z a

6

a n uðnÞ jzj > jaj

z
ðz e a Þ

7

e na uðnÞ jzj >e a

az
ðz aÞ

8

na n uðnÞ jzj > jaj

2

z sin ðaÞ

9

sinðanÞuðnÞ jzj >1

z

2

2 z cos ðaÞþ 1

z½z cos ðaÞ

10

cos ðanÞuðnÞ

j z j >

1

z

2

2 z cos ðaÞþ 1

½a sinðbÞz

11

a n sin ðbnÞuðnÞ jzj > jaj

z

2

½ 2 a cos ðbÞz þ a

2

z½z a cosðbÞ

12

a n cos ðbnÞuðnÞ jzj > jaj

z

2

½ 2 a cos ðbÞz þ a 2

½e a sin ðbÞz

13

e an sin jzj >e a

ðbnÞuðnÞ

z

2

½ 2 e a cos ðbÞz þ e 2a

z½z e a cos ðbÞ

14

e an cos jzj >e a ðbnÞuðnÞ

z

2

½ 2 e a cos ðbÞz þ e 2a

A z
z P

Az
z P þ

2 jAjjP j n cos

15 ðnq þ 4ÞuðnÞ

where are complex

constants defined by
P ¼jP j : q; A ¼jAj : 4

P and A

EXAMPLE 5.3
Find the z-transform for each of the following sequences:
a. xðnÞ¼10uðnÞ
b. xðnÞ¼10sinð0:25pnÞuðnÞ