The z-Transform - Digital Signal Processing: Fundamentals and Applications - page 151

From MATLAB, we have
» [R,P,K] [ residue([1 0],[1 L 1.5 0.5])

R [

2
L 1
P [

1.0000
0.5000
K [
[]
»

Then the expansion is written as

X ðzÞ¼ 2z

z
z 0:5

z 1

b. From the MATLAB entry
» N [ conv([1 0 0],[1 1])
N [
1100
» D [ conv([1 L 1], [1 L 1 0.5])
D [
1.0000 L 2.0000 1.5000 L 0.5000

we get

z 2 z þ 1
z 1 z 2 z þ 0:5 ¼

z 3 þ z 2
z 3 2z 2 þ 1:5z 0:5

Y ðzÞ¼

and

z 2 þ z
z 3 2z 2 þ 1:5z 0:5

Y ð z z ¼

Using the MATLAB residue function yields
» [R,P,K] [ residue([1 1 0],[1 L 2 1.5 L 0.5])
R [
4.0000
L 1.5000 L 0.5000i
L 1.5000 D 0.5000i
P [
1.0000
0.5000 D 0.5000i
0.5000 L 0.5000i
K [

[]
»

Then the expansion is shown below

A z
z p

Bz
z p 1 þ

Az
z p þ

X ðzÞ¼