Introduction to Digital Signal and System Analysis - Tutorsindia

Introduction to Digital Signal and System Analysis
Z Domain Analysis
Table 5.3 Summary of properties of 2 nd order systems
System function About Zeros About Poles
Transfer
function
H(z)
Zeros:
When z =Zero, H(z) = 0
Poles:
When z =Pole, H(z) = ∞
Frequency
response
|H(Ω)|
When Ω = q
1 |H| = min
If r 1 =1 and Ω = q , |H|=0
1
(reject frequency)
When Ω = q
2 ,
|H| = max (peak gain)
Problems
Q5.1 Find the Z-transform for a digital signal given by
↑
2
( 0.35) ,( 0.35)
x[
n]
= [1, 0.35,
, ...]
3
and find the Z-transform if the signal has been changed to
↑
2
( 0.35) ,( 0.35)
x[
n]
= [1, 0.35,
, ...]
3
Q5.2 A digital signal is described as
x[
n]
=
⎧
⎨
0
⎩( 0.9)
n
for
for
n < 0
n ≥ 0
Find the sum ∑ ∞
=0
n
x [ n]
and the Z-transform of the signal.
Q5.3 Expend the following z-transform functions as power series in
at n=1):
a)
b)
c)
X ( z)
X ( z)
X ( z)
1
= z − 0.6
z
= z + 1.2
z + 1
= z −1
−1
z , and find their first five sample values (starting
84
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