Introduction to Digital Signal and System Analysis - Tutorsindia

Introduction to Digital Signal and System Analysis
Z Domain Analysis
b)
H z)
=
( z
4
z
− z + 0.8)( z −1.36z
+ 0.922)
(
2
2
Q5.12 Find the pass and reject frequencies for the filter given by the transfer function:
2
( z −1)
( z − z + 1)
( z + 0.9z
+ 0.81)
H ( z)
=
2
.
z
.
Q5.13 Find the digital signal x[n] and y[n] given by the Z-transforms
z
X ( z)
= , and z − 0.25
z + 0.75
Y ( z)
= . z − 0.25
Q5.14 Using the smallest possible number of z-plane poles and zeros, design a filter with the following frequency
performance:
Complete rejection at W = 0
Complete rejection at W = p / 3
A pass-band at W = 2p / 3
The poles are placed at radius r = 0. 9 in the z-plane and there should be no unnecessary delay in the output signal.
Determine the transfer function H (z)
for the filter.
Q5.15 Find and sketch the poles and zeros of the following transfer functions. Visualize and sketch the magnitude of the
system’s frequency response over 0 < W < p .
3 2
z − z
H ( z)
=
2
+ 0.8z
− 0.8
a) z ( z + 0.8)
b)
3
z − 2z
H ( z)
=
2
z
2
+ 2z
−1
( z + 0.9z
− 0.81)
87
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