Digital Signal Processing Reference
In-Depth Information
i.
Find expressions for a minimum-phase system
H
1
(
z
) and an all-
pass system
H
ap
(
z
) such that:
Hz
()
=
H zH
()
()
z
1
ap
ii.
Plot the pole-zero plots of
H
(
z
),
H
1
(
z
), and
H
ap
(
z
).
c.
A simple model for multipath channel is described by the difference
equation:
−
8
α
xn
()
=
sn
()
−
e
sn
(
−
8
)
We wish to recover
s
(
n
) from
x
(
n
) with a linear time-invariant system.
Find the causal and stable system function
H
(
z
)
= Y
(
z
)
/X
(
z
) such that
its output
y
(
n
)
= s
(
n
)
.
d.
Consider a causal LTI system described by the difference equation:
yn
()
=
p xn
()
+
p xn
(
−
1
)
−
d yn
(
−
1
)
0
1
1
where
x
(
n
) and
y
(
n
) denote, respectively, its input and output.
Determine the difference equation of its
inverse
system.
2.3
Computer Laboratory: Simulation of Continuous Time
and Discrete-Time Signals and Systems
This section consists of examples in MATLAB,
3
followed by the laboratory
exercises. Please test the example problems, before proceeding to the exercises.
MATLAB Examples
Example:
Solve the following difference equation for 0
≤
n
≤
10:
y
(
n
) =
y
(
n
- 1) + 2
y
(
n
- 2) +
x
(
n
- 2)
given that
x
(
n
) = 4 cos(
π
n
/8),
y
(0) = 1 and
y
(1) = 1.
Solution:
>> y=[1 1]
>> x(1)=4
