ECE501
Introduction to Analog and Digital Communications
Autumn 2011
Homework #5
Oct. 28, 2011
HOMEWORK ASSIGNMENT #5
Due Fri. Nov. 4, 2011
(in class)
Reading: Online lecture notes through page 66; text Ch 6.16.7; text Ch. 9.19.3
Problems:
1.
True or false
Let
g
[
n
] be a pulse shaping filter,
q
[
n
] be the matched filter for
g
[
n
], and
p
[
n
] be the
convolution of
g
[
n
] and
q
[
n
]. Suppose that
p
[
n
] is a
Nyquist pulse
. Finally, let there
P
= 7 samples
per symbol interval. Answer the following as always True or possibly False, and give a very, very
brief reason.
(a)
p
[0] = 0
(b)
p
[0] = 1
(c)
p
[7] = 0
(d)
g
[0] = 1
(e)
g
[7] = 1
2.
Eye Diagram:
Here you will use the discretetime baseband model to simulate a realvalued digital
communication system and then plot an eye diagram to interpret the outputs. The programs
pam.m
and
srrc.m
are available on the course webpage.
(a) Using
pam
, generate a 4ary PAM symbol sequence with length
N
= 100 and variance 1.
(b) Using
srrc
, generate
{
g
[
k
]
}
, a sampled SRRC pulse shape with total time span 4
T
, rolloff
parameter
α
= 0
.
5, and oversampling factor
P
= 16.
(c) Implement the discretetime complexbaseband system below assuming a noiseless and trivial
discretetime channel (i.e., ˜
w
[
k
] = 0 and
˜
h
[
k
] =
δ
[
k
]).
a
[
n
]
↑
P
a
↑
[
k
]
g
[
k
]
˜
m
[
k
]
˜
h
[
k
]
˜
w
[
k
]
˜
v
[
k
]
y
↑
[
k
]
y
[
n
]
q
[
k
]
↓
P
+
Remember than upsampling can be accomplished via
a
up = zeros(1,P*N);
a
up(1:P:P*N) = a;
and that downsampling can be accomplished via
y = y
up(1:P:P*N);
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 Fall '08
 Schniter,P
 constellation diagram, discretetime baseband model, symbol sequence

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