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ECE 5620
Spring 2011
Homework #4: Issued Mar. 2, Due Mar. 18 at 5 p.m.
Complete all seven problems.
1. Problem 2 in Chapter 9 of the text.
2. Problem 3 in Chapter 9 of the text.
3. Problem 4 in Chapter 9 of the text. Assume that the channel input must be
nonnegative.
4. Let
{
Z
(
t
)
}
∞
t
=
∞
be continuoustime Gaussian white noise with power spec
tral density
S
Z
(
f
) =
N
o
2
.
Suppose that
{
Z
(
t
)
}
∞
t
=
∞
is passed through an ideal lowpass ﬁlter whose
transfer function satisﬁes

H
(
f
)

2
=
(
1
if

f

< W
0
otherwise.
Let
{
˜
Z
(
t
)
}
∞
t
=
∞
denote the output of the ﬁlter. The output is sampled at the
Nyquist rate,
2
W
.
Show that
{
˜
Z
(
n
2
W
)
}
∞
n
=
∞
is Gaussian discretetime white noise and deter
mine its average power.
5. Consider a discretetime additive white Gaussian noise channel with signal
tonoise ratio
S
.
(a) Plot the capacity as a function of
S
in MATLAB or an equivalent pro
gram.
(b) Suppose now that the input to the channel is restricted to the two values
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This note was uploaded on 10/03/2011 for the course ECE 5620 at Cornell University (Engineering School).
 '08
 WAGNER

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