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Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.02
Intro to EECS II
Spring 2008
Homework #5: Energy and Noise
Issued: March 7, 2008
Due: March 14, 2008
1. Consider the probability density function
f
X
(x)
of random variable
X
shown below in Figure 1.
0.5
0.5
1
x
()
X
f
x
Figure 1
a)
What is the mean of
X
?
b)
What is the variance of
X
?
c)
What is the probability of
0.1
≤
X
≤
0.2
?
2. Consider the digital receiver and accompanying signals shown below:
t
t
4
0
in(t)
out[n]
Sample
Slice
x
f
X
(x)
PDF of Noise at sample t
o
(at a given sample t
o
, n(t
o
) = X)
0
4
0
n(t)
Noise
t
o
3
3
6
1
a)
Assuming that the probability of sending a 0 symbol is 1/2, the probability of sending a
4 symbol is 1/2, what is the slicing threshold position that results in smallest bit error
rate? What is that bit error rate?
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b)
Given the same conditions as in part (a), what is the SignaltoNoise Ratio (SNR) at the
receiver?
Specify the SNR(dB) = 10log10(Z), where Z = var(signal)/var(noise).
c)
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This note was uploaded on 08/23/2009 for the course EECS 6.02 taught by Professor Terman during the Spring '08 term at MIT.
 Spring '08
 Terman
 Computer Science, Electrical Engineering

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