EE 567
Homework 6
Due Monday, October 15, 2012
Work all 4 problems.
Problem 1. Consider a rstorder PLL as described in class, i.e., the loop
lter is H (f ) = 1. Then
e (f ) =
1
1 (f ).
1 + K0 /jf
We wish to investigate the loop behavior in the presence o
EE 567
Homework 6 Solutions
Problem 1. Consider a rstorder PLL as described in class, i.e., the loop
lter is H (f ) = 1. Then
e (f ) =
1
1 (f ).
1 + K0 /jf
We wish to investigate the loop behavior in the presence of a frequency
modulated input. We have
m
EE 567 Exam 2 Solutions
Due December 3, 2012 at 6:40 p.m.
Inst: Dr. C.W. Walker
Problem
Points
1
15
2
8
3
10
4
8
5
6
6
5
7
12
8
16
9
20
Total
Score
100
Instructions and Information:
1) Print your name at the top of the page and indicate if you are an onc
EE 567
Homework 1
Due Monday, August 1, 2015
Work all 4 problems.
Problem 1. Compute the Fourier transform of the triangular pulse, T ri(t),
where
t + 1, 1 t 0,
1 t, 0 < t 1,
T ri(t) =
0,
elsewhere
and sketch a plot of its graph in the frequency domain. Y
EE 567
Homework 5
Due Monday, October 5, 2015
Work all 3 problems.
Problem 1. Lathi and Ding 5.29 (b). Prove that
Jn () = (1)n Jn ().
Hint: Show first that
Z
e
j( sin xnx)
dx = 2
Z
0
cos( sin x nx)dx.
Problem 2. For general FM with modulating wave m(t) w
Name: _
Oncampus or DEN student: _
EE 567 Midterm
October 26, 2015
Inst: Dr. C.W. Walker
Problem
Points
1
Score
Problem
Points
7
6
10
2
6
7
12
3
10
8
12
4
10
9
8
5
10
10
15
Total
Score
100
Instructions and Information:
1) Print your name and assigned cla
EE 567
Project 1
Due Monday, August 31, 2015
Work all 2 problems.
In class we reviewed the continuous time Fourier transform. Here we
are going to look at the discrete version of this. Given a finite sequence
x(n), n = 0, 1, . . . , N 1, let WN = ei2/N .
EE 567
Project 2
Due Monday, September 14, 2015
Note: In this problem you are to use Matlab.
Problem 1. Let s(t) = 6 cos(2f t) where f = 20 Hz. Let us sample
s(t) at the sampling rate of fs = 50 Hz to obtain the discrete time signal
s(nTs ) = 6 cos(2f nTs
EE 567
Project 6
Due Monday, October 12, 2015
Note: In this problem you are to use Matlab.
Problem 1. A device produces a unit impulse every time a positive going
zero crossing occurs. Show that placing a T sec integrator after the device
produces an appr
EE 567
Homework 8
Due Monday, November 9, 2015
Work all 3 problems.
Problem 1. In class we had that the gain for a parabolic antenna is
2 df 2
c
g=
3
108
and the halfpower beamwidth is
b = 3.06
108
dfc
radians.
The actual gain of the antenna will be red
EE 567
Project 5
Due Monday, October 5, 2015
Note: In these problems you are to use Matlab.
Problem 1. In Project 3 we considered the DSBSC modulated signal
s(t) = m(t) cos(2fc t + )
where m(t) = 2 cos(2fm t), fc = 1000 Hz, fm = 10 Hz and = /4. At the
de
EE 567: Communication Systems
Fall 2015
Lecture: Monday 6:409:20 p.m. in OHE 100B
Discussion: TBD
Instructor: Christopher Wayne Walker, Ph.D.
Office: PHE 414
Office Hours: Monday 5:156:30 p.m.
Daytime phone: (213) 7407654 USC during office hours
or (31
EE 567
Homework 3
Due Monday, September 21, 2015
Problem 1. Lathi and Ding 4.21 (i) (a and b only). You are given the
baseband signal m(t) = cos 1000t.
a. Sketch the spectrum of m(t).
b. Sketch the spectrum of the DSBSC signal m(t) cos 10, 000t.
Solutio
EE 567
Project 2
Due Monday, September 14, 2015
Note: In this problem you are to use Matlab.
Problem 1. Let s(t) = 6 cos(2ft) where f = 20 Hz. Let us sample
s(t) at the sampling rate of fs = 50 Hz to obtain the discrete time signal
s(nTs ) = 6 cos(2fnTs )
EE 567
Project 3
Due Monday, September 21, 2015
Note: In this problem you are to use Matlab.
Problem 1. Consider the DSBSC modulated signal
s(t) = m(t) cos(2fc t + )
where m(t) = 2 cos(2fm t), fc = 1000 Hz, fm = 10 Hz and = /4. At the
demodulator we comp
EE 567
Homework 9
Due Monday, November 16, 2015
Work all 3 problems.
Problem 1. In class we had the likelihood ratio test as
p(zs1 ) H>1 P (s2 )
L(z) =
.
p(zs2 ) H<2 P (s1 )
Assume that P (s1 ) = P (s2 ) = 0.5. We stated that this is equivalent to
H1
z(
EE 567
Homework 3
Due Monday, September 21, 2015
Problem 1. Lathi and Ding 4.21 (i) (a and b only). You are given the
baseband signal m(t) = cos 1000t.
a. Sketch the spectrum of m(t).
b. Sketch the spectrum of the DSBSC signal m(t) cos 10, 000t.
Problem
EE 567
Project 8
Due Monday, November 9, 2015
Work all 2 problems.
Note: In this project you are to use Matlab.
Problem 1. Suppose we have a 9bit A/D converter. Let us number these
512 levels from 1 to 512. Then the 0 voltage level lies halfway between l
EE 567
Homework 1
Due Monday, August 1, 2015
Work all 4 problems.
Problem 1. Compute the Fourier transform of the triangular pulse, T ri(t),
where
t + 1, 1 t 0,
T ri(t) =
1 t, 0 < t 1,
0,
elsewhere
and sketch a plot of its graph in the frequency domain.
EE 567
Homework 2
Due Monday, September 14, 2015
Work all 7 problems.
Problem 1. Lathi and Ding 2.11. Find the average power of the signals in
Fig. P2.11 (see page 3).
Solution
(a) Average Power of the signals can be computed as:
1
Pg = lim
T T
Z
T /2

EE 567
Project 7
Due Monday, October 19, 2015
Note: In this problem you are to use Matlab.
Problem 1. Let Xn , n = 1, 2, . . . be independent normally (Gaussian)
distributed random variables each with mean 0 and variance 1 (standard
normal). Let
Ym =
NX
+
EE 567
Midterm Solutions
Fall 2015
Problem 1. Define
RT (t) =
1, T /2 < t T /2,
0, elsewhere.
Compute the Fourier transform of
x(t) = RT (t) cos(2fc t)
and sketch a plot of its graph in the frequency domain. Identify where the
approximate zerocrossings o
EE 567
Homework 4
Due Monday, September 28, 2015
Problem 1. Lathi and Ding 5.14 (modified). Over the interval 0 t 1
a PM signal is given by
sP M (t) = 10 cos(13, 000t).
It is known that the carrier frequency is 5000 Hz. If kp = 1000 determine
m(t) over t
EE 567
Homework 6
Due Monday, October 12, 2015
Work all 4 problems.
Problem 1. Consider a rstorder PLL as described in class, i.e., the loop
lter is H(f) = 1. Then
e (f)
=
1
1 + K0 /jf
1 (f).
We wish to investigate the loop behavior in the presence of a
EE 567
Homework 9
Due Monday, November 16, 2015
Work all 3 problems.
Problem 1. In class we had the likelihood ratio test as
p(zs1 )
L(z) =
p(zs2 )
H1
>
<
H2
P (s2 )
.
P (s1 )
Assume that P (s1 ) = P (s2 ) = 0.5. We stated that this is equivalent to
H1
EE 567
Homework 11
(Not to be handed in)
Work all 8 problems.
Problem 1 (from EE 567 Final, Fall 2014). A certain FM wave with
carrier frequency fc = 1 MHz and frequency sensitivity 50 KHz has a modulating wave given by
m(t) = 3 cos(21000t).
a. Find the i
Name: _
Oncampus or DEN student: _
EE 567 Final
December 14, 2015
Inst: Dr. C.W. Walker
Problem
Points
1
Score
Problem
Points
12
5
12
2
10
6
10
3
12
7
20
4
9
8
15
Total
Score
100
Instructions and Information:
1) Print your name and indicate Oncampus or
EE 567
Homework 5
Due Monday, October 5, 2015
Work all 3 problems.
Problem 1. Lathi and Ding 5.29 (b). Prove that
Jn () = (1)n Jn ().
Hint: Show first that
Z
j( sin xnx)
e
dx = 2
Z
cos( sin x nx)dx.
0
Solution
Proof:
1 Z
1 Z j(sinxnx)
e
dx =
cos(sinxnx
EE 567
Homework 8
Due Monday, November 9, 2015
Work all 3 problems.
Problem 1. In class we had that the gain for a parabolic antenna is
2
g=
3
dfc
108
!2
and the halfpower beamwidth is
108
b = 3.06
dfc
!
radians.
The actual gain of the antenna will be r