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
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 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 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 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
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 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
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
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 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
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
Homework 3
Due Monday, September 19, 2016
Problem 1. Lathi and Ding 4.22 (i) and (ii) only.
Problem 2. Lathi and Ding 4.27.
Problem 3. Lathi and Ding 4.32.
Problem 4. Lathi and Ding 4.42 (i) and (ii) only.
Problem 5. In this problem you are to
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
Handout 2
Fall 2016
Generation of FM Waves
There are two basic methods of generating FM waves. One is indirect FM
and the other is direct FM.
In the indirect method of producing frequency modulation, the modulating wave is first used to produce a n
EE 567
Project 9
Due Monday, November 16, 2015
Note: In this problem you are to use Matlab.
Problem 1. A BPSK signal is utilized at 5000 bits/sec. The waveforms
are s1 (t) = A cos(0 t) and s2 (t) = A cos(0 t), where A = 1 mV and the
singlesided noise den
100 pts
EE 567 Midterm Fall 2015
N = 18 Mean = 70 Median = 70.5 STD = 14.9
Score Grade
Score Grade
99 A
69 A91 A
66 B+
88 A
65 B+
82 A
64 B+
82 A
58 B
78 A57 B
75 A52 B74 A50 B72 A40 C
EE 567
Project 9
Due Monday, November 16, 2015
Note: In this problem you are to use Matlab.
Problem 1. A BPSK signal is utilized at 5000 bits/sec. The waveforms
are s1 (t) = A cos(!0 t) and s2 (t) = A cos(!0 t), where A = 1 mV and the
singlesided noise d
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 5
Due Monday, October 2, 2017
Work all 4 problems.
Problem 1. Consider a firstorder PLL as described in class, i.e., the loop
filter is H(f) = 1. Then
e (f) =
1
1 (f).
1 + K0 /jf
We wish to investigate the loop behavior in the presence of
EE 567
Homework 2
Due Monday, September 11, 2017
Work all 6 problems.
Problem 1. Lathi and Ding 2.12.
Problem 2. Lathi and Ding 2.13.
Problem 3. Lathi and Ding 2.16.
Problem 4. Lathi and Ding 2.18 (a), (b), (c).
Problem 5. Pulse Coded Modulation (PCM)
Inkar Shoganova
EE 567
Prof. Christopher Walker
November, 7, Fall 2016
Midterm Rework
Problem. 1(Problem 7)
Problem 7. Consider the transmission of a signal as shown in the following diagram.
 s1
 s2
x(t)
Receiver
Transmitter
s3
A signal is transmitted