ECEN 661 -Modulation Theory
Spring 2006
Practice Midterm Exam #2
Problem 1.
(a) For a full response CPFSK modulation format with a modulation index, h , prove that the
asymptotic relative power efficiency is bounded by
1 sinc ( 2 h ) .
(b) Since h = 0.71
Name _
ID Number _
EE661 -Modulation Theory
Spring 2011
Midterm Exam #1
Instructions: This exam is closed book. However, you may bring in one sheet of notes which is
limited to one side of an 8.5x11 (inch) sheet of paper. You may include any material you
ECEN 661 - Modulation Theory
Homework #9
Assignment Date: 4/13/06
Due Date: 4/20/06
1. Phase Estimation for Binary PAM. Consider a binary PAM signal of the form
sl ( t ) =
bn p ( t nTs )
where p ( t ) is the pulse shape used and the data bits are b n 1 .
ECEN 661 - Modulation Theory
Homework #9 Solutions
1.
(a) Starting from the expression developed in class, we solve for the phase estimate according to
Re [ yn e j ] Im [ yn e j ]
= 0,
n
where y n =
( n + 1 ) Ts
nT
r l ( t ) p * ( t nT s ) dt . Let y n,
ECEN 661 - Modulation Theory
Homework #10
Assignment Date: 4/28/06
Due Date: Not to be turned in.
1. A voice-band telephone channel has a passband characteristic in the frequency range
300 Hz < f < 3 kHz .
(a) Select a symbol rate and a power efficient co
ECEN 661 - Modulation Theory
Homework #10 Solutions
1.
(a) Assuming a root-raised cosine transmitted pulse shape. The occupied bandwidth will be
( 1 + ) Rb
B = ( 1 + ) R s = - ,
log 2 ( M )
where M is the constellation size. Since 0 < < 1 we have,
Rb
In t
ECEN 661 -Modulation Theory
Spring 2006
Midterm Exam #1 Solutions
Problem 1. (15 points)
Consider a 4-ary two-dimensional signalling format that uses the basis functions f 1 ( t ) and f 2 ( t )
as shown. Note that while the basis functions are
orthogonal,
ECEN 661 -Modulation Theory
Spring 2006
Midterm Exam #2 Solutions
Problem 1. (30 points)
Let cfw_ a n be a sequence of binary IID data bits where a n cfw_ 1 . These data bits are to be transmitted via PAM, but first they are precoded according to
4
3
b
ECEN 661 -Modulation Theory
Spring 2006
Practice Midterm Exam #1
Problem 1.
The signal constellation shown is known as
the 32-point cross (32-CR) constellation. In
all parts of this question, assume that all 32
points in the constellation are equally like
ECEN 661 -Modulation Theory
Spring 2006
Pracice Fianl Exam
Problem 1.
The PSD of a narrowband Gaussian
noise process, N ( t ) , is as shown in the
figure at right.
(a) Find and sketch the PSD of the I
and Q components of the narrowband
noise process.
(b)
EE 661
Solution to Homework # 1
Spring 2007
Given: February 1, 2007
Due: February 15, 2007
1. In communicating through fading channels (we will deal with them later), it is often the practice to
transmit pilot symbols periodically so that the receiver can
ECEN 661
Homework # 2
Spring 2007
Given: March 6, 2007
Due: March 22, 2007
1. Pulse-position modulation (PPM) is a popular modulation scheme for optical free-space channels. Under M -ary PPM, a signaling interval of T seconds is divided into M equal lengt
Problem 5.21 :
The optimum decision boundary of a point is determined by the perpedicular bisectors of each
line segment connecting the point with its neighbors. The decision regions for this QAM constellation are depicted in the next figure:
0
0
0
0
Prob
ECEN 661
Homework 5
Georghiades
Given: April 23, 2007
Due: May 1, 2007.
1. Consider the convolutional code generated by g0 = (101), g1 = (111) and g2 = (111).
(a) Construct a state and a trellis diagram for this code.
(b) Find the transfer-function of the
ECEN 661 - Modulation Theory
Homework #8 Solutions
1.
(a) As described in class, comparing z 0 with z 1 is the same as comparing z 0 2 with z 1 2 .
z0 2
>
<
z1 2
rn + rn 1 2
>
<
rn rn 1 2
*
r n 2 + r n 1 2 + 2 Re [ r n r n 1 ]
>
<
*
r n 2 + r n 1 2 2 Re [
ECEN 661 - Modulation Theory
Homework #8
Assignment Date: 3/30/06
Due Date: 4/6/06
1. Analysis of DPSK.
r l ( t ) Matched
Filter
rn
Delay
( )*
x
sgn ( Re [ ] )
dn
Consider the standard DPSK receiver shown above. In this problem you will directly evaluate
ECEN 661 - Modulation Theory
Homework #7 Solutions
GMSK:
The GMSK phase pulse shape for BT=0.3 is shown in the figure below. Note that for all practical
purposes, q ( t ) = 0 for t < 1.5 T and q ( t ) = 1 2 for t > 1.5 T . Hence, with insignificant loss i
Name _
ID Number _
EE661 -Modulation Theory
Spring 2011
Midterm Exam #2
Instructions: This exam is closed book. However, you may bring in one sheet of notes which is
limited to one side of an 8.5x11 (inch) sheet of paper. You may include any material you
ECEN 661 - Modulation Theory
Take Home Final
Assignment Date: 4/29/11
Due Date: 5/6/11
Preface: The final exam in this course will be a take-home exam. The exercise described here is
to be turned in by noon on Friday May 6th. This assignment is to be done
EE661 -Modulation Theory
Spring 2011
Practice Midterm Exam #1
Problem 1. (25 points)
Zero-mean, white Gaussian noise with a PSD of
N 0 2 is passed through a BPF whose transfer
function is as described in the figure.
(a) Find the variance of the I and Q co
ECEN 661 - Modulation Theory
Homework #1
Assignment Date: 1/19/03
Due Date: 1/26/03
1. An audio signal m ( t ) is FM modulated to produce
s ( t ) = A cos 2 f c t + 2 k f
t
m ( ) d ,
where f c is the carrier frequency and k f is the frequency deviation co
8S
j
S mki T
lj g&(
g&(
R l j H0)" q R mki F0)"
1
j 90`" x
& (
& $"
%#
&
%"
&D
H0EB F" e2 fEXH" d2 `2)CV
B b & D B b B
&D
H0EB H" d2 fE4F" d2 `2p
B
& D B b B
1 & B
cH" 2
1 & B 1 & B
cH" 2 2cH" 02
cfw_
1
& cfw_ " #
&
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Dcfw_
T H& j )20)"
g
ECEN 661 - Modulation Theory
Homework #2
Assignment Date: 1/26/06,
Due Date: 2/2/06
1. Text 4.3.
2. Text 4.10
3. Text 4.11
4. For each of the following modulation formats, derive an expression relating the minimum
(Euclidean) distance between points in th
ECEN 661 - Modulation Theory
Homework #2 Solutions
1.
(a). Start with (4.1-38):
n ( t ) = x ( t ) cos ( c t ) y ( t ) sin ( c t ) .
Next compute the autocorrelation of the bandpass process,
E [ n ( t ) n ( t + ) ] = E [ x ( t ) x ( t + ) ] cos ( c t ) cos
ECEN 661 - Modulation Theory
Homework #3
Assignment Date: 2/2/06,
Due Date: 2/9/06
1. Text 4.14.
2. Suppose we use a QPSK modulation format. Relative to the data rate, calculate the 3dB bandwidth, the first null bandwidth, and the 40dB bandwidth for each
ECEN 661 - Modulation Theory
Homework #3 Solutions
1.
(a)
u(t)
2
an g ( t 2 nT )
=
2
+
n
bn g ( t 2 nT T )
2
n
Since the shifted pulses in each series are non-overlapping, all cross terms will be zero and hence
this simplifies to:
u(t) 2 =
2
2
an g 2 (
ECEN 661 - Modulation Theory
Homework #4
Assignment Date: 2/09/06
Due Date: 2/16/06
1. Text 4-34.
2. Text 5-9.
3. Text 5-10.
4. Text 5-15.
5. Text 5-19.
6. MATLAB Problem
On the course web page is a file called HW4P6.mat. This file contains a signal calle