DORDT UNIVERSITY ENGINEERING DEPARTMENT
INTRODUCTION TO COMMUNICATION SYSTEMS—EGR 363
(Spring 2023)

PROBLEM SETS

(Last update: 5/06/2023 2:38 pm)
PS #   Assigned Due Returned Problems Assigned
(In Proakis & Salehi unless otherwise noted)
14

4/28 5/05 5/06   Topics: Probabiity and Random processes, Beyes'
  Read: Section 5.1
 
  Do 5.1, 5.2, 5.3, 5.5
13

4/21
4/28
4/29
  Topics: Angle modulation basics, FM, PM
  Read Ch 4 Sec. 4.2, 4.3, 4.4
 
  Do 4.4, 4.5, 4.20
 
  Note textbook errata in Problem 4.20
12

4/17
4/21
4/22
  Topics: Angle modulation basics, FM, PM
  Read Ch 3 Sec. 3.2.4, Ch 4 Sec. 4.1
 
  Do 3.17, 4.1, 4.2
 
  Note textbook errata on page 163, Figure 4.2
  Note textbook errata in Problem 4.2
11

3/31
4/12
4/15
  Topics: SSB, Hilbert Transform, VSB
              Superheterodyne tuning, image freq.
  Read Ch 3 Sec. 3.2.3, 3.2.4, 3.4, 3.5
              Ch 2 Sec. 2.6, slides
 
  Do 3-A (←click link), 2.62, 3.16
10

3/24
3/31
4/03
  Topics: SSB, Hilbert Transform, VSB
              Superheterodyne tuning
  Reveiw Ch 2, Sec. 2.3 Ch 3 Sec. 3.2.3 thru 3.3
 
  Do 2.51, 2.59.1, 3.24
9

3/03
3/24
3/28
  Topics: Fourier Trans., Mod. Thm, DSB-SC, DSB-LC
  Read Ch 2, Sec. 2.3 Ch 3 Sec. 3.2.3 thru 3.3
 
  Do 2.47, 2.50, 3.11, 3.14
8

2/24
3/03
3/04
  Topics: Linear Modulation, DSB-SC
  Read Ch 3 Sec. 3.1, 3.2.1, 3.2.2
 
  Do 3.2, 3.3, Repeat 3.3 using DSB-LC, 3.5
 
  On problem 3.3, Let f0 = 5 Hz and let A = 1 V.
  Also let the modulation index a = 1.0.
  Use a computer to make your plots. It is too
  tedious to achieve the needed plot accuracy
  when plotting by hand. Matlab, Desmos, and
  many other programs can do this task for you.
  Here is a hint in Matlab code that provides
  one way to express the message signal m1(t):
  m1 = (2*t).*(u(t) - u(t - 0.5)) + ...
   (-2*t + 2).*(u(t - 0.5) - u(t - 1.5)) + ...
   (2*t - 4).*(u(t - 1.5) - u(t - 2.0))

  When you repeat the problem for DSB-LC make
  use of Equation 3.2.6 on page 127.
 
  On problem 3.5, you may make your plots by
  hand, but maintain good accuracy on properly
  scaled axes. When you draw an impulse, make
  the height of the impulse represent the area
  under the impulse.
 
  Note errata on pages 151 and 152.
7

2/17
2/24
2/25
  Topics: Fourier Transform
  Read Ch 2 Sec. 2.2
 
  Do 2.39.6, 2.43 part (b) only, 2.46.2
 
  Hints:
  See all the hints for PS#5 below.
  In Problem 2.39.6 the fundamental period is not
  1/f0. If you doubt this statement, let f0 = 60 Hz,
  for example, and plot the time-domain signal.
  Then find the fundamental period by observing the
  plot.
  Problem 2.46.2 can be done using tables found
  in your textbook, pages 78 and 79. Euler's
  is also helpful in recognizing the result.
6

2/13
2/17
2/18
  Topics: Fourier Series
  Read Ch 2 Sec. 2.2
 
  Do 2.39.2, 2.39.5, 2.42
 
  Hints:
  See all the hints for PS#5 below.
 
  Problem 2.42 is asking you to find the time-
  domain dot product x(ty(t) and show
  that it is the same as the frequency-domain dot
  product of xn·yn. To do this, in the time-domain
  dot product (L.H.S. of the given eq.), replace x(t)
  with its equivalent from the F.S. synthesis
  equation. Similarly substitute for y(t). Make sure
  the two summations use different index (harmonic
  number) variables such as n and k. (Not n and n.)
  Integrate term-by-term. (In other words, invoke
  distribution of multiplication with respect to
  addition to re-order operations and move the
  integration operation fully inside the
  summations.) This creates a double summation
  of integrals. The Fourier series coefficients xn and
  yk are constants with respect to the integration.
  Notice that if the two indices of summation
  (harmonic numbers) are not equal, the basis
  functions are orthogonal. his causes most terms
  in the double-summation to be zero. The only
  terms that remain non-zero occur when the
  indices of summation happen to be equal. Thus
  the double summation can be reduced to the
  single summation given in the problem statement.
5

2/03
2/10
2/14
  Topics: Fourier Series
  Read Ch 2 Sec. 2.2
 
  Do 2.36, 2.39.1, 2.39.4
 
  Hints:
  For problem 2.36 the author expects you to let
  the basis signals equal zero outside of the
  defined interval [α, α + T0].
 
  Slides 2 and 3 from 2/06 elaborate
  on the definition of the dot product of two
  signals. These slides might be helpful in
  working Problem 2.36.
 
  Divide-by-zero errors are possible mistakes
  when working the F.S. analysis integral. Do you
  see something like (2 – n) in a denominator? Then
  this solution is good only if n ≠ 2. Handle the
  n = 2 case separately by substituting n = 2 early,
  before the (2 – n) gets expressed in a denom.
 
  Keep Euler's rule in mind. Remember that com-
  plex exponentials can be written as cos() + jsin()
  or similar trigonometric forms and vice versa.
 
  Terms like cos(2πn) can be reduced.
  cos(2πn) = 1 for all n
 
  Terms like cos(πn) can be reduced to
  cos(πn) = (–1)n
 
  Similar maneuvers can be made with sin()
  functions involving multiples of π.
 
  In the answer for 2.39.1, xn = 0 for most n but
  not every n.
 
  The answer for 2.39.4 for odd n can be
  expressed in the form (integer)/(pn)2. Here p is
  a real constant and n is the harmonic number.
  If n is even but not zero, then xn equals a "special
  integer." If n = 0, then xn = x0 = a rational number.
 
  Note: errata on textbook page 107, Prob. 2.38
  This problem is not assigned, but an error in
  this problem statement could be confusing when
  working Problem 2.36. In the first integral in
  the problem statement of problem 2.38 the "1"
  and the "0" are interchanged from where they
  should be. The integral evaluates to 0 if ij
  and it evaluates to 1 if i = j
 
  The problems stated mostly as word problems.
4

1/30
2/03
2/04
  Topics: Linearity, convolution
  Read Ch 2 Sec. 2.1
  Read and observe Problems 2.37, 2.38 on pages
  106-107. These are theorems that relate to
  transforms in general. The proofs requested are
  tedious (hence not assigned), but the theorems
  are famous.
 
  Do 2.31, 2.34, 2.35
 
  Do the problem statements look like gibberish
  to you? Try reading them entirely spelled out
  as word problems.
3

1/20
1/27
2/02
  Topics: Linearity, convolution
  Read Ch 2 Sec. 2.1
 
  Do 2.7, 2.16, 2.24, 2.28
2

1/13
1/20
1/21

Sent
to
your
Dordt
e-mail
on
1/21
at
about
5:30
PM or
later.
  Topics: Types of signals & systems
  Read: Ch 1 Sec. 1.4, Ch.2 through Sec. 2.1
 
  Do (p. 101) 2.1 (all parts), 2.5, 2.6
  Use a computer to make the plots for 2.1.
  Octave or Matlab are recommended.
  Here is a m-file to get you started.
  DDB's "Toolbox" files including u.m, rect.m,
  sinc.m and triangle.m can be downloaded as a
  zip archive DDB_TBX.ZIP.
  Hint: At the command line in Octave or Matlab
  type, "help sign" [enter]. Also try
  "help addpath", "help help" and "help exit".
  After file rect.m is on the path-list, note
  what happens when you type "help rect" in the
  command window. Compare to the comments in
  the source file, rect.m.
 
  Note errata on pages 29 and 42, and 101,
  102, and 105.
 
  Click the due date (link) to turn your work in
  electronically. (Applies to all future
  assignments as well. See note 4 below.)
1

1/13 1/16 ---   Topics: History of and overview of Comm Systems
  Read Chapter 1.
  (There is nothing to turn in.)

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