(In Proakis & Salehi unless otherwise noted)
Functions of RVs, Rand.processes, EX(x)
Read Section 5.2, review Section 5.1
Do 5.9, 5.10, 5.11, 5.12
Also, please complete the course evaluation.
and also this course evaluation.
Hints on 5.11
Part 3) You can't use Eq. 5.1.11 (Why?) Use
techniques discussed in class on 12/07
Part 4) The integral you encounter is not too
hard. What is (d/dy)(exp(–y2/2σ2))?
Part 5) You can use Eq. 5.1.11.
Note:
Problem 5.12 continues in the textbook on p. 239.
New topic: Intro to Probability
Read Section 5.1
Do 4.5, 4.20, 5.1, 5.2, 5.3, 5.5
Note textbook errata on page 163.
Note textbook errata on page 187, Prob. 4.20.
on probability.
Do 4.1, 4.2, 4.4
Note textbook errata on page 163.
the Hilbert transform. Text Section 2.6 and
Chapter 3
Do 2.62, 2.65, 3.14, 3.16.
Read Sections 3.2.4 to end of Chapter 3
Do 3.24 and 3-A (not in textbook)
Note textbook errata on page 163.
Read Sections 3.2.3 and 2.6 (pages 95–98)
Do 3.17
Read Section 3.2.2 and pages 141–143 on
Envelope Detector.
Do 3.11
Do 2.39, 2.43 part b only
For solutions, see PS#5 and PS#6
and demodulation of the above
Read Ch 3 Introduction through 3.2.2
Do 2.43 part (b) only, 2.44 using only part (b)
of 2.43, 3.1, 3.3, 3.5, and note errata on
pages 151 and 152, also. . .
Use a computer to plot Eq. 3.2.6 (page 127).
Let mn(t) = cos(2πfmt) and let a = 0.75, Ac = 10,
fm = 440 Hz, and fc = 20 kHz. Turn that case
in for a grade, but use your computer code to
explore. What happens if a > 1? (try a = 1.2)
What happens as fc is lowered toward fm?
Be sure your plots have enough samples. You
should have at least 10 samples per cycle of
of cos(2πfct) and you should plot at least one
cycle of mn(t).
Use a computer for the plots for Problem 3.3.
Octave or Matlab are recommended.
Hint for Problem 2.43(b): Follow the style of the
example on textbook page 53 and note that
xn can be expressed without any trigonometric
or complex exponential functions.
Hint for Problem 2.44. Use Eq. 2.3.57
on textbook page 79. Also see pages 81 - 82.
Express each answer as a synthesis of basis
signals. (A finite summation in each case.)
Hint for Problem 3.3
Note: On Tuesday, 9/26, we decided in class that future
homework assignments will be due on Thursdays. The
due date for this assignment was also changed to the
Wednesday before Heartland break.
Read Ch. 2, Sec 2.3, Review Sec. 2.2
Do 2.37 part 2, 2.39, 2.42, and
also evaluate this integral:
![Integral from minus inf.
to inf. of {[2exp(-5t) +sin(10(pi)t)]delta(t)}dt](Integral_1.png)
Also evaluate the convolution
where
and
Read Ch. 2 Section 2.2
Do 2.31, 2.37 part 1 (other parts will be
assigned later), find [Λ(t)sgn(t)u(t)] ★ u(t)
where sgn is the signum function and u is the
unit step function. The open-delta represents
the unit triangle function and the star
represents convolution.
Hint on Problem 2.37.1:
In geometric terms, let αi represent an
i-dimensional vector. Let βi represent another
i-dimensional vector. Then the left-hand side
of the inequality is the dot-product of the two
vectors. On the right-hand side of the inequality
one finds the product of the lengths of the
two vectors. The inequality essentially states
that the dot-product of two vectors (having
non-negative elements) is less than or equal to
the product of the lenghts of the vectors.
In communucation systems the vectors
represent discrete-time signals. The "lengths"
of each signal represent the square-roots of
the power of each signal.
Optional: For a nice review and a few more
details, see how Prof. Oppenheim covers
Convolution in a 50 min. lecture at MIT.
Lecture 4, Convolution | MIT
Hint: You can watch it in 25 min. at 2x speed!
Review Ch 2 Sec. 2.1; Read Ch 2 Sec. 2.2.
Do 2.7, 2.16, 2.24, 2.34
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.
(On 8/31 at 2:27 PM Prof. De Boer moved Problem 2.16
to the next assignment.)
Read Chapter 1.
(There is nothing to turn in.)