Random Signals for Communications and Signal Processing
EE 416

Fall 2015
EE 416 Homework Assignment 1 Revised
1. (20 points)
(a) Let A, B be events. Draw a Venn diagram that illustrates P (A B) =
P (A) + P (B) P (A B)? How does this equation simplify when (i) A and
B are disjoint or (ii) when A and B are independent. For arbit
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
EE 416 Homework 1, Fall 2013
1. (20 points)
Let A, B be finite sets. Which is smaller in cardinality: AB or AB? When are they equal?
Solution:
AB is usually smaller than AB, as shown in Fig 1.1. And AB equals to AB when A equals to B.
a. Solve for special
Random Signals for Communications and Signal Processing
EE 416

Fall 2009
c 2008 James A. Ritcey, UWEE 416
1
EE 416 Homework Assignment 1
DUE: Next Wednesday. Always include matlab printout on white and not black background.
1. Let A, B be nite sets. Which is smaller in cardinality: A B or A B? When are they
equal?
2. If P (A)
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
close all; clear all; clc;
T=1000; % number of trials
D=365; % number of possible birthdays
P=30; % max number of people
for t=1:T
for p=1:P
birthdays= 1+floor(rand(p,1).*D); % generate birthdays
num_unique = length(unique(birthdays);
num_next1 =lengt
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
EE 416
Final Exam, Fall 2015
Monday Nov 9, 2015
10:30 AM 12:20 PM
Closed Book, in Class
Name :
Student Number: :
1. Problem 1:
2. Problem 2:
3. Problem 3:
4. Problem 4:
5. Problem 5:
6. Problem 6:
Score:
Instructions:
110 minutes, Closed Book, 4 pages pe
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
\
pisllg WHAWMLOIB 56I®\an
~
1. (10 points) [Discrete RVs]
A fading channel can be put into one of two Groups, Urban 07‘ Rural. The SNR of the
channel depends on the group, and is either Low 07" Medium 07‘ High.
We know that
PI Low I Rural] = 0.6 P[ M
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
EE 416
Final Exam, Fall 2014
Monday Dec. 8, 2014
8:3010:20am
Closed Book, in Class Exam
Name :
Student Number: :
1. Problem 1:
2. Problem 2:
3. Problem 3:
4. Problem 4:
Score:
Instructions:
110 minutes, Closed Book, 4 pages personal notes, back and front
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
EE 416
Final Exam, Fall 2013
Monday Dec. 9, 2013
8:3010:20am
Closed Book, in Class
Name :
Student Number: :
1. Problem 1:
2. Problem 2:
3. Problem 3:
4. Problem 4:
5. Problem 5:
6. Problem 6:
Score:
Instructions:
110 minutes, Closed Book, 4 pages persona
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
function HW5Nhist(T);
% function HW5Nhist(T);
% T iid Normal
sqrt2=sqrt(2);
mu=6;sig2=2;Nbins=25;
sig1=sqrt(sig2);
x=randn(T,1);x=mu+sig1*x;
Nsigs = 5;Xend = mu +sig1*[Nsigs,+Nsigs];
Xend
[xKnt, outKnt,xCenter,xDelta] = myHistc(x,Nbins, Xend);
% keep o
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
BB 416
Midterm Exam, Autumn 2014
Wednesday Nov. 5, 2013,
10:3012:15 AM
Name: cfw_H O k  Student Number:
1. Problem 1:
2. Problem 2:
3. Problem 3:
4. Problem 4:
5. Problem 5:
Score:
Instructions:
Boldface type (mostly) indicates a RV, x, t
Closed Book, 4
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
c JARitcey EE416 Fall 2011, Communications I
1
1
Linear Prediction
An interpretation of the mean. Here we examine a simple prediction problem:
Given a RV y with known PDF p(y), nd the best constant c that approximates y. Unless
y is a known constant, with
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
EE 416
Final Exam, Fall 2011
Monday Dec. 12, 2011
8:3010:20am
Closed Book, in Class
Name (Last, First):
1. Problem 1:
2. Problem 2:
3. Problem 3:
4. Problem 4:
5. Problem 5:
6. Problem 6:
Score:
Instructions:
110 minutes, Closed Book, 6 pages personal no
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
Designing MMSE Filters for Interference Rejection
Professor James A. Ritcey
Department of Electrical Engineering
University of Washington
[email protected]
November 21,2014
1
Introduction
Background A desired lowpass signal, highpass interference
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
a
E/éllﬂo Minnie/M Sondhonr
FALLZOM
l. (20 points).
302 u‘lf' PM» F
‘ S
,1:
Discrete RV
A fading channel can be put into one of three Channel Classes, Urban, Suburban, 01"
Rural. The SNR of the channel depends on the class, and is either Low or High.
We
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
Sets and Counting
JA Ritcey
EE4162014
Please elaborate with your own illustrations!
Elementary Set Theory
Universe superset containing any element of
interest. This is the complement of the empty set.
Subset collection of none, some, or all elements
S
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
EE 416 Communications I:
Random Signals
Professor Jim Ritcey
Dept of Electrical Engineering
Box 352500/ Room 454 EE1
Seattle WA 98195
2065434702
[email protected]
Ritcey Bio Sketch
BSE & Math Duke University
5 years with GE Aerospace radar 7
co
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
Probability Intro
Professor Jim Ritcey
EE 416
Revised Fall 2014
Please elaborate with your own sketches
Disclaimer
These notes are not complete, but they should
help in organizing the class flow.
Please augment these notes with your own
sketches and mat
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
Discrete Random Variables
Professor Jim Ritcey
University of Washington
EE416 Communications I
Revised Oct 2011
Random Variables
RVs  numerical outcomes of random experiments
Replace cfw_tails, heads by S = cfw_0,1
S=2
Replace cfw_red, green, blue,
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
Probability 2
Professor Jim Ritcey
EE 416
Please elaborate with your own
sketches
Disclaimer
These notes are not complete, but they should
help in organizing the class flow.
Please augment these notes with your own
sketches and math. You need to activel
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
PDF [XI IX! ‘
lx‘(121)'
the node comes online at an
minty that the ﬁrst ma.
: 0.01 is a “mall inm'
amt
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 t “r rat“V
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. 'E‘_' .5": Jun' random Mi Wi‘h “ability I [3. What is the (uncondit
Random Signals for Communications and Signal Processing
EE 416

Fall 2015
110 CHAPTER 1
3.63 In a simple detection scheme, the received signal is X = A‘iHJ'~ $110.". it ix gm.“
that A is the desired signal of magnitude 9 V01“ and ‘1‘" "0‘5" "“ "il‘mnlv
distributed in the range —5 to 5. A detection probability, pd. of 099 is