Chapter 5
Bandwidth of Digital Signals
The goals of this chapter are to first to determine the bandwidth of digital signals. Because the signals
are random (due to the random nature of the data) we need to determine the power spectral density
of the rando
Chapter 1
Introduction
The goal of communication systems is to transmit information from one location and reliably receive that
information at a second location. There are two important resources that are needed for reliable communications. These resource
Chapter 2
Background on Signals and Systems
In this chapter we review the basic concepts of signals and systems that are needed in understanding
digital communication systems. First we show how points in space as described in Chapter 1 can be
mapped into
Chapter 6
Binary Communication: Optimum
Receiver, Optimum Signals
The goal of this chapter is to derive the optimal threshold, filter, signals for a binary communications
system that consists of transmitter that communicates one bit of information using o
Chapter 3
Simulation of Signals and Noise
The goal of this chapter is to be able to generate signals and noise in time and frequency domain in
MATLAB
3.1 Review of Signals
Consider a signal x(t) with Fourier Transform X ( f ). Suppose X ( f ) is zero for
Chapter 4
Error Probability for Binary Signals
The goal of this chapter is to be able to determine the error probability in a system with two signals and a
receiver filter in the presence of additive white Gaussian noise. The error probability is a functi
Appendix A
Maximal length sequences: m-sequences
Maximal length shift register sequences are used in many applications including spread-spectrum systems. They
are sometimes called pseudo-noise (PN) sequences because they seem to have noise like properties
EECS 455: Solutions to Problem Set 4
1. A data signal consists of an infinite sequence of rectangular pulses of duration T . That is
s(t) =
l=
bl pT (t lT )
where pT (t) is 1 for 0 t T and zero elsewhere. The data is represented by bl and is either
+1 or
EECS 455: Solutions to Problem Set 2
1. (a) Consider two signals of duration T seconds.
r
2
cos(2 f0t)pT (t)
0 (t) =
T
r
2
1 (t) =
cos(2 f1t)pT (t).
T
Determine the minimum separation between f0 and f1 so that 0 (t) and 1 (t) are orthogonal.
Solution:
(0
EECS 455: Solutions to Problem Set 3
1. (a) Consider a complex sequence of length N=10;
x = (1 j, 1 + j, 1 + j, 1 + j, 1 + j, 1 + j, 1 + j, 1 j, 1 j, 1 + j)
Now consider a matched filter h(n) = x (N n) Determine the output of the matched filter
when the i
EECS 455: Solutions to Problem Set 1
Due: Wednesday, September 13, 2015.
1. A communication system transmits one of 8 equally likely signals. The signal (waveforms)
are represented by the vectors shown below by some. suitable set of orthonormal signals.
(
(c) Now consider the effect with noise. Determine the probaiblity of error with and without
multipath. Your answers should be in terms of the Q function and Eb /N0 .
Solution: Without multipath
Pe = Pcfw_y(T ) < 0|b0 = +1
= Pcfw_ E + < 0|b0 = +1
= Pcfw_ <
EECS 455: Solutions to Exam I, Fall 2012
1. (a) A communication system has (null-to-null)bandwidth of 20MHz available. The requirement is for a system with error probability Q( 16). The received power is P = 1016 Watts.
The noise power spectral density is
EECS 455: Solution to Problem Set 5
1. (a) A communication system with data rate of 30Mbps is desired using a bandwidth of
10MHz. What is the minimum received signal-to-noise ratio (Eb /N0 ) required to achieve
reliable (arbitrarily small error probabilit
NOTES FOR EXAM 1
#include <iostream> means that it can now take input from the keyboard.
input/output operations require that you include the input/output standard file
from the C+ standard library. This includes things like <, endl, cout, cin, etc.
using
Wednesday, October 12, 2016
Announcements
HKN office hours next week
Complete your mid-term online evaluations now
Todays agenda
10/10/16 10/18/16
Review for exam
Next time (10/19/16)
Read section 6.2 and 6.3
Midterm Exam #1 information
Wednesday, October
EECS 215 Winter Semester 2015 Midterm Exam Iece
Name (Last, First):
Uniqname:
Rules:
a) Nominal exam time: Wednesday, February 11, 2015, 3:30 to 5:30 PM.
Due to medical issues, a smaller number of students may be taking this
exam as late as Friday. Do not
Your name: _
EECS 215.
Midterm Exam #1
February 9, 2016
This text consists of 8 problems with points as indicated to total 100 points.
Read through the entire exam before beginning.
Show all work (on the pages provided in this booklet) to earn partial cre
The University of Michigan
Electrical Engineering & Computer Science
EECS 281: Data Structures and Algorithms
Fall 2015
M IDTERM E XAM , PRACTICE
Written Portion
Wednesday October 28, 2015
7:10PM 8:40PM (90 minutes)
Name:
Uniqname:
Student ID:
Uniqname of
The University of Michigan
Electrical Engineering & Computer Science
EECS 281: Data Structures and Algorithms
Fall 2015
M IDTERM E XAM , PRACTICE
Multiple-Choice Portion, KEY 1
Wednesday October 28, 2015
7:10PM 8:40PM (90 minutes)
I NSTRUCTIONS :
The exa
The University of Michigan
Electrical Engineering & Computer Science
EECS 281: Data Structures and Algorithms
Fall 2015
M IDTERM E XAM , PRACTICE
Multiple-Choice Portion, KEY 1
Wednesday October 28, 2015
7:10PM 8:40PM (90 minutes)
I NSTRUCTIONS :
The exa
The University of Michigan
Electrical Engineering & Computer Science
EECS 281: Data Structures and Algorithms
Fall 2015
M IDTERM E XAM , PRACTICE
Written Portion
Wednesday October 28, 2015
7:10PM 8:40PM (90 minutes)
Name:
Uniqname:
Student ID:
Uniqname of
Lecture 14
Binary Search Trees
EECS 281: Data Structures & Algorithms
1
Search
Retrieval of a particular piece of information from
large volumes of previously stored data
Purpose is typically to access information within
the item (not just the key)
Rec
Lecture 13
Trees and Tree Algorithms
EECS 281: Data Structures & Algorithms
1
Informal Definition: Tree
Mathematical abstraction that plays a central role
in the design and analysis of algorithms
Build and use explicit data structures that are
concrete r
Lecture 11
QuickSort
EECS 281: Data Structures & Algorithms
Two Problems with Simple
Sorts
They might compare every pair of elements
Learn only one piece of information/comparison
Contrast with binary search: learns N/2 pieces of
information with first
Lecture 12
Midterm Exam Review
EECS 281: Data Structures & Algorithms
Time and Location
When: Wednesday October 28th, 7:00pm (Michigan time, so 7:10) 8:40pm (90min)
Where: (by uniqname)
Room
First Uniqname In This Room
Last Uniqname In This Room
CHRYS22