ECE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 6 SOLUTION
1. Recall the derivation of the maximum likelihood detector for AWGN channels. The same
principle can be extended to other decision making problems. Suppose that v[n] is an i.
ELE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 7
DUE 10/31 IN CLASS
1. (Chap. 4 Prob. 24) Consider an OFDM communication system and a discrete-time
channel with taps cfw_h[ ]L=0 . Show mathematically why the cyclic prex length Lc mus
ELE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 7 SOLUTION
1. (Chap. 4 Prob. 24) Consider an OFDM communication system and a discrete-time
channel with taps cfw_h[ ]L=0 . Show mathematically why the cyclic prex length Lc must
satisfy
ELE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 1 SOLUTION
1. Find the time autocorrelation of the signal x(t) = eat u(t) and estimate the 95%-power bandwidth of the above signal, where a > 0 and u(t) is a standard step function.
Solu
ECE 5000: Introduction to Analog and Digital Communications
Spring 2015
Course Description
An introduction to communications channel modeling, analog communication schemes, digital communication
schemes, error rate analysis, and error control coding.
Cour
ELE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 4 SOLUTION
1. (Chap. 2 Prob. 15) A favorite sampling problem. Consider the continuous-time signal
xc (t) = cos(10t) + sin(3t + /2).
Let T be the sampling period and reconstruction period
ELE 5000: INTRODUCTION TO ANALOG AND
DIGITAL COMMUNICATIONS
HOMEWORK 1
DUE 1/26 IN CLASS
Reading Assignment: Madhow (2.1-2.3, 2.5-2.7); book can be
downloaded from Carmen.
1. Let x(t) = eat u(t) and estimate the 90%-energy bandwidth of the
above signal, w
ECE 5000: Introduction to Analog and Digital Communications
Midterm Examination 1 Solution
Due to misallocation, the total points of all three problems add up to 95; therefore everyone is
given an extra 5 points as long as she writes her name on the cover
ELE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 3
DUE 9/19 IN CLASS
1. (Chap. 2 Prob. 3) Let x[n] and y [n] be two independent zero-mean complex WSS
random signals with autocorrelations Rxx [k ] and Ryy [k ], respectively. Determine t
ELE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 2 SOLUTION
1. Consider the message signal
m(t) = 2 cos(2t),
and its AM modulated signal
s(t) = [A + m(t)] cos(100t).
(1) Sketch s(t) respectively when A = 0 and A = 5.
(2) Sketch the Fou
ECE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 1 SOLUTION
1. Find the time autocorrelation of the signal x(t) = eat u(t) and estimate the 90%-power bandwidth of the above signal, where a > 0 and u(t) is a standard step function.
Solu
ECE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 3
DUE 2/13 IN CLASS
Recommended reading: Heath 3.9-3.11, Madhow 2.8
1. Consider the continuous-time signal
xc (t) = cos(10t) + sin(3t + /2).
Let T be the sampling period and reconstructi
ECE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 2 SOLUTION
1. Consider the message signal
m(t) = 2 cos(2t),
and its AM modulated signal
s(t) = [A + m(t)] cos(100t).
(1) Sketch s(t) respectively when A = 0 and A = 5.
(2) Sketch the Fou
ECE 5000: Introduction to Analog and Digital
Communications
Midterm Examination 1
Feb. 14, 2014, 11:30 12:25 PM
Closed Book, Closed Notes
1 page cheat sheet. No calculator.
Name:
OSU ID:
Problem Your Score Possible
1
30
2
38
3
32
Total
100
1. (30 pts) We
ECE 5000: Introduction to Analog and Digital Communications
2014 Spring Midterm Examination 1 Solution
1. (30 pts) We are interested in transmitted a message signal m(t) = cos(4t). Assume the carrier
frequency is 1000Hz.
(a) (8 pts) Write the AM modulated
ECE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 5
DUE 3/9 IN CLASS
Reading: Heath Chapter 4.1-4.5
1. Consider the following new M = 8 point constellation illustrated in Fig. 1.
Figure 1. An 8-point constellation.
(1)
(2)
(3)
(4)
Compu
ECE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 4
DUE 3/2 IN CLASS
1. Let E1 and E2 be two events and P(E1 ) = 1/4. Evaluate P(E2 ) for each of the scenarios below:
(1)
(2)
(3)
(4)
(5)
c
E2 = E1 .
E1 and E2 are disjoint and P(E1 E2 )
ECE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 4
DUE 3/2 IN CLASS
1. Let E1 and E2 be two events and P(E1 ) = 1/4. Evaluate P(E2 ) for each of the scenarios below:
(1)
(2)
(3)
(4)
(5)
c
E2 = E1 .
E1 and E2 are disjoint and P(E1 [ E2
ECE 5000: Introduction to Analog and Digital
Communications
Lecture 3: Sampling Theorem, Complex Baseband model
Yuejie Chi
Dept. of Electrical and Computer Engineering
Ohio State University
Sampling
Reduce a continuous signal to a discrete signal: samplin
Notes
ECE 5000: Introduction to Analog and Digital
Communications
Lecture 0: Introduction
Reading: Madhow Chapter 1
Yuejie Chi
Dept. of Electrical and Computer Engineering
Ohio State University
Course Information
Time: Mon/Wed/Fri 1:50 - 2:45pm
Location:
ECE 5000: Introduction to Analog and Digital
Communications
Lecture 1: Reviews for Signal and Systems
Yuejie Chi
Dept. of Electrical and Computer Engineering
Ohio State University
Linear Time-Invariant System
What is a linear time-invariant system?
If inp
Notes
ECE 5000: Introduction to Analog and Digital
Communications
Lecture 5: Introduction to Digital Modulation
Yuejie Chi
Dept. of Electrical and Computer Engineering
Ohio State University
Digital Communications
The transmitted message is discrete-time b
ECE 5000: Introduction to Analog and Digital Communications
Midterm 1 Review Sheet
The most important goal of this course is to understand the fundamentals of digital communication
systems.
Analog communication schemes can be regarded as a component (mo
ECE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 3 SOLUTION
1. A favorite sampling problem. Consider the continuous-time signal
xc (t) = cos(10t) + sin(3t + /2).
Let T be the sampling period and reconstruction period. Let xs (t) = xc (
Notes
ECE 5000: Introduction to Analog and Digital
Communications
Lecture 5: Introduction to Digital Modulation
Yuejie Chi
Dept. of Electrical and Computer Engineering
Ohio State University
Digital Communications
The transmitted message is discrete-time b
Notes
ECE 5000: Introduction to Analog and Digital
Communications
Lecture 4: Primer on Random Variables and Random Processes
Yuejie Chi
Dept. of Electrical and Computer Engineering
Ohio State University
Randomness in Communications
I
Randomness in source:
ECE 5000: Introduction to Analog and Digital
Communications
Lecture 6: Error Analysis
Reading: Chapter 3.7-3.8
Yuejie Chi
Dept. of Electrical and Computer Engineering
Ohio State University
Symbol Detection in the AWGN Channel
I
So far we have discussed ho
ECE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 2 SOLUTION
1. Consider the message signal
m(t) = 2 cos(2t),
and its AM modulated signal
s(t) = [A + m(t)] cos(100t).
(1) Sketch s(t) respectively when A = 0 and A = 5.
(2) Sketch the Fou
ECE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 4
DUE 9/29
1. Let E1 and E2 be two events and P(E1 ) = 1/4. Evaluate P(E2 ) for each of the scenarios below:
(1)
(2)
(3)
(4)
(5)
E2 = E1c .
E1 and E2 are disjoint and P(E1 E2 ) = 1/2.
E1
ECE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 1 SOLUTION
1. Find the time autocorrelation of the signal x(t) = eat u(t) and estimate the 90%-power bandwidth of the above signal, where a > 0 and u(t) is a standard step function.
Solu
ECE 5000: INTRODUCTION TO ANALOG AND DIGITAL
COMMUNICATIONS
HOMEWORK 3
DUE 9/22
Recommended reading: Heath 3.9-3.11, Madhow 2.8
1. Consider the continuous-time signal
xc (t) = cos(10t) + sin(3t + /2).
Let T be the sampling period and reconstruction period