EE279 Introduction to Digital Communication
Handout 3
Solutions to Homework 1
Stanford University
Problem 1. Three events E1 , E2 and E3 , dened on the same space, have probabilities
P (E1 ) = P (E2 ) = P (E3 ) = 1/4. Let E0 be the event that one or more
EE279 Introduction to Digital Communication
Handout 1
Homework 1
Stanford University
Due January 15, 2014
Problem 1. Three events E1 , E2 and E3 , dened on the same space, have probabilities
P (E1 ) = P (E2 ) = P (E3 ) = 1/4. Let E0 be the event that one
EE279 Introduction to Digital Communication
Stanford University
Due January 29, 2014
Handout 5
Homework 3
Problem 1. (Artifacts of Suboptimality) Let H take on the values 0 and 1 equiprobably.
Conditional on H = 0, the observation Y is N (1, 2), and, cond
EE279 Introduction to Digital Communication
Handout
Homework 5
Problem 1. (Average Energy of PAM).
Exercise 9. in Section 4.10. of the lecture note.
Problem 2. (Bit Error Probability).
Exercise 13. in Section 4.10. of the lecture note.
Problem 3. (m-ary F
EE279 Introduction to Digital Communication
Stanford University
Due February 5, 2014
Handout
Homework 4
Problem 1. (Robust Decoding Rule) Consider the binary hypothesis testing problem and
assume the prior probabilities are unknown. In this case, our deci
Chapter 6
Convolutional Coding and Viterbi
Decoding
6.1
Introduction
In this chapter we shift focus to the encoder/decoder pair. The general setup is that of
Figure 6.1, where N (t) is white Gaussian noise of power spectral density N0 /2 . The
details of
EE279 Introduction to Digital Communication
Handout 4
Solutions to Homework 2
Stanford University
Due January 22, 2014
Problem 1. (Hypothesis Testing: Uniform And Uniform)
Solution 1. (i) Let l(y ) be the number of 0s in the sequence y .
PY |H (y |0) =
1
Stanford University
EE 279 Introduction to Digital Communication
Practice problems for Midterm
Problem 1. Lecture notes Exercise 6 from Chapter 3(On-O Signaling)
Solution 1. (On-O Signaling)
(a) The maximum likelihood receiver for the observable Y (t) use
EE279 Introduction to Digital Communication
Handout
Solutions to Homework 3
Stanford University
Due January 29, 2014
Problem 1. (Artifacts of Suboptimality) Let H take on the values 0 and 1 equiprobably.
Conditional on H = 0, the observation Y is N (1, 2
EE 279 Professor Cox Solution to Final 1. (12pt) a) ii) b) i) iii) c) i) iv) d) vi) 2. (35pt)
t
Winter 2005-2006 HO #
In phase-acceleration modulation we have: f (t ) = f c + K ! x(" )d" . Therefore to recover the signal we should extract the phase
EE279 Introduction to Digital Communication
Handout 13
Solutions to Homework 5
Stanford University
Due February 19, 2014
Problem 1. (Average Energy of PAM).
(2,2,2 marks)
m
Solution 1. (a) The pdf of S can be written as fS (s) = i2 m +1 (s (2i 1)a) while
EE279 Introduction to Digital Communication
Handout
Solutions to Homework 4
Stanford University
Due February 5, 2014
Problem 1. (Robust Decoding Rule) Consider the binary hypothesis testing problem and
assume the prior probabilities are unknown. In this c
Chapter 2
Receiver Design for Discrete-Time
Observations
2.1
Introduction
The focus of this ad the next chapter is the receiver design. The task of the receiver can
be appreciated by considering a very noisy channel. Roughly speaking, this is a channel
fo
Stanford University
EE 279 Introduction to Digital Communication
Practice problems for Midterm
Problem 1. Lecture notes Exercise 6 from Chapter 3(On-O Signaling)
Problem 2. Lecture notes Exercise 7 from Chapter 3(Matched Filter Intuition)
Problem 3. Lectu
EE279 Introduction to Digital Communication
Handout
More practice problems for nals
Problem 1. Exercise 6.11 (Trellis with Antipodal Signals)
Problem 2. Exercise 6.12 (Viterbi for Bianry Erasure Channel)
Stanford University
EE279 Introduction to Digital Communication
Handout
Solutions for additional problems
Stanford University
Problem 1. (Trellis with Antipodal Signals)
Solution 1.
2.
1. For (j 1 , j +1 ) = (+1, +1), the condition is a c b + d.
For (j 1 , j +1 ) = (+1, 1),
Chapter 5
Nyquist Signalling
5.1
Introduction
In this and the following chapter, we focus on widespread signaling techniques. This
chapter is devoted to the waveform former and its receiver-side counterpart, the n -tuple
former. Chapter 6 focuses on the e
Chapter 4
Signal Design Trade-Os
4.1
Introduction
In Chapters 2 and 3 we have focused on the receiver, assuming that the signal set was
given to us. In this chapter we introduce the signal design. We have three main goals in
mind: (i) Introduce the design
Chapter 7
Passband Communication via Up/Down
Conversion
7.1
Introduction
We speak of baseband communication when we refer to communication via signals that
have their energy in some frequency interval [ B , B ] around the origin (Figure 7.1(a).
Much more
EE279 Introduction to Digital Communication
Handout 2
Homework 2
Stanford University
Due January 22, 2014
Problem 1. (HypothesisTesting: Uniform And Uniform)
Exercise 1. of Lecture notes Section 2.13 (page 71)
Problem 2. (Lie Detector)
Exercise 5. of Lect
EE279 Introduction to Digital Communication
Handout
Homework 6
Stanford University
Due February 26, 2014
Problem 1. Fourier Transform Prove the following properties of Fourier Transform:
1. frequency shift: h(t)ej 2f0 t
2. time shift: h(t s)
hF (f )ej 2f
EE279 Introduction to Digital Communication
Handout 16
Solutions to Homework 6
Stanford University
Due February 26, 2014
Problem 1. Fourier Transform
Prove the following properties of Fourier Transform:
1. frequency shift: h(t)ej 2f0 t
2. time shift: h(t
EE279 Introduction to Digital Communication
Handout
Homework 7
Stanford University
Due March 5, 2014
Problem 1. Exercise 18 (Energy Eciency of PAM) from chapter 4
Problem 2. Exercise 1 (Matched Filter Basics) from chapter 5
Problem 3. Exercise 2 (Dierenti
EE279 Introduction to Digital Communication
Handout
Solutions to Homework 7
Stanford University
Due March 5, 2014
Problem 1. (Energy Eciency of PAM).
(2,2,2,2,2 marks)
Solution 1.
1.
C
Es (k ) = 2 (22k 1).
2. We equate the given approximation for Q functi
EE279 Introduction to Digital Communication
Stanford University
Handout
Solutions to practice problems
Problem 1. (Nyquist Criterion).
Solution 1. For g (t) to be a Nyquist pulse, its Fourier Transform must satisfy:
gF (f + k/T ) = T.
(1)
For shifts of (t
EE279 Introduction to Digital Communication
Handout
Practice problems
Stanford University
Problem 1. Exercise 5.4 (Nyquist criterion)
Problem 2. Exercise 5.7 (Mixed questions)
Problem 3. Exercise 6.1 (Power spectral density)
Problem 4. Exercise 6.2 (Power
EE279 Introduction to Digital Communication
Handout
Homework 8
Stanford University
Due March 14, 2014
In this assignment, you will transmit an image over a simulated AWGN channel and
assess the performance of convolutional coding vs. uncoded transmission.
% BITS2IMG Converts a vector of bits to an image
% X = BITS2IMG(S, B, M, N) returns an M x N matrix X whose entries
% are of type UINT8 that is obtained by reconstructing the image from
% the bit sequence S. B is the number of bits per pixel, and M and N
Chapter 4
Signal Design Trade-Os
4.1
Introduction
In Chapters 2 and 3 we have focused on the receiver, assuming that the signal set was given
to us. In this chapter we introduce the signal design. The problem of choosing a convenient
signal constellation