ECEN 455: Assignment 4
Problems:
1. (LA: 8.1.2) Let V be a vector space over F . Show that the sum of two inner products on V is an inner
product on V . Is the difference of two inner products an inner product? Show that a positive multiple
of an inner pr

ECEN 455: Assignment 3
Problems:
1. A discrete-time source generates three independent symbols A, B , and C with probabilities
0.9, 0.08, and 0.02, respectively. Determine the entropy of the source.
2. Design a binary Human code for a discrete-time source

ECEN 455: Assignment 7
Problems:
1. (CSE: 7.31) A Hadamard matrix is dened as a matrix whose elements are 1 and its row vectors are
pairwise orthogonal. In the case where n is a power of 2, and n n Hadamard matrix is constructed
by means of the recursion

% define symbolic variables s and t
syms s t
% define input function
ut = t ^ 0; % input is step function
sint = sin(pi*t); % input is sin(pi*t)
sys = (s+1)/(s^2+5*s+6); % system transfer function
yt = sys_response(sys, ut) % input is step function
yt2 =

Assignment 1
Problems:
1. A defective coin minting machine produces coins whose probability of heads is a random
variable P with PDF
pep , p [0, 1],
fP (p) =
0,
otherwise.
A coin produced by this machine is selected and tossed repeatedly, with successive

COSC 4214: Digital Communications
Instructor: Dr. Amir Asif
Department of Computer Science and Engineering
York University
Handout # 3: Baseband Modulation
Topics:
1. Character Coding (Formatting Textual Data)
2. Pulse Code Modulation (Formatting Analog S

COSC 4214: Digital Communications
Instructor: Dr. Amir Asif
Department of Computer Science and Engineering
York University
Handout # 2: Random Signals
Topics:
1. Random Variables: probability density function, mean, variance, and moments
2. Random process

Chapter 6
Channel Coding
6.1
6.1.1
Introduction
What is channel coding and why do we use it?
Channel coding is the art of adding redundancy to a message in order to
make it more robust against noise. It is used because noise and errors are
essentially una

Chapter 1
Digital Communication
The advent of data transmissions over physical channels has transformed the
modern communication landscape. The term digital communication broadly
refers to the transfer of information using digital messages or bit streams.

Chapter 5
Discrete-Time Communication
Most digital communication systems operate by converting digital data into
continuous waveforms that can be conveyed through some physical medium to
a receiver. For example, digital communication through wires (e.g.,

CSE4214: DIGITAL COMMUNICATIONS PROJECT 3: CONVOLUTIONAL CODES Instructor: Dr. Amir Asif Department of Computer Science and Engineering York University, Toronto, ON M3J 1P3
The students will complete the following project in Matlab and submit their soluti

ECEN 455 Lab 5: Binary Linear Codes
Due Tuesday 11/23/10
Overview:
This exercise will introduce the concept of linear codes used to protect transmitted data from
errors caused by noise in the environment. First, we will use a simple code dened by
110
P =

ECEN 455 Lab 4: Source Coding
Overview:
Bits are the universal unit of information in todays digital world. Any information source can
be represented using bits and bits can be transmitted reliably over an unreliable physical channels.
In this lab, we stu

Assignment 2
Problems:
3
1. Illustrate the eect of undersampling x(t) = cos(2f0 t) for a sampling rate of fs = 2 f0 .
2. Let X be a non-negative discrete r.v. with pmf Pr(X = i) = pi (for i = 0, 1, . . .) and cdf (for
x = 0, 1, . . .)
x
FX (x)
Pr(X x) =
p

Assignment 4
Problems:
1. Let X denote a random variable distributed on the set A = cfw_a1 , a2 , . . . , aN with corresponding probabilities cfw_p1 , p2 , . . . , pN . Let Y be another random variable dened on the same set
but distributed uniformly. Sho

ECEN 455: Assignment 5
Due Monday 11/14/11
Reading:
Required: First Course in Digital Communications Chapter 6
Problems:
1. Calculate the probability of message error PB for a 12-bit data sequence encoded with a
(24, 12) linear block code when the probab

ECEN 455: Assignment 7
Problems:
1. (CSE: 7.31) A Hadamard matrix is dened as a matrix whose elements are 1 and its row vectors are
pairwise orthogonal. In the case where n is a power of 2, and n n Hadamard matrix is constructed
by means of the recursion

ECEN 455: Assignment 8
Problems:
1. (CSE: 8.3) In a binary PAM system, the clock that species the sampling of the correlator output is
offset from the optimum sampling time by 10%.
(a) If the signal pulse used is rectangular, determine the loss in SNR due

ECEN 455: Assignment 8
Problems:
1. (CSE: 8.3) In a binary PAM system, the clock that species the sampling of the correlator output is
offset from the optimum sampling time by 10%.
(a) If the signal pulse used is rectangular, determine the loss in SNR due

ECEN 455: Assignment 9
Optional Problems:
1. (CSE: 8.17) When the additive noise at the input to the modulator is colored, the lter matched to
the signal no longer maximizes the output SNR. In such a case we may consider the use of a prelter
that whitens

ECEN 455: Assignment 9
Optional Problems:
1. (CSE: 8.17) When the additive noise at the input to the modulator is colored, the lter matched to
the signal no longer maximizes the output SNR. In such a case we may consider the use of a prelter
that whitens

COSC 4214: Digital Communications
Assignment # 1: Signals and Spectra
Due Date: October 14, 2004
1. Determine the energy spectral density Gx(f) of a square pulse
1 T t T
2
2
x(t ) =
0 elsewhere.
Also, calculate the normalized energy Ex in the pulse.
2. D

COSC 4214: Digital Communications
Assignment # 1: Signals and Spectra
Due Date: Quiz will be held on September 28, 2006
1. Determine the energy spectral density Gx(f) of a square pulse
1 T t T
2
2
x(t ) =
0 elsewhere.
Also, calculate the normalized energ

COSC 4214: Digital Communications
Assignment # 3: Intersymbol Intereference, Equalization, and Broadband Modulation
Coverage: Sections 3.3 3.4 (upto 3.4.3.2) and Sections 4.1 4.4
Due Date: November 21, 2006
In Chapter 4, we covered a wide range of digital

COSC 4214: Digital Communications
Assignment # 4: Channel Coding
Coverage: Section 6.1 6.7, Sections 7.1 7.3
Due Date: November 29, 2006
Problem 1 (Probability of Symbol Error): Calculate the probability of message error for a 12-bit data
sequence encoded

COSC 4214: Digital Communications
Instructor: Dr. Amir Asif
Department of Computer Science and Engineering
York University
Handout # 4: Baseband Demodulation
Topics:
1. Fundamentals: Vector View of Signals and Noise; SNR
2. Detection of Binary Signals in