Theory of Signals and Systems

The details
Computer Science and Electronic Engineering (School of)
Colchester Campus
Postgraduate: Level 7
Thursday 08 October 2020
Friday 18 December 2020
24 May 2019


Requisites for this module



Key module for

MSC H61012 Electronic Engineering,
MSC H64112 Global Communication Systems,
MPHDH60248 Engineering,
PHD H60248 Engineering,
MENGH613 Electronic Engineering,
MENGH614 Electronic Engineering (Integrated Masters, Including Placement Year),
MENGH642 Communications Engineering

Module description

This module provides a mathematical foundation for the study of communication systems and understanding their operation. It starts with review of basic mathematical concepts, such as general operations with functions in signal processing, Fourier transforms, probability density functions, and convolution.

It then uses these tools to examine the operation of modern communication systems, such as analogue (linear CW) and digital modulation, including amplitude modulation, frequency modulation, phase modulation, and multisymbol phase and quadrature amplitude modulation techniques. Fourier analysis is further applied to processing of energy and power signals, signal modulation theorem, introduction of concepts of correlation functions and spectral density of signals and their relationship represented by the Wiener-Khinchine theorem. Various sources of random signals and noise, including quantisation noise, thermal Nyquist-Johnson noise, and additive white-Gaussian noise (AWGN) and their quantitative analysis and contributions to bit error rate (BER) in digital systems are studied in detail. As a practical example of communication system operation and underlying signal processing, basics of digital optical-fibre transmission system are considered and tested in the lab experiment. The course finishes with a discussion of basics of information theory, concepts of self-information and information entropy and their applications to source coding and evaluation of performance bounds (Shannon-Hartley law), and identifies how close commercially important systems are to these bounds.

Module aims

The module aims to provide a mathematical foundation for the study of communication systems and their operation.

Module learning outcomes

On completion of the course, the student is expected to:

1. Perform the shift and scale communication functions, using Woodward's notation.
2. Calculate the mean and variance using a probability density function.
3. Apply the Fourier Transform as a signal processing tool.
4. Understand and evaluate effect of noise in communications.
5. Analyse analogue and digital signal modulation techniques.
6. Analyse signal processing and transmission in optical-fibre communication systems.
7. Apply concepts of information theory to design Huffman codes to compress data.
8. Describe and apply the Shannon-Hartley bound.

Module information

Outline Syllabus

Mathematical review:
Shifting and scaling functions, Woodward's notation.

Probability methods in communications:
Sample space, discrete and continuous random variables; Conditional probability and statistical independence, Bayes theorem’ Cumulative distribution function (CDF) and probability density function (pdf); Probability models and their application in communications; Statistical averages, calculation of mean and variance, tail function.

Transform theory:
Linear time-invariant systems, Fourier series; Definition of Fourier forward and inverse transforms, some Fourier transform pairs; Modulation theorem; Energy and power signals and spectra, Parseval’s and Rayleigh’s theorems; Convolution integral and autocorrelation function, energy and power spectral density.

Analysis of amplitude modulation; Time and frequency domain performance, baseband and bandpass signals, fractional bandwidth; Types of linear CW modulation, DSBTC and DSBSC modulation schemes.
Analysis of digital transmission, signal sampling (Nyquist theorem), modulation (PAM), and coding (PCM); Signal space and signal constellations; ASK, FSK and PSK modulation schemes, Multisymbol signalling, phase modulation and quadrature amplitude modulation (QAM) techniques.
Analysis of signal processing and transmission in optical-fibre communication systems.

Noise in digital communication systems:
Noise and its calculation, noise correlation functions and power spectral density (Wiener-Khinchine theorem); Sources of noise, quantisation noise, thermal Nyquist-Johnson noise, additive white Gaussian noise (AWGN) in communication systems, Signal-to-noise ratio (SNR), bit-error rate (BER) in digital systems and its calculation.

Information theory and coding:
Introduction to information theory, information measure, self-information, information entropy, redundancy of message; Information coding, code performance; Discrete memoryless sources (DMSs), message statistics, digital source coding, the Huffman algorithm, code efficiency estimate; Shannon coding theorem and Shannon-Hartley bound.

Learning and teaching methods

A combination of lectures and classes


  • Couch, Leon W.; Kulkarni, Muralidhar; Acharya, U. Sripati. (©2013) Digital and analog communication systems, Harlow: Pearson Education.
  • Carlson, A. Bruce; Crilly, Paul. (2009) Communication Systems, London: McGraw-Hill Education - Europe.

The above list is indicative of the essential reading for the course. The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students. Further reading can be obtained from this module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Coursework   Assignment 1 - Report on Practical Exercises and Essays    50% 
Coursework   Assignment 2 - Report on Laboratory Experiment    25% 
Written Exam  Progress Test 1 - Week 9     25% 
Exam  120 minutes during Early Exams (Main) 

Overall assessment

Coursework Exam
40% 60%


Coursework Exam
40% 60%
Module supervisor and teaching staff
Dr Nick Zakhleniuk, email: naz@essex.ac.uk.
Dr Nick Zahkleniuk
School Office, e-mail csee-schooloffice (non-Essex users should add @essex.ac.uk to create full e-mail address), Telephone 01206 872770.



External examiner

Prof Raouf Hamzaoui
De Montfort University
Available via Moodle
Of 39 hours, 28 (71.8%) hours available to students:
11 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).


Further information

* Please note: due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.

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