EEEN30110 Signals and Systems

Academic Year 2023/2024

Linear, time-invariant (LTI) systems often provide a first approximation of the behaviour of systems close to an operating region. This module offers an introduction to the analysis of LTI systems both in continuous and discrete-time. It is impossible to provide an analysis procedure for systems without introducing signals and the tools principle tools used for their analysis. Within the module, the mathematical ideas are described, which underpin the very important concept of the frequency content of a signal and the frequency response of a system. The module covers the mathematics required to undertake a study of dynamics, communication theory, signal processing, advanced circuit theory and control theory, with engineering examples. Above all the module also provides advanced techniques for the solution of linear, constant coefficient, ordinary differential and difference equations, motivated by engineering applications in which the equations of motion are of this form.

Module Outline:
LTI systems: introduction, main definitions and examples.
Signals and systems: basic definitions.
The continuous and discrete-time Fourier series.
The continuous and discrete-time Fourier transform.
The Laplace transform.
The z-transform.

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Curricular information is subject to change

Learning Outcomes:

On successful completion of this subject the student will be able to:

1. Explain the mathematical basis for the frequency content of a signal with particular reference to the Fourier series and the Fourier transform.

2. Explain the mathematical basis of the frequency response of a linear, time-invariant system, analog or discrete-time.

3. Derive mathematical models for and analyse the response of linear, time-invariant systems, analog or discrete-time.

4. Effectively solve linear, constant coefficient ordinary differential and difference equations.

5. Effectively employ MATLAB in the analysis of signals and systems.

Indicative Module Content:

The topics outlined in the content will be complemented with examples. Computer-based simulations and experiments will complement the learning.

1. SIGNALS AND SYSTEMS:
Exponential and Sinusoidal Signals
The Unit Impulse and Unit Step Functions
Continuous-Time and Discrete-Time Systems
Basic System Properties

2. LINEAR TIME-INVARIANT SYSTEMS
Discrete-Time LTI Systems: The Convolution Sum
Continuous-Time LTI Systems: The Convolution Integral
Properties of Linear Time-Invariant Systems
Causal LTI Systems Described by Differential and Difference Equations

3. FOURIER SERIES REPRESENTATION OF PERIODIC SIGNALS
The steady-state response of stable LTI Systems to complex exponential inputs
Fourier Series Representation of Continuous-Time Periodic Signals
Properties of Continuous-Time Fourier Series
Fourier Series Representation of Discrete-Time Periodic Signal
Properties of Discrete-Time Fourier Series
Fourier analysis of LTI Systems

4. THE CONTINUOUS-TIME FOURIER TRANSFORM
Representation of Aperiodic Signals: The Continuous-Time Fourier Transform
The Fourier Transform for Periodic Signals
Properties of the Continuous-Time Fourier Transform
The Convolution Property
The Multiplication Property
The frequency response of systems characterised by Linear Constant-Coefficient Ordinary Differential Equations

5. THE DISCRETE-TIME FOURIER TRANSFORM
Representation of Aperiodic Signals: The Discrete-Time Fourier Transform
The Fourier Transform for Periodic Signals
Properties of the Discrete-Time Fourier Transform
The Convolution Property
The Multiplication Property
The frequency response of systems characterised by Linear Constant-Coefficient Ordinary Difference Equations

6. THE LAPLACE TRANSFORM
The Laplace Transform
The Inverse Laplace Transform
Properties of the Laplace Transform
Some Laplace Transform Pairs
Analysis and Characterisation of LTI Systems Using the Laplace Transform

7. THE Z-TRANSFORM
The z-Transform
Properties of the z-Transform
Some Common z-Transform Pairs
Analysis and Characterisation of LTI Systems Using z-Transforms

Student Effort Hours: 
Student Effort Type Hours
Lectures

28
Laboratories

10
Specified Learning Activities

17
Autonomous Student Learning

60
Total

115
Approaches to Teaching and Learning:
1. Lectures first introduce the ideas behind the theory that is going to be developed;
2. The formalisation of the idea leads to the development of the theory;
3. Software is used to develop experiments illustrating the main features of the theory; 
Requirements, Exclusions and Recommendations
Learning Requirements:

Differential and Integral Calculus to advanced level 1 or better.
Differential Equations to advanced level 1 or better.
Algebra, vectors and complex numbers to advanced level 1 or better.


Module Requisites and Incompatibles
Not applicable to this module.
 
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Lab Report: 3 laboratory reports Varies over the Trimester n/a Graded No

100

Carry forward of passed components
No
 
Resit In Terminal Exam
Spring No
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Feedback individually to students, on an activity or draft prior to summative assessment
• Feedback individually to students, post-assessment
• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Name Role
Afua Boakyewaah Appiah Tutor
Prarthana Saikia Tutor
Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
 
Autumn
      
Lecture Offering 1 Week(s) - 1, 2, 3, 4, 5, 6, 7, 9, 10 Mon 11:00 - 11:50
Lecture Offering 1 Week(s) - 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Tues 14:00 - 14:50
Lecture Offering 1 Week(s) - 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Wed 12:00 - 12:50
Laboratory Offering 1 Week(s) - 1, 2, 5, 8, 11 Fri 12:00 - 13:50
Laboratory Offering 2 Week(s) - 1, 2, 5, 8, 11 Fri 15:00 - 16:50
Autumn