48540 Signals and Systems

Warning: The information on this page is indicative. The subject outline for a particular session, location and mode of offering is the authoritative source of all information about the subject for that offering. Required texts, recommended texts and references in particular are likely to change. Students will be provided with a subject outline once they enrol in the subject.

Subject handbook information prior to 2025 is available in the Archives.

UTS: Engineering: Electrical and Data Engineering
Credit points: 6 cp

Subject level:

Undergraduate

Result type: Grade and marks

Requisite(s): 48520 Electronics and Circuits
Anti-requisite(s): 41090 Information and Signals

Recommended studies:

circuit analysis in both the time and frequency domains, utilising mathematics involving solutions to differential equations using time-domain techniques as well as transform methods

Description

This subject presents the theoretical basis for system analysis and gives students skills in using the techniques to design components of real control/communication systems. The derivation of models from real-world devices through measurement and the comparison of model predictions with experimental results is emphasised in the laboratory component of the course. A group project that requires the design and implementation of part of a control/communication system allows students to apply their knowledge to a real-life problem. Topics include signal types and their representation in the time and frequency domains; modelling systems with differential or difference equations and transforms of the equations; signal operations and processing; the relationship between discrete and continuous quantities and the mathematical techniques applicable to each; the effects of feedback; time and frequency domain performance of systems; system stability; and control design techniques and simple communication systems. Through learning activities students also gain study skills, including academic literacy skills, and an appreciation of the different fields of practice of engineering and the interdisciplinary nature of engineering. Class time is used for lectures, tutorials, laboratories and project work. There are a number of formal laboratory sessions that apply control and communication theory, which also familiarise students with the laboratory equipment. The subject culminates in the design and implementation of a control system and communication system for a remote-controlled robot.

Subject learning objectives (SLOs)

1.	Apply the mathematical tools associated with transform theory to the analysis and design of continuous-time and discrete-time systems. (D.1)
2.	Analyse, design, simulate and test parts of a communication system and a control system in both the time-domain and frequency-domain. (D.1)
3.	Model real and complex systems using a hierarchical approach, and be able to simplify them with appropriate assumptions. (D.1)
4.	Measure time and frequency characteristics of signals and systems using appropriate laboratory equipment. (D.1)
5.	Communicate technical ideas, decisions, calculations and experimental results in a written document. (E.1)

Course intended learning outcomes (CILOs)

This subject also contributes specifically to the development of the following Course Intended Learning Outcomes (CILOs):

• Technically Proficient: FEIT graduates apply abstraction, mathematics and discipline fundamentals, software, tools and techniques to evaluate, implement and operate systems. (D.1)
• Collaborative and Communicative: FEIT graduates work as an effective member or leader of diverse teams, communicating effectively and operating within cross-disciplinary and cross-cultural contexts in the workplace. (E.1)

Contribution to the development of graduate attributes

Engineers Australia Stage 1 Competencies

This subject contributes to the development of the following Engineers Australia Stage 1 Competencies:

• 1.3. In-depth understanding of specialist bodies of knowledge within the engineering discipline.
• 2.2. Fluent application of engineering techniques, tools and resources.
• 3.2. Effective oral and written communication in professional and lay domains.

Teaching and learning strategies

This subject uses a problem-based learning strategy that allows students to research and develop their own solutions to complex design challenges. There are a number of formal laboratory sessions. Students then undertake a substantial group project that reinforces the theoretical content and culminates in a formal written presentation of their work.

Class class time occurs in two 2 hour sessions per week. The first 2 hour session is used to conduct class activities, such as collaborative problem solving. The second 2 hour session is used to conduct hands-on activities.

1. Prior to each class session, students will be required to study the Notes and associated readings and prepare questions relating to the weekly content and the assesment tasks they are working on.

2. At the beginning of the class session, academic staff will discuss with the entire group the challenges they are facing. Students faced with similar challenges will be prompted to come together to facilitate collaborative discussions and work on tutorial exercises in a group setting.

3. Prior to each lab session, students will be required to complete pre-lab work.

4. In the lab session, students will work in groups of 2 on their tasks. Academic staff are available in each lab to review work and provide immediate feedback.

5. For the final project, lab time will be used for one-on-one consultations on particular aspects of a student's work.

Content (topics)

The content covered is divided into the following sections:

1. Signals and Systems in the Time-Domain

2. Signals and Systems in the Frequency-Domain

3. Transfer Functions

4. Discrete-Time Systems

5. Control Systems

6. State-Variables

7. Design Project

Each of these sections addresses an important aspect in modern systems. The intention is that, as you work your way through the subject, your learning will be cumulative. That is, the content you cover in one section should directly help you to understand the topics that follow. A weekly learning schedule, based on a recommended study sequence of the sections, is given in the Study Guide. For each of the above sections, a separate list of topics, exercise problems and suggested reading is also provided in the Study Guide.

Below is a brief summary of the content that is later covered in detail in the Notes.

Prerequisite knowledge

You are expected to have successfully completed introductory subjects in Mathematics and Circuit Analysis. Specifically, you should be able to analyse a second-order circuit using differential equations, phasors and Laplace transforms, as well as simulating the response using MATLAB®.

Section 1 – Signals and Systems in the Time-Domain

Most signals are shown to be made up of a small set of simple signals, which are formalised and categorised. The importance of the sinusoid is emphasised and the phasor definition is given new meaning by introducing the concept of negative frequency. Linear systems are described by their differential equations. The solution of a first-order system for an arbitrary input is shown to lead to the convolution integral – an alternative way to describe a system.

Section 2 – Signals and Systems in the Frequency-Domain

The orthogonal properties of the sinusoid are used to build a “frequency-domain” picture of signals. Periodic signals are shown to consist of a set of harmonically related sinusoids – the Fourier Series and the concept of a spectrum are thus introduced. The spectrum sheds new light on the behaviour of systems, especially those naturally considered to operate in the frequency-domain, such as filters. The concept of the Fourier Series is extended to almost any arbitrary signal by introducing the Fourier Transform. The concept of a system’s frequency response operating on a signal’s spectrum to produce a new output spectrum is introduced. The complementary operations of sampling and reconstruction; and modulation and demodulation; are introduced as important underlying concepts of modern communication and signal processing systems.

Section 3 – Transfer Functions

The Laplace Transform and the concept of the s-domain and transfer functions is developed as a generalisation of Fourier analysis. It is then shown how all linear systems can be analysed for nearly any input in the s-domain. This leads to a simple description of systems in terms of blocks containing transfer functions. The concept of stability of a system is introduced, as well as the nature of step responses and sinusoidal responses of systems. The frequency response is revisited but in terms of synthesis using Bode plots rather than analysis. The time-domain response of the step-input of a system is analysed and performance measures of a system’s step-response are introduced. Feedback – the cornerstone of modern control theory – is introduced and some of the advantages of feedback are examined.

Section 4 – Discrete-Time Systems

Modern systems use digital signal processing and are therefore inherently discrete-time systems. The analysis of such systems in the frequency-domain leads to the z-transform – which has a correspondence with the Laplace Transform. The properties of the z-transform are introduced, and simple systems and signals analysed in the z-domain. Discretization of signals, and reconstructing them back into the continuous-time domain is a basic operation of digital signal processing systems. The effects of this operation are examined. The discretization of systems is also looked at from the point of view of matching in the frequency-domain and time-domain.

Section 5 – Control Systems

Automatic control systems are a fact of modern life. This section looks at how control systems are specified and designed. It introduces the concept of designing with poles and zeros, and shows the utility of the root locus method. The effect of system discretization, used in a digital implementation of a control system, is examined briefly.

Section 6 – State-Variables

The idea of representing a system in terms of only input and output behaviour is challenged by the method of state-variables, which attempts to encapsulate the internal time-domain behaviour of a system. It’s power as an analysis and design method becomes evident when it is shown how initial conditions and multiple inputs and outputs are easily handled by state-variables. The set of state equations which describe a system are solved in both continuous-time and discrete-time, and it is shown how the solution can be easily applied to high-order systems. State-variable feedback is introduced.

Section 7 – Design Project

This section brings all the other sections together in a project that requires the analysis and design of a communication scheme and a control scheme. You will be required to interpret specifications for each scheme and come up with sound engineering designs using a variety of methods. The designs will be simulated and then experimentally verified.

Assessment

Assessment task 1: Lab assignments

Intent:	Students demonstrate their skills in modelling and practical applications of signal theory.
Objective(s):	This assessment task addresses the following subject learning objectives (SLOs): 1, 2, 3 and 4 This assessment task contributes to the development of the following Course Intended Learning Outcomes (CILOs): D.1
Type:	Laboratory/practical
Groupwork:	Individual
Weight:	25%

Assessment task 2: Project

Intent:	Students demonstrate their ability to analyse a set of specifications, design, simulate, test and practically demonstrate a simple control scheme and a simple signal processing scheme.
Objective(s):	This assessment task addresses the following subject learning objectives (SLOs): 1, 2, 3, 4 and 5 This assessment task contributes to the development of the following Course Intended Learning Outcomes (CILOs): D.1 and E.1
Type:	Project
Groupwork:	Group, group assessed
Weight:	15%

Assessment task 3: Quiz

Intent:	Students demonstrate their knowledge of signals.
Objective(s):	This assessment task addresses the following subject learning objectives (SLOs): 1, 2 and 3 This assessment task contributes to the development of the following Course Intended Learning Outcomes (CILOs): D.1
Type:	Quiz/test
Groupwork:	Individual
Weight:	20%

Assessment task 4: Final Exam

Intent:	Students demonstrate their knowledge of systems.
Objective(s):	This assessment task addresses the following subject learning objectives (SLOs): 1, 2, 3 and 5 This assessment task contributes to the development of the following Course Intended Learning Outcomes (CILOs): D.1 and E.1
Type:	Examination
Groupwork:	Individual
Weight:	40%

Minimum requirements

In order to pass the subject, a student must achieve an overall mark of 50% or more.

Required texts

Lathi, B.P., Linear Systems and Signals, 2nd Ed., Oxford University Press, 2005. ISBN 0-19-515833-4

McLean, P., 48540 Signals and Systems Notes, UTS, 2016.

Recommended texts

Kamen, E.W. and Heck, B.S., Fundamentals of Signals and Systems Using the Web and MATLAB®, 2nd Ed., Prentice Hall, 2000. ISBN 0-13-017293-6

References

Carlson, G.E., Signal & Linear System Analysis, 2nd Ed., Wiley & Sons, 1997.

Haykin, S., Communication Systems, 3rd Ed., Wiley, 1994.

Kamen, E.W. and Heck, B.S., Fundamentals of Signals and Systems Using the Web and MATLAB®, 2nd Edition, Prentice Hall, 2000.
ISBN 0-13-017293-6

Kuo, B.C., Automatic Control Systems, 7th Ed., Prentice-Hall, 1995.

Ogata, K., Modern Control Engineering, 2nd Ed., Prentice-Hall, 1990.

Shinners, S., Modern Control System Theory and Design, Wiley, 1992.

Van de Vegte, J., Feedback Control Systems, 3rd Ed., Prentice-Hall, 1994.

Other resources

Canvas provides past exams, links to simulation programs and MATLAB® examples and a Discussion Board. All Faculty computer laboratories in Building 11 have been set up with MATLAB®, the Control System Toolbox and the Signal Processing Toolbox. The Signals Lab (CB11.11.302) also has MATLAB® installed for use in the practical sessions.