Unit Outline

This unit presents students with both fundamental and advanced concepts of signals and the response of linear systems. Students will engage with a variety of topics including the modelling of real-world systems, analysis of system responses and stability under varying conditions, and the design of systems to achieve desired responses. The unit is designed to prepare students for future learning and applications in areas such as control systems, power systems, and renewable energy systems.

Throughout the unit, students will develop skills in mathematical modelling and simulations to solve complex problems. They will learn to derive and transform the impulse response of linear, time-invariant systems, apply the convolution theorem, determine the stability and frequency response of systems, and analyse stochastic signals. Additionally, students will gain hands-on experience in designing signal processing systems and filters.

By the end of this unit, students will be equipped with the knowledge and skills necessary to tackle advanced topics in engineering and to apply these principles in practical scenarios. The learning experiences provided will include lectures, problem-solving sessions, group projects, and laboratory work, ensuring a comprehensive understanding of both theoretical and practical aspects of signals and systems.

Intended Learning Outcomes

As per the Assessment and Results Policy 1.3, your results will reflect your achievement against specified learning outcomes.

On completion of this unit, you will be able to:


1	Derive and transform the impulse response of linear, time-invariant systems.
2	Apply the convolution theorem to linear, time-invariant systems.
3	Determine the stability and frequency response of linear signals and systems.
4	Apply principles of stochastic signal analysis to model randomness in signals and their effect on linear systems.
5	Design signal processing systems and filter responses.

Requisites


REQUISITE TYPE	REQUISITES
Pre-requisite	KMA252

Alterations as a result of student feedback

New NextENG unit delivery.

How will I be Assessed?

For more detailed assessment information please see MyLO.

Assessment schedule


ASSESSMENT TASK #	ASSESSMENT TASK NAME	DATE DUE	WEIGHT	LINKS TO INTENDED LEARNING OUTCOMES
Assessment Task 1:	Group Project 1	Week 7	30 %	LO1, LO2, LO3, LO5
Assessment Task 2:	Group Project 2	Week 12	30 %	LO1, LO2, LO3, LO4
Assessment Task 3:	Final Exam	Exam Period	40 %	LO1, LO2, LO3, LO4, LO5

Assessment details

Assessment Task 1: Group Project 1

Task Description:

An investigation and design project composed of four main problems to be completed using both an analytic approach and computer simulations. Each problem has elements of problem-solving and can be researched and investigated broadly.

The first problem is around the design of dual-tone multi-frequency signalling. The second problem is an investigation into the features of linear systems that make them preferable to non-linear systems in terms of analysis and control. The third problem is design, implementation and analysis of a fourth-order linear system using a state space representation. The fourth problem investigates simple image processing filters using convolution.

A complete description of the task will be available on MyLO. Problems 1,2 and 4 are to be completed in groups of two and problem 3 is to be completed individually. Individual submissions are required to be uploaded to MyLO.

Peer Review will be a component of this assessment. Generative AI use permitted and acknowledge.

Task Length:

15 Page Report

Due Date:

Week 7

Weight:

30 %

CRITERION #

CRITERION

MEASURES INTENDED

LEARNING OUTCOME(S)


1	Derive a linear, time-invariant differential equations of dynamic systems representing real-world processes.	LO1
2	Derive a transfer function of the system response.	LO1
3	Derive the state space representation of a linear time-invariant system.	LO1
4	Perform continuous convolution to obtain the system's impulse response.	LO2
5	Perform continuous convolution to obtain the system's response to various inputs.	LO2
6	Design and evaluate Butterworth filters, Chebyshev Type 1 and 2 filters.	LO5
7	Apply eigenvalue analysis to determine the stability of systems represented in state space.	LO3
8	Apply state space concepts to determine the impulse response of linear systems.	LO2

Assessment Task 2: Group Project 2

Task Description:

An investigation and design project composed of four main problems to be completed using both an analytic approach and computer simulations. Each problem has elements of problem-solving and can be researched and investigated broadly.

The first problem investigates the use of the Laplace transform to solve multivariable systems. The second problem involves the research and optimisation of a climate model with multiple degrees of freedom. The third problem is design, implementation, and analysis of audio signals in the presence of noise. The fourth problem is an investigation into statistical signal estimation.

A complete description of the task will be available on MyLO. Problems 1,3 and 4 are to be completed in groups of two and problem 2 is to be completed individually. Individual submissions are required to be uploaded to MyLO.

Peer review will be part of this assessment. Generative AI use permitted and acknowledge.

Task Length:

15 Page Report

Due Date:

Week 12

Weight:

30 %

CRITERION #

CRITERION

MEASURES INTENDED

LEARNING OUTCOME(S)


1	Transform dynamic system response between the time domain and Laplace domain using the Laplace transform.	LO1
2	Transform dynamic system responses between the time domain and Fourier domain using the Fourier transform.	LO1
3	Identify the state variables of a dynamic system.	LO1
4	Model a simplified climate process as a linear time invariant system.	LO1
5	Define how initial conditions and input signals are applied to a dynamic system.	LO2
6	Analyse the response of a simplified climate process.	LO2
7	Describe the limitations of a simplified climate model.	LO4
8	Explain the concept of a stochastic processes and the difference between an ergodic processes and time ensembles	LO4
9	Apply the Nyquist sampling theorem to analyse a linear time invariant system.	LO3
10	Perform discrete convolution to obtain the system's response to various inputs.	LO2

Assessment Task 3: Final Exam

Task Description:

This formally evaluates all ILOs.
The exam will be centrally invigilated and will assess all non-practical unit content.
Students will apply fundamental principles of linear systems and signals to solve a range of system behaviours and problems.
Assessment security checkpoint for all non-practical assessment criteria.
Generative AI use is not permitted.

Task Length:

3 hours

Due Date:

Exam Period

Weight:

40 %

CRITERION #

CRITERION

MEASURES INTENDED

LEARNING OUTCOME(S)


1	Transform dynamic system response between the time domain and Laplace domain using the Laplace transform.	LO1
2	Transform dynamic system responses between the time domain and Fourier domain using the Fourier transform.	LO1
3	Transform dynamic system responses between the discrete time domain and Fourier domain using the discrete Fourier transform.	LO1
4	Transform dynamic system responses between the discrete time domain and z-domain using the z-transform.	LO1
5	Derive the state space representation of a linear time-invariant system.	LO1
6	Perform continuous convolution to obtain the system's impulse response.	LO2
7	Perform discrete convolution to obtain the system's impulse response using the Dirac delta function.	LO2
8	Calculate the bounded-input and bounded-output stability conditions of a linear time invariant system in response to a continuous system.	LO3
9	Calculate the bounded-input and bounded-output stability conditions of a linear time invariant system in response to a discrete system.	LO3
10	Calculate and evaluate the power spectral density, cross correlation and autocorrelation function of signals.	LO4
11	Determine if a signal is strictly stationary or wide sense stationary.	LO4
12	Derive the bandlimited response of a system.	LO4
13	Apply state space concepts to determine the impulse response of linear systems.	LO2
14	Design and evaluate Butterworth filters, Chebyshev Type 1 and 2 filters.	LO5
15	Explain what is an ideal filter while considering the principles of causality.	LO5
16	Apply sampling theorem to create discrete realisation of analogue filters.	LO5
17	Derive linear, time-invariant differential equations of dynamic systems representing real-world processes.	LO1
18	Use partial fraction expansion to aid in deriving system output responses.	LO1
19	Derive the Bode plots of both magnitude and phase responses.	LO3
20	Discretise continuous signals and systems while applying sampling theorem.	LO2

How your final result is determined

To pass this unit, you need to demonstrate your attainment of each of the Intended Learning Outcomes, achieve a final unit grade of 50% or greater, and pass any hurdle tasks.

To pass ILO1 your aggregate mark on the components of Final Exam, Group project 1 and Group project 2 assessing ILO1 weighted according to their contribution to the final mark, must be greater than or equal to 50%.

To pass ILO2 your aggregate mark on the components of Final Exam, Group project 1 and Group project 2 assessing ILO2 weighted according to their contribution to the final mark, must be greater than or equal to 50%.

To pass ILO3 your aggregate mark on the components of Final Exam, Group project 1 and Group project 2 assessing ILO3 weighted according to their contribution to the final mark, must be greater than or equal to 50%.

To pass ILO4 your aggregate mark on the components of Final Exam and Group project 2 assessing ILO4 weighted according to their contribution to the final mark, must be greater than or equal to 50%.

To pass ILO5 your aggregate mark on the components of Final Exam and Group project 1 assessing ILO5 weighted according to their contribution to the final mark, must be greater than or equal to 50%.

Academic progress review

The results for this unit may be included in a review of your academic progress. For information about progress reviews and what they mean for all students, see Academic Progress Review in the Student Portal.

Submission of assignments

Where practicable, assignments should be submitted to an assignment submission folder in MYLO. You must submit assignments by the due date or receive a penalty (unless an extension of time has been approved by the Unit Coordinator). Students submitting any assignment in hard copy, or because of a practicum finalisation, must attach a student cover sheet and signed declaration for the submission to be accepted for marking.

Academic integrity

Academic integrity is about acting responsibly, honestly, ethically, and collegially when using, producing, and communicating information with other students and staff members.

In written work, you must correctly reference the work of others to maintain academic integrity. To find out the referencing style for this unit, see the assessment information in the MyLO site, or contact your teaching staff. For more detail about Academic Integrity, see Important Guidelines & Support.

Requests for extensions

If you are unable to submit an assessment task by the due date, you should apply for an extension.

A request for an extension should first be discussed with your Unit Coordinator or teaching support team where possible. A request for an extension must be submitted by the assessment due date, except where you can provide evidence it was not possible to do so. Typically, an application for an extension will be supported by documentary evidence: however, where it is not possible for you to provide evidence please contact your Unit Coordinator.

The Unit Coordinator must notify you of the outcome of an extension request within 3 working days of receiving the request.

Late penalties

Assignments submitted after the deadline will receive a late penalty of 5% of the original available mark for each calendar day (or part day) that the assignment is late. Late submissions will not be accepted more than 10 calendar days after the due date, or after assignments have been returned to other students on a scheduled date, whichever occurs first. Further information on Late Penalties can be found on the Assessments and Results Procedure.