Unit Outline

This unit introduces fundamental and advanced concepts to design, analyse and evaluate signals and the response of linear systems. The topics covered include: (1) definitions of signals, generalised functions, definition of linear, time-invariant systems, the convolution theorem, impulse responses, step responses. (2) Continuous time convolution, LTI systems as ODEs, solving ODEs to obtain the impulse response and system response to an input signal, the zero-state and zero-input responses, bounded-input bounded-output stability conditions. (3) Discrete time convolution, LTI systems as difference equations, solving difference equations to obtain the impulse response and system response to an input signal, bounded-input bounded-output stability conditions. (4) Discrete state space analysis, obtaining state variables and state equations, closed-form state space analysis of system outputs to discrete input signals, eigenvalue analysis for BIBO stability conditions. (5) Transform theory, including the continuous and discrete Fourier Transform, the Laplace Transform and the z-transform, the inverse Fourier Transform, partial fraction expansion for the Laplace and z-transform inverses, the Nyquist Sampling Theorem. (6) Filter design, ideal filter design, causality and discrete considerations for ideal filters, Butterworth filters, Chebyshev Type 1 and 2 filters, discrete realisation of analogue filters, the bilinear transform and frequency pre-warping. (7) Frequency domain BIBO stability, transfer function poles and zeros, Magnitude and Phase Bode plots. (8) Introduction to Stochastic Processes, time and ensemble domain average, autocorrelation and cross-correlation functions, the ergodic theorem, wide-sense stationary processes. (9) Application of stochastic signals to linear systems, Parseval’s Theorem, Power Spectral Density, output statistics of linear systems with WSS input signals.

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.	Design signal processing systems and network filter responses.
4.	Determine the stability and frequency response of linear signals and systems.
5.	Apply principles of stochastic signal analysis to model randomness in signals and their effect on linear systems.

Requisites


REQUISITE TYPE	REQUISITES
Pre-requisite	(KME271 or KMA252) AND KME272

Alterations as a result of student feedback

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:	Semester test 1	Week 5	15 %	LO2, LO3, LO5
Assessment Task 2:	Group project 1	Week 6	10 %	LO2, LO3, LO5
Assessment Task 3:	Semester test 2	Week 10	15 %	LO1, LO2, LO4, LO5
Assessment Task 4:	Group project 2	Week 13	20 %	LO1, LO2, LO4, LO5
Assessment Task 5:	Final Exam	Exam Period	40 %	LO1, LO2, LO3, LO4, LO5

Assessment details

Assessment Task 1: Semester test 1

Task Description:

Two-hour written invigilated closed-book test covering the first four weeks of the unit. This includes introduction to signals and linear systems, continuous and discrete time convolution, impulse and step responses, continuous and discrete time-domain linear systems analysis, state space analysis

Task Length:

2-hour test

Due Date:

Week 5

Weight:

15 %

CRITERION #

CRITERION

MEASURES INTENDED

LEARNING OUTCOME(S)


1	Apply signal processing techniques successfully to various systems which may include network and filter responses	LO2
2	Successfully apply fundamentals of digital signal processing to stated problems.	LO3
3	Understand and interpret system performance and relate back to acceptable solutions.	LO5

Assessment Task 2: Group project 1

Task Description:

An investigation and design project composed of three 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 signaling. 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. A complete description of the task will be available on MyLO at the date of task distribution. To be completed in groups of two.

Task Length:

Written report - 12 page maximum (appendices excluded)

Due Date:

Week 6

Weight:

10 %

CRITERION #

CRITERION

MEASURES INTENDED

LEARNING OUTCOME(S)


1	Design and evaluate appropriate signal processing system.	LO2
2	Apply fundamentals of digital signal processing to all three systems	LO3
3	Evaluate system performance and ensure desired responses meet expected outcomes.	LO5

Assessment Task 3: Semester test 2

Task Description:

Two-hour written invigilated closed-book test covering the first nine weeks of the unit, with a focus on weeks five through nine. This includes all relevant introductory content from the first four weeks, transform theory (Fourier, Laplace, z-transform), inverse transforms, partial fraction decomposition, ideal filters, Nyquist sampling theorem, Bode plots, magnitude and phase responses, linear systems analysis.

Task Length:

2-hour test

Due Date:

Week 10

Weight:

15 %

CRITERION #

CRITERION

MEASURES INTENDED

LEARNING OUTCOME(S)


1	Solve signal decomposition and transforms, stochastic signalproperties and correlation, and the ergodic theory to practical problems in timed fashion.	LO1
2	Design signal processing systems, network and filter responses in timed scenario.	LO2
3	Solve problems using appropriate transformation theory in timed scenario.	LO4
4	Evaluate system performance and desired responses in timed scenario.	LO5

Assessment Task 4: 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 model of a car suspension system with two 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 at the date of task distribution. To be completed in groups of two.

Task Length:

Written report - 20 page maximum (appendices excluded)

Due Date:

Week 13

Weight:

20 %

CRITERION #

CRITERION

MEASURES INTENDED

LEARNING OUTCOME(S)


1	Evaluate, manipulate and analyse signals using decomposition and transforms, stochastic signal properties and correlation, and the ergodic theory.	LO1
2	Design practical signal processing systems that will conform to the specifications.	LO2
3	Investigate and apply appropriate transformation theory to solve systems.	LO4
4	Specify your own contribution in the group project regarding the evaluation of the system performance and quantify desired responses have been produced.	LO5

Assessment Task 5: Final Exam

Task Description:

The final exam is conducted in the formal examination period. See the Examinations and Results page: http://www.utas.edu.au/exams/
on the University's website, or access your personal exams timetable by logging into the
eStudent Centre - Personal Exams Timetable
for specific date, time and location closer to the examination period.

Task Length:

3-hour exam

Due Date:

Exam Period

Weight:

40 %

CRITERION #

CRITERION

MEASURES INTENDED

LEARNING OUTCOME(S)


1	Solve signal decomposition and transforms, stochastic signalproperties and correlation, and the ergodic theory to practical problems in timed scenario.	LO1
2	Design signal processing systems, network and filter responses in timed scenario	LO2
3	Apply fundamentals of digital signal processing using a state space representation in timed scenario.	LO3
4	Solve problems using appropriate transformation theory in timed scenario	LO4
5	Evaluate system performance and desired responses in timed scenario.	LO5

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.

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.

Review of results and appeals

You are entitled to ask for a review of the marking and grading of your assessment task if there is an irregularity in the marking standards or an error in the process for determining the outcome of an assessment. Details on how to request a review of a mark for an assignment are outlined in the Review and Appeal of Academic Decisions Procedure.