Signals and Linear Systems unit (ENG204)

Introduction

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.

Summary

Unit name	Signals and Linear Systems
Unit code	ENG204
Credit points	12.5
College/School	Sciences and Engineering School of Engineering
Discipline	Engineering
Coordinator	Doctor Brian Salmon
Available as an elective?	Yes
Delivered By	University of Tasmania
Level	Intermediate

Availability

Specific information on 2027 unit availability will be available in August

Learning Outcomes

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

Fee Information

2027 fee information will be available in August.

Requisites

Prerequisites

KME271 or KMA252

Teaching

Assessment	Group project 1 (10%)|Semester test 1 (15%)|Semester test 2 (15%)|Group project 2 (20%)|Final Exam (40%)
Timetable	View the lecture timetable | View the full unit timetable

Textbooks

Required	Required readings will be listed in the unit outline prior to the start of classes.

The University reserves the right to amend or remove courses and unit availabilities, as appropriate.