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The aim of this subject is twofold: firstly, to develop an understanding of the fundamental tools and concepts used in the analysis of signals and the analysis and design of linear time-invariant systems path in continuous–time and discrete-time; secondly, to develop an understanding of their application in a broad range of areas, including electrical networks, telecommunications, signal-processing and automatic control.
The subject formally introduces the fundamental mathematical techniques that underpin the analysis and design of electrical networks, telecommunication systems, signal-processing systems and automatic control systems. Such systems lie at the heart of the electrical engineering technologies that underpin modern society. This subject is one of four that define the Electrical System Major in the Bachelor of Science and it is a core requirement in the Master of Engineering (Electrical). It provides the foundation for various subsequent subjects, including ELEN90057 Communication Systems, ELEN90058 Signal Processing and ELEN90055 Control Systems.
Signals – continuously and discretely indexed signals, important signal types, frequency-domain analysis (Fourier, Laplace and Z transforms), nonlinear transformations and harmonics, sampling;
Systems – viewing differential / difference equations as systems that process signals, the notions of input, output and internal signals, block diagrams (series, parallel and feedback connections), properties of input-output models (causality, delay, stability, gain, shift-invariance, linearity), transient and steady state behaviour;
Linear time-invariant systems – continuous and discrete impulse response; convolution operation, transfer functions and frequency response, time-domain interpretation of stable and unstable poles and zeros, state-space models (construction from high-order ODEs, canonical forms, state transformations and stability), and the discretisation of models for systems of continuously indexed signals.
This material is complemented by exposure to the use of MATLAB for computation and simulation and examples from diverse areas including electrical engineering, biology, population dynamics and economics.
Intended learning outcomes
On completion of this subject students should be able to:
- Apply fundamental mathematical tools to model, analyse and design signals and systems in both time-domain and frequency-domain
- Value the broad applicability of the mathematics of signals and systems theory, particularly within electrical engineering
- Articulate the similarities and differences between the mathematical tools needed for dealing with continuous-time systems/signals versus their discrete-time counterparts
- Use MATLAB to study the behaviour of signals and systems as they arise in a variety of contexts.
On completion of this subject students should have developed the following generic skills:
- Ability to apply knowledge of basic science and engineering fundamentals;
- Ability to undertake problem identification, formulation and solution;
- Ability to utilise a systems approach to design and operational performance;
- Ability to communicate effectively, with the engineering team and with the community at large;
- Capacity for independent critical thought, rational inquiry and self-directed learning;
- Expectation of the need to undertake lifelong learning, capacity to do so.
Last updated: 11 May 2021