Stochastic Signals and Systems

This subject has the following teaching availabilities in 2010:

431-221 Fundamentals of Signals and Systems and 431-201 Engineering Analysis A (prior to 2001, 421-204 Engineering Analysis A) and 431-202 Engineering Analysis B (prior to 2001, 421-205 Engineering Analysis B) or equivalent.

This subject builds on the concepts developed in 431-221 Fundamentals of Signals and Systems. It aims to give students basic skills in the modelling and analysis of stochastic signals and systems for the analysis and design of modern telecommunication systems and control systems.

Topics include basic concepts: introduction to probability concepts; discrete and continuous random variables, and their distributional properties and moments; transformation of random variables; simulation of random variables; sums of random variables and central limit theorem; random signals in communications: random processes; stationarity; models of stochastic signals used in communications system analysis, including Gaussian processes, signal spectra and power spectral density; linear communication and control systems with stochastic inputs; poisson process; stimulation of communcation systems.

On completing this subject the student should be able to:

• Define fundamental probabilistic concepts such as the axioms of probability, random variables, independence, expectation and stochastic processes;
• List several important distribution functions and explain why they are significant;
• Use the laws of large numbers, the central limit theorem, and inequalities to approximate and bound probabilities;
• Analyse probabilistic models of engineering systems;
• Formulate probabilistic models for engineering systems;
• Use software tools (e.g. MATLAB) to simulate stochastic models of engineering systems.

• Assignments: 10%
• Laboratory reports: 20%
• Tests: two midsemester tests worth 5% each
• Final written Examination: 60%, with hurdle requirement.

This subject is not available as a breadth subject.

• Ability to apply knowledge of basic science and engineering fundamentals

• Ability to communicate effectively, not only with engineers but also with the community at large

• In-depth technical competence in at least one engineering discipline

• Ability to undertake problem identification, formulation and solution

• Ability to utilise a systems approach to design and operational performance

• Ability to function effectively as an individual and in multi-disciplinary and multi-cultural teams, with the capacity to be a leader or manager as well as an effective team member

• Expectation of the need to undertake lifelong learning, capacity to do so

• Capacity for independent critical thought, rational inquiry and self-directed learning

• Intellectual curiosity and creativity, including understanding of the philosophical and methodological bases of research activity

• Openness to new ideas and unconventional critiques of received wisdom

• Profound respect for truth and intellectual integrity, and for the ethics of scholarship

Credit may not be obtained for both 431-325 Stochastic Signals and Systems and 620-201 Probability.