431-221 Fundamentals of Signals and Systems

431-201 Engineering Analysis A (prior to 2001, 421-204 Engineering Analysis A) or 2003 summer subject 431-225 Engineering Analysis A (old) or equivalent and 431-210 Circuit Analysis.

This subject introduces students to the fundamental principles of signals and systems. Signals and systems theory will be treated in a generic engineering context, but with an emphasis to prepare students for the application of basic knowledge to the areas of communication and control engineering. The subject will approach the signals and systems theory, treating equally mathematical analysis as well as engineering synthesis. Students will learn how to model particular systems and signals environments, using time and frequency domain ideas. Students will learn how to represent and analyse signals and systems with specific properties using the MATLAB software environment.

Topics include:

Signals: definition of a signal with examples; periodic and aperiodic signals; continuous and discrete-time signals (sinusoidal, exponential, step, impulse). 1-dimensional and 2-dimensional signals; and representations of signals in time and frequency domains.

Transforms: Laplace, Fourier, z and discrete-time Fourier; sampling theorem; aliasing; and norms of signals.

Systems: definitions of inputs, outputs and a system. Basic model properties: memory, invertibility, causality, stability, time-invariance, linearity; classification of system models; representations of Linear time invariant (LTI) systems (continuous-time and discrete-time): input-output models (including mulitple-input mulitple-output); state space models; impulse response; convolution representations; transfer function, poles and zeros; block diagrams (series, parallel and feedback connections); frequency response and Bode plots; relationships between the time and frequency response of a system; and norms of systems.

All concepts are illustrated by examples from control theory, signal processing and telecommunications.

One written examination not exceeding three hours, assignments and/or project reports. Students will be notified of the weighting of assessment components at the beginning of the semester.