# ECS515U Signals and Systems Theory

Module code: ECS515U

Credits: 15
Semester: SEM2

This module aims to give you an understanding of basic signal and system concepts, e.g. average value, the difference between periodic, non-periodic and random signals, and orthogonality. It further aims to give a working understanding of the use of transform techniques, including Fourier, Laplace and Z, and an appreciation of the effects of noise on signals and signal processing.

Topics covered include:

• Concepts of signals and systems in continuous and discrete time.
• Ideas behind linear, time invariant systems and functions.
• Periodic and non-periodic, random, energy signal and power signal.
• Explain and use signal average values.
• Define signal symmetry, and to explain the concept and use of orthogonality.
• Introduce the Fourier trigonometric series.
• Introduce frequency domain representation and the Fourier transform.
• Show how the Fourier transform is applied to some simple aperiodic signals and how to interpret the results.
• Introduce discrete time signals and sampling, including aliasing and the unit sample sequence.
• Explain FIR and IRR discrete time systems.
• Show response of a discrete time system is convolution of the input sequence with the unit sample response.
• Introduce the Z-transform, and apply to discrete time signals and systems.
• Show that stability of discrete time systems can be examined by using Z-transform techniques.
• Introduce the Laplace transform and the complex frequency terms.
• Study certain simple applications of the Laplace transform, e.g. to the unit step function, the exponential function, the sinusoid and to combinations of these.
• Inverse Laplace transform.

Level: 5