Aims

The aims of the course are to:

• Cover three basic topics in signals and systems which provide the basis for further topics in signal processing, communications, control and related subjects.
• Introduce the z-transform, which is the generalisation of the Laplace transform to discrete time systems.
• Introduce digital filtering.
• Introduce stochastic processes.

Objectives

As specific objectives, by the end of the course students should be able to:

• Be familiar with the theory and application of the z-transform.
• Analyse the stability of discrete-time systems
• Understand the use of correlation and spectral density functions.
• Analyse the behaviour of linear systems with random inputs.

Content

Enabling theory, application and design, Dr T. O’Leary and Dr F. Forni

Introduction to signals and systems, discrete time signals and systems, Z-transform (5L – O’Leary)

• Discrete signals and systems, LTI systems, convolution. 
• z-transform and solution of linear difference equations
• System analysis in the z-domain. 
• Impulse and frequency responses.

Applications & digital filtering (8L – Forni)

• Design and properties of digital feedback systems. Nyquist stability criterion. 
• Design and properties of Digital Filters, FIR and IIR
• Analysis of systems with discrete/continuous interfaces.
• DTFT/DFT and links to z-transforms 
• The Fast Fourier Transform (FFT)
• Windowed spectral analysis of data 
• Introduction to 2D filtering, image analysis

Introduction to random processes and linear systems (3L – O’Leary)

• Continuous time random processes, correlation functions, spectral density.
• Response of continuous time linear systems to random excitation.