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
• 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

Introduction to signals and systems, discrete time signals and systems, Z-transform

• 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

• 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 random processes and linear systems

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