BEng Mechatronic Engineering / Course details

This unit will cover the following:

Induction and overview (2 lectures):Introduction to the course, motivation for why we need to study signals and systems. Demonstration of Matlab and Simulink as computer software tools for analysing signals and systems.

Mathematical fundamentals (2 lectures):Revision of complex numbers, ordinary differntial equations and other mathematics required for studying signals and systems.

Concepts (4 lectures):Definitions of systems, signals and mathematical models of them. Focus on continuous-time and discrete-time signals and linear time-invariant systems.

Convolution (4 lectures):The system impulse response and is use to represent a system. Description of an input signal as a continuum of impulses. Showing how these can be combined to give the convolution operation which calculates the system output. Convolution for both discrete-time and sontinuous-time signals and systems.

Fourier series and transforms (4 lectures): Concept of basis functions. Fourier series representation of signals. Fourier transform representation of signals in the frequency domain. Fourier transform properties.

Laplace transforms (3 lectures):  Laplace transform for representing signals and systems. Similarities and differences between the Fourier transform and the Laplace transform.

Transfer functions of continuous-time systems (2 lectures): Transfer functions in both Laplace and Fourier domains. System frequency response and Bode diagram from the Fourier transfer function. Physical realizability, stability, and poles/zeros from the transfer function.

Transfer functions of discrete-time systems (2 lectures):The Laplace transform of discrete impulses sequences leading to the z transform. Properties of the z transform. Transfer functions for discrete-time systems working in z domain.

Tutorials (1 lecture):  Feedback and working of the lab work. Additional tutorial questions are embedded in the lecture notes.

The course unit aims to:

Introduce the mathematical tools for analysing signals and systems in the time and frequency domains, and provide a basis for applying these techniques in control and communications engineering.

ILO1 - Analyse and develop simple mathematical models for representing signals and systems

ILO2 - Convert time domain models into frequency, Laplace and Z domain models of signals and linear time-invariant systems (continues and discrete) and vice versa

ILO3 - Analyse and calculate system impulse responses and system responses for given inputs of linear time-invariant systems using convolution (time domain), system transfer function (frequency, Laplace and Z domains)

ILO4 - Define and explain the signal and system properties and relationship between continuous-time and discrete-time signals and systems

ILO5 - Apply basic Matlab and Simulink tools for analysis and simulation of continuous and discrete-time systems.

Coursework:

Two laboratory sessions, working on computer based simulations in Matlab and Simulink. Each forms 5% of the unit assessment. Laboratory duration: 6 hours in total (3 per session.)

Coursework carried out in own time, working on computer based simulations in Matlab and Simulink. Forms 10% of the unit assessment.

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