# Unit information: Signals and Systems in 2021/22

Unit name Signals and Systems EENG21000 10 I/5 Teaching Block 1 (weeks 1 - 12) Dr. Agrafiotis Not open EMAT10100 or EMAT10004; EENG11002. None Department of Electrical & Electronic Engineering Faculty of Engineering

## Description including Unit Aims

In this unit the characteristics and inter-relations of linear (continuous and discrete) signals and systems will be discussed. Principles of sampling theory, aliasing, correlation, convolution, and spectral analysis will be presented. Analysis of linear systems using Laplace and Z transform, and pole-zero representation of filter transfer functions will be considered. Stability analysis of linear systems in both continuous and discrete domains will be presented. The characterisation of systems in the time and frequency domains, impulse response, transfer functions, and frequency response will be discussed.

Introduction: objectives of the course - analyse, predict and control signals and systems; some example applications in electrical engineering (circuit analysis, communications, DSP and control); examples in other disciplines (economics, medicine etc.).

Signal Description: sources; representations (analytic and graphical); classification of signals (periodic, harmonic, random, deterministic, impulse and step functions); elementary operations on signals (scaling, time shifting, addition, quantisation); properties of signals (energy, spectrum, correlation).

System Description: system models; derive simple systems (RC networks, mechanical); classification of systems (continuous/discrete, linear/nonlinear, time-invariant/time varying, causal/acausal, stable/unstable); system representation (differential/difference);

System Response and Convolution: system characterisation: impulse and step response; convolution and its properties; convolution summation/integral; graphical interpretation of convolution; examples in communications (transmission channel) and DSP (filtering).

Transforms (Fourier, Laplace and Z): review of transforms; differential equations and Laplace; difference equations and z transform; properties of these transforms and their relationships to each other.

Continuous-Time v. Discrete-Time Systems: system description -differential and difference equations and solutions; steady-state and transient response; finding the impulse response; system analysis using Laplace transforms and z-transforms ; stability in the s-plane and z-plane; examples in circuit theory, communications and digital filtering.

Sampling and Sampling Theorem: sampling of continuous signals; sampling theorem; impulse sampling; signal reconstruction; spectrum of sampled signals;

Transfer Function and Frequency Response: transfer function representation of systems; pole-zero representation in s-plane and z-plane; derive frequency response from transfer functions; graphical methods of evaluating frequency response; stability and system behaviour.

Applications: Circuit Theory: RC networks and frequency response; Communications: amplitude modulation and equalisation; DSP: filter design and filtering; Control: system identification.

Students will be well prepared for any course on Communications, Control or DSP in the following years.

## Intended Learning Outcomes

Having completed this unit, students will be able to:

1. Analyse continuous-time systems and discrete time system in the time domain using convolution, transform domain or in the frequency domain.
2. Distinguish between, and use, Laplace Transform, Z Transform and Fourier Transform.
3. Design a continuous-time system or a digital filter using pole-zero locations and frequency response.

## Teaching Information

Teaching will be delivered through a combination of synchronous and asynchronous sessions, including lectures, practical activities supported by drop-in sessions, problem sheets and self-directed exercises.

## Assessment Information

Formative: Technical Note & Online Test 1

Summative: Exam (January, 100%)

## Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. EENG21000).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.