EE-2027 Signals and Systems

1. wind Bridge movement EE-2027 Signals and Systems Dr Martin Brown E1k, Main Building martin.brown@manchester.ac.uk http://personalpages.umist.ac.uk/staff/martin.brown/signals

2. Course Structure • Timetable • 20 lectures, 2 per week • 4 tutorials (Matlab/Simulink exercises) • 76 hours private study • Assessment • 20% Coursework • 80% Exam • 10 credit module • Relationship to other Modules • Pre-requisites: EE1.9 Engineering Mathematics 2 • Dependent modules: EE2.10 Feedback Control Systems, EE2.11 Communication Principles

3. Reading List/Resources • Essential • AV Oppenheim, AS Willsky: Signals and Systems, 2nd Edition, Prentice Hall, 1997 • D Hanselman, B Littlefield “Mastering Matlab 6: A comprehensive tutorial and reference”, Prentice Hall, 2001 • JB Dabney, TL Harman “Mastering Simulink 4”, Prentice Hall 2001. • Recommended • Haykin “Signals and Systems, John Wiley and Sons, 2002 • http://www.mit.edu/~6.003/ - Signals and Systems at MIT • http://dynamo.ecn.purdue.edu/~bouman/ee301/ - Signals and Systems at Purdue • http://www.jhu.edu/~signals/index.html - on-line set of Java applets demonstrating various signals and system concepts

4. Course Aims • To introduce the mathematical tools for analysing signals and systems in the time and frequency domain and to provide a basis for applying these techniques in control and communications engineering • Mathematical understanding and Matlab/Simulink-based application • Analyse both continuous time and discrete time signals and systems • Analysis performed in both time and frequency domain • Tools can be used for communications and control

5. Course Learning Objectives • Academic knowledge • Understand and develop simple mathematical models for representing signals and systems • Understand the relationship between time and frequency domain models of dynamic systems • Convert time to frequency-domain models and vice versa • Understand the relationship between continuous and discrete-time models • Intellectual skills • Build a mathematical model from a real-life problem related to signals and systems • Interpret results achieved by mathematical solutions • Practical skills • Apply Matlab/Simulink tools for analysis and simulation of continuous and discrete time systems • Analyse mathematical solutions in the context of the original problem • Transferable skills • Choose appropriate approach in problem solving situation • Present and communicate formalised results and conclusions

6. Course Syllabus (i) • 1 Concepts (3 lectures): Systems, signals, mathematical models. Continuous-time and discrete-time signals. Energy and power signals. Linear systems. Examples for use throughout the course, introduction to Matlab and Simulink tools • 2 Linear systems, Convolution (3 lectures): Impulse response, input signals as continuum of impulses. Convolution, discrete-time and continuous-time properties • 3 Basis functions (3 lectures): Concept of basis function. Fourier series representation of time functions. Fourier transform and its properties. Examples, transform of simple time functions. • 4 Sampling Discrete-time systems (2 lectures): Sampling theorem, discrete Fourier transform

7. Course Syllabus (ii) • 5 Laplace transform (3 lectures): Laplace transform as Fourier transform with convergence factor. Properties of the Laplace transform • 6 Transfer Function of Continuous-Time Systems (3 lectures): Transfer function, frequency response, Bode diagram. Physical realisability, stability. Poles and zeros, rubber sheet analogy. • 7 Transfer Function of a Discrete-Time Systems (3 lectures): Impulse sampler, Laplace transform of impulse sequence, z transform. Properties of the z transform. Examples. Difference equations and differential equations. Digital filters.