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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 EE-2027 SaS, L1 1/7 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 EE-2027 SaS, L1 2/7 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 EE-2027 SaS, L1 3/7 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/Simulinkbased 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 EE-2027 SaS, L1 4/7 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 EE-2027 SaS, L1 5/7 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 EE-2027 SaS, L1 6/7 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. EE-2027 SaS, L1 7/7