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EE-2027 SaS, L11/7 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 Bridge wind movement

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EE-2027 SaS, L12/7 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

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EE-2027 SaS, L13/7 Reading List/Resources Essential AV Oppenheim, AS Willsky: Signals and Systems, 2 nd 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

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EE-2027 SaS, L14/7 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/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

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EE-2027 SaS, L15/7 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

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EE-2027 SaS, L16/7 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

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EE-2027 SaS, L17/7 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.

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