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CE00998-3 Coding and Transformations Sept – Nov 2011.

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Presentation on theme: "CE00998-3 Coding and Transformations Sept – Nov 2011."— Presentation transcript:

1 CE00998-3 Coding and Transformations Sept – Nov 2011

2 Schedule WeekGrande LecturePetite LectureTutorialLab 6 Sep IntroductionIntro to MAPLEIntro MAPLEIntegration 13 Sep Integration by PartsStep FunctionsMatricesProgramming 20 Sep Fourier Series ExamplesMAPLE 27 Sep FSOdd & Even FunctionsExamplesMAPLE 4 Oct FSComplex FormExamplesAssignment 1 11 Oct Class Test 1Fourier TransformsExamplesMAPLE 18 Oct FTPropertiesExamplesMAPLE 25 Oct FTGeneralised FunctionsExamplesAssignment 2 1 Nov Class Test 2Discrete FTExamplesMAPLE 8 Nov DFTFast FTExamplesAssignment 3 15 Nov DFTHuffman CodingExamplesMAPLE 22 Nov Class Test 3

3 Fourier Series Class Test 10.00-11.00 next Monday (11 th October 2010) D109 / D105 It will last 50 mins What will I need to do? -4 questions, covering -Theory -Finding Fourier series -Odd/even functions -Complex form -No Maple

4 Assignment 1 You can use the Maple session this week Submit by 3.30 Monday 18 th October 2010 –Faculty Reception (Octagon L2) –Summary report (max 4 pages) plus appendices –Include Assignment Submission Form (available from Faculty Reception) Electronic copy –Submit via Assignment on Blackboard

5 Week 5 Fourier Series Home Work Exercises 2 (see p15 of notes)

6 Finding the Fourier Series The coefficients are given by (so is…? …the mean value of f(x))

7 Odd and Even Functions Even Function Odd Function

8 Exercise (i) Find the Fourier Series for Using Heaviside functions (eg for Maple)? T=4

9 Exercise (i) This is an ODD function, so….

10 Exercise (i) Find

11 Exercise (i)

12 So the series is First four terms are

13 Exercise (i) What does it look like? 1 term 2 terms 3 terms

14 Exercise (i) 4 terms 10 terms 25 terms

15 Exercise (ii) Find the Fourier series for T=4

16 Exercise (ii) Using Heaviside functions?

17 Exercise (ii) This is an EVEN function, so….

18 Exercise (ii) Easy integration for T=4

19 Exercise (ii) Find

20 Exercise (ii)

21 So the series is First three terms are

22 Exercise (ii) What does it look like? 1 term 2 terms 3 terms

23 Exercise (ii) 4 terms 10 terms 25 terms

24 The Assignment Temperature distribution in a solid bar Solution: 0 1 Find b n by setting t=0:

25 The Assignment Need a Fourier sine series: 0 1 Need ‘odd periodic extension’ Take T=2 so that

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