CE00998-3 Coding and Transformations. Schedule WeekGrande LecturePetite LectureTutorialLab 7 Sep IntroductionIntro to MAPLEIntro MAPLEIntegration 14 Sep.

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Presentation transcript:

CE Coding and Transformations

Schedule WeekGrande LecturePetite LectureTutorialLab 7 Sep IntroductionIntro to MAPLEIntro MAPLEIntegration 14 Sep Integration by PartsStep FunctionsMatricesProgramming 21 Sep Fourier Series ExamplesMAPLE 28 Sep FSOdd & Even FunctionsExamplesMAPLE 5 Oct FSComplex FormExamplesAssignment 1 12 Oct Class Test 1Fourier TransformsExamplesMAPLE 19 Oct FTPropertiesExamplesMAPLE 26 Oct FTGeneralised FunctionsExamplesAssignment 2 2 Nov Class Test 2Discrete FTExamplesMAPLE 9 Nov DFTFast FTExamplesAssignment 3 16 Nov DFTHuffman CodingExamplesMAPLE 23 Nov Class Test 3

Fourier Series Class Test 9.00 next Monday (12 th October) It will take 40 mins What will I need to do? -Section A (20 marks) 10 multi-choice questions (2 mins each) -Section B (20 marks) 1 long question (eg Tutorial questions) -No Maple

Fourier Series Maple Assignment Submit by 3.30 Monday 19 th October –to Faculty Reception (Octagon L2) –do not to me Include –an Assignment Submission Form (available from Faculty Reception) –an electronic copy on disc

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

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

Exercise (i) Find the Fourier series for T=2

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

Exercise (i) Find

Exercise (i) So the series is First few terms are

Exercise (i) What does it look like?

Exercise (i) Rate of convergence Magnitude of Size of terms decreases slowly Terms for ‘large’ n are still important Convergence rate is ‘slow’

Exercise (ii) Find the Fourier series for T=2

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

Exercise (ii) Easy integration for T=2

Exercise (ii) Find

Exercise (ii) So the series is First few terms are

Exercise (ii) What does it look like?

Exercise (ii) What does it look like?

Exercise (ii) Rate of convergence Magnitude of Size of terms decreases rapidly Terms for ‘large’ n are not important Convergence is ‘rapid’