Section A1 (BASA Headquarters: ProblemSolving)A1.1Substituteyourgroup’svariables(A,BandC)intothecorrespondingsignals,andgraph two periods (0 to 10 seconds) of each signal by hand. These should be presented as separatefigureswithkeyelementsofeachsignallabeled(suchasamplitudeandgradient changes,axes,unitsetc.whereapplicable).Ensurescannedmaterialiseasilyreadable. (Criteria:1)Parts A1.2 to A1.9 can be presented as either handwritten or using typeset equations.A1.2DeterminethetrigonometricandcomplexexponentialFourierseriesofs1(t)fromfirst principles i.e. Using the integral definitions. Do not convert from one form to the other. Show all working. (Criteria:1a)A1.3 Explain how the trigonometric and exponential coefficients change for the signal s(t) =s1(t) + 2. Describe in words, do not show mathematically. (Criteria: 1c)A1.4Expandthesignals2(t)intotheFourierseriesofyourchoosing(trigonometricorcomplex) from first principles, then convert to the other form. Show all working. (Criteria:1a)A1.5 Clearly explain your choice of Fourier series for first principle expansion of s2(t).A1.6 Calculate the coefficients a0, anand bnfor n ≤3, and the cncoefficients for −3 ≤n ≤3 for s2(t). Show all working. (Criteria: 1b)A1.7 Derive the Fourier series of s3(t) from first principles (trigonometric or complex), then convert to the other form. Show all working. (Criteria: 1a)A1.8 Clearly explain your choice of Fourier series for first principle expansion of s3(t).A1.9 Calculate the coefficients a0, anand bnfor n ≤3, and the cncoefficients for −3 ≤n ≤3 for s3(t). Show all working. (Criteria: 1b)A1.10 Classify each of the the test signals as either even, odd or neither? Justify your answer using the mathematicaldefinitions. (Criteria: 1c)Section A2 (BASA Headquarters: Training Exercise)This section should be implemented in MATLAB preparation.m. Be sure to include relevant figuresandcodesnippetswhenpresentingyourresultsinyourreport.Discusswhatyouare doing, and most importantlywhy.A2.1 Generate and plot a periodic signal based on s2(t) named s2hinf 1.The signal is to span 5 cycles (periods) and have a total of 500 sample points (i.e. 100 points per period).A2.2Computethetrigonometriccoefficientsofs2(t),numericallyusingMATLAB.Donotuse the trapz or symsfunctions.A2.3 Create a 4 500 matrix called s2matrix. The first row represents the DC component of s2(t). Each remaining row contains a single harmonic component of the signal for n∈{0,1,2,3}A2.4Nowcreateavectors2approxwhichcontainsanapproximationofthesignals2(t).You canuses2matrixtodothis.A2.5Inthesamefigureass2hinf,andusingdifferentcolours,alsoplotthefollowingFourier series approximations using the trigonometriccoefficients:Hint: this can be implemented in a forloop•Anapproximationofs2(t)usingtheDCcomponentandthefundamentalfrequency,Anapproximationofs2(t)usingtheDCcomponent,thefundamentalfrequencyand the secondharmonic,Anapproximationofs2(t)usingtheDCcomponent,thefundamentalfrequencyand thesecondandthirdharmonics.Notethatthefundamental,secondharmonicand third harmonic correspond to n = 1, 2, 3respectively.Labeltheaxesappropriatelyandincludealegend.Ensurethesignalandallapproxima- tionscanbeeasilyseeninthereport.Usedifferentlinestylesifnecessary.(Criteria:1b, 2a)A2.6 For s3(t), repeat the steps of A2.1 to A2.5 using exponential coefficients, and a 7 500 matrix.Maintainnamingconventionsi.e.s3hinf,s3matrixands3approx.(Criteria: 1b,2a)A2.7 What can be said about the approximations when the number of harmonics used in- creases?Arethepreviousapproximationssufficienttorepresentthesesignals?Whyor whynot?Whatarethepracticalbenefitsanddrawbacksofusing3harmonicsasopposed tomoreorfewer?Hint:Considerwhatitwouldbeliketodobyhand.(Criteria:1c)

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