3: Complex Fourier Series
    •Euler’sEquation
    •ComplexFourierSeries
    •AveragingComplex
    Exponentials
    •ComplexFourierAnalysis
    •FourierSeries↔
    ComplexFourierSeries
    •ComplexFourierAnalysis
    Example
    •TimeShifting
    •Even/OddSymmetry
    •Antiperiodic⇒Odd
    HarmonicsOnly                    3: Complex Fourier Series
    •SymmetryExamples
    •Summary
    E1.10 Fourier Series and Transforms (2014-5543)                 ComplexFourier Series: 3 – 1 / 12
                         Euler’s Equation
     3: Complex Fourier Series                    iθ
     •Euler’sEquation       Euler’s Equation: e      =cosθ+isinθ                                  [see RHB 3.3]
     •ComplexFourierSeries
     •AveragingComplex
     Exponentials
     •ComplexFourierAnalysis
     •FourierSeries↔
     ComplexFourierSeries
     •ComplexFourierAnalysis
     Example
     •TimeShifting
     •Even/OddSymmetry
     •Antiperiodic⇒Odd
     HarmonicsOnly
     •SymmetryExamples
     •Summary
     E1.10 Fourier Series and Transforms (2014-5543)                                    ComplexFourier Series: 3 – 2 / 12
                         Euler’s Equation
     3: Complex Fourier Series                    iθ
     •Euler’sEquation       Euler’s Equation: e      =cosθ+isinθ                                  [see RHB 3.3]
     •ComplexFourierSeries                       iθ   −iθ
     •AveragingComplex      Hence: cosθ = e +e
     Exponentials                                   2
     •ComplexFourierAnalysis
     •FourierSeries↔
     ComplexFourierSeries
     •ComplexFourierAnalysis
     Example
     •TimeShifting
     •Even/OddSymmetry
     •Antiperiodic⇒Odd
     HarmonicsOnly
     •SymmetryExamples
     •Summary
     E1.10 Fourier Series and Transforms (2014-5543)                                    ComplexFourier Series: 3 – 2 / 12
                         Euler’s Equation
     3: Complex Fourier Series                    iθ
     •Euler’sEquation       Euler’s Equation: e      =cosθ+isinθ                                  [see RHB 3.3]
     •ComplexFourierSeries                       iθ   −iθ
     •AveragingComplex      Hence: cosθ = e +e
     Exponentials                                   2
     •ComplexFourierAnalysis                   eiθ−e−iθ
     •FourierSeries↔                 sinθ =        2i
     ComplexFourierSeries
     •ComplexFourierAnalysis
     Example
     •TimeShifting
     •Even/OddSymmetry
     •Antiperiodic⇒Odd
     HarmonicsOnly
     •SymmetryExamples
     •Summary
     E1.10 Fourier Series and Transforms (2014-5543)                                    ComplexFourier Series: 3 – 2 / 12