1．OverviewofFourierAnalysis
1.1 HistoryofFourierAnalysis
1.2 IllustrativeExamples
1.2.1 ShapeofSound
1.2.2 ImageProcessing
1.2.3 HealthMonitoringofRailroadTracks
1.2.4 StructuralControl
1.3 KeyPointsofFourierAnalysis
Problems
2．MathematicalFundamentalsforFourierAnalysis
2.1 ComplexNumber
2.2 DifferentialandIntegralCalculus
2.2.1 DifferentialCalculus
2.2.2 IndefiniteandDefiniteIntegralCalculus
2.3 PartialDerivatives
2.4 ExponentialandLogarithmicFunctions
2.5 TrigonometricFunctions
2.6 VariousFunctions
2.6.1 HyperbolicFunctions
2.6.2 HeavisideStepFunction
2.6.3 DiracDeltaFunction
Problems
3．FourierSeries
3.1 PeriodicPhenomena
3.2 ExpressionofaPeriodicFunction
3.3 ComplexFormofFourierSeries
Problems
4．FourierTransform
4.1 DefinitionofFourierTransform
4.2 PropertiesofFourierTransform
4.3 Spectrum,EnergySpectralDensity,andCorrelationFunction
4.4 FourierTransformsofSpecialFunctions
Problems
5．SignalSamplingandReconstruction
5.1 TheSamplingTheorem
5.2 SelectionofSamplingPeriod
5.3 ReconstructionofSignalfromItsSamples
Problems
6．DiscreteFourierTransformandFastFourierTransform
6.1 DiscreteFourierTransform
6.2 FastFourierTransform
Problems
7．ApplicationstoEngineeringProblems
7.1 AnalysisofSound
7.2 AnalysisofSeismicWave
7.3 ProcessingofSurfaceElectromyography(sEMG)
Problems
8．ApplicationtoMathematicalProblemsinEngineering
8.1 LinearSystemandImpulseResponse
8.2 PartialDifferentialEquation
Problems
9．Multi-DimensionalFourierTransform
9.1 DefinitionofMulti-DimensionalFourierTransform
9.2 ApplicationtoImageCompression
9.3 ApplicationtoComputerizedTomography
Problems
10．LaplaceTransform
10.1 DefinitionofLaplaceTransform
10.2 FrequencyResponse
10.3 ComparisonofFourierandLaplaceTransforms
Problems
Appendix
References
AnswerstoProblems
Index
