内容

目次

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