义-连续时间傅立叶变换

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1、SignalsandSystemsChapter4TheContinuous-TimeFourierTransformLiuKe,SchoolofAutomationEngineeringReviewLTIChapter2:Time-Domain:ConvolutionChapter3:Frequency-Domain:frequencyresponseLTIReviewChapter4Chapter5Chapter9Chapter10aperiodiccontinuous-timesignalaperiodicdiscrete-timesignalLT

2、IThecontentsofthechapterTheFouriertransformofaperiodicsignalTheFouriertransformofperiodicsignalThepropertiesofFouriertransformLinearconstantcoefficientsdifferentialequation4.1Representationofaperiodicsignal:thecontinuous-timeFouriertransformTheenvelopofTherepresentationofFouriert

3、ransformConvergenceofFouriertransformSomeexamples(a)T=4T1(b)T=8T1(c)T=16T1EnvelopofTakDevelopmentIntroductionperiodicChapter3aperiodicChapter4Thekey:FouriertransformSummaryFourierseriesperiodicsignalFouriertransformaperiodicsignal4.1.2ConvergenceofFouriertransformViewofenergyfini

4、teenergy(squareintegrable)Thedirichletconditions(1)x(t)absolutelyintegrable;(2)finitenumberofmaximaandminimawithanyfiniteinterval;(3)finitenumberofdiscontinuitieswithanyfiniteinterval;eachofdiscontinuitiesmustbefinite4.1.3Exampleofcontinuous-timeFTExample4.1Example4.2Example4.3Ex

5、ample4.4Example4.5Dualityproperty4.2TheFouriertransformforperiodicsignalsExample4.6T=4T1Example4.7Example4.84.3Propertiesofthecontinuous-timeFouriertransform4.3.1Linearity4.3.2TimeShifting4.3.3ConjugationandConjugateSymmetry4.3.4DifferentiationandIntegration4.3.5TimeandFrequencyS

6、caling4.3.6Duality4.3.7Parseval’sRelation4.3.1Linearity4.3.2TimeShiftingtimeshiftdon’tchangethemagnitudeofFouriertransformtimeshiftistointroduceintoaphaseshiftExample4.9DeterminetheFTofx(t)Method1:Method2:4.3.3ConjugationandconjugatesymmetryIfx(t)isrealIfx(t)isrealandoddIfx(t)isr

7、ealandevenIfx(t)isrealExample4.104.3.4DifferentialandintegralExample4.11Example4.124.3.4Timeandfrequencyscaling4.3.5DualityExample4.13Someusefulproperties4.3.7Parseval’srelationExample4.14Assignments4.3（b），4.4，4.6，4.84.4Theconvolutionpropertyh(t)H(jw)Theresponseofcascadesystemh(t

8、)、H(jw)completelycharacterizeanLTIsystem