Chapter-6-Time-And-Frequency-Characterization-of-Signals-And-Systems.ppt

Chapter6TimeAndFrequencyCharacterizationofSignalsAndSystems 罗欣UESTC 2012 2013 1 Introduction Intime domain theLTIsystemischaracterizedbyh t orh n Infrequency domain theLTIsystemischaracterizedbyH j orH ej InanalyzingLTIsystem itisoftenparticularlyconvenienttoutilizethefrequencydomain differentialanddifferenceequationsandconvolutionoperationsinthetimedomainbecomealgebraicoperationsinthefrequencydomain Insystemdesign therearetypicallybothtime domainandfrequency domainconsiderations 6 1TheMagnitude phaseRepresentationoftheFourierTransform Forsignalx t Forsignalx n Magnitudespectrum Phasespectrum Conclusion EffectsofPhase NotonsignalenergydistributionasafunctionoffrequencyCanhavedramaticeffectonsignalshape character Constructive DestructiveinterferenceIsthatimportant Dependsonthesignalandthecontext 6 2TheMagnitude phaseRepresentationoftheFrequencyResponseofLTISystem Continuous timeSystemcharacterization Impulseresponse Frequencyresponse gain Phaseshift Discrete timeSystemcharacterization Impulseresponse Frequencyresponse gain Phaseshift 6 2 1LinearandNonlinearPhase Linearphase Nonlinearphase Example Result Linearphase simplyarigidshiftintime nodistortion MagnitudeResponseisconstant Nonlinearphase distortionaswellasshift Linearphase X2 j X1 j e j Linearphase Nonlinearphase Originalsignal EffectofLinearandNonlinearPhase All PassSystem Thecharacteristicsofanall passsystemarecompletelydeterminedbyitsphase shiftcharacteristics 6 2 2GroupDelay Definition Example Note ifthevaluesofarerestrictedtoliebetween and weobtaintheprincipal phasefunction Linearwith near 0 Impulseresponseandoutputofanall passsystemwithnonlinearphase 6 2 3Log MagnitudeandBodePlots Magnitudespectrum Phasespectrum alogarithmicscaleforfrequencyinCT Forreal valuedsignalsandsystems plotfor 0 2 LCCDE ATypicalBodeplotforasecond ordersystem20log H j and H j vs log 40dBdecade Changesby Note indiscrete timesystem ThemagnitudesofFouriertransformandfrequencyresponsesareoftendisplayedindBforthesamereasonsthattheyareincontinuoustime However forrealh n weneedonlyplotfor0 withlinearscale Lowpassfilter 1 Continuoustime 2 Discretetime 6 3Time DomainPropertiesofIdealFrequency selectiveFilters ImpulseresponseofIdeallowpassfilter ImpulseresponseofIdealLowpassfilter StepresponseofIdealLowpassfilter tr Risetime Basicparameteroflowpassfilter 6 4Time DomainandFrequency domainAspectsofNon idealFilters Sometimeswedon twantasharpcutoff Oftenhavespecificationsintimeandfrequencydomain Trade offsRealization anticausalh t Homework 6 56 236 27 CTRationalFrequencyResponses IfthesystemisdescribedbyLCCDEs LinearConstant CoefficientDifferentialEquations then Hi j FirstorSecond orderfactors First ordersystem hasonlyoneenergystoringelement e g LorC Second ordersystem hastwoenergystoringelements e g LandC PrototypicalSystems DTRationalFrequencyResponses IfthesystemisdescribedbyLCCDEs LinearConstant CoefficientDifferenceEquations then Hi j FirstorS