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1、QuadratureSignals:Complex,ButNotComplicatedbyRichardLyonsIntroductionQuadraturesignalsarebasedonthenotionofcomplexnumbersandperhapsnoothertopiccausesmoreheartachefornewcomerstoDSPthanthesenumbersandtheirstrangeterminologyofj-operator,complex,imaginary,
2、real,andorthogonal.Ifyou'realittleunsureofthephysicalmeaningofcomplexnumbersandthej=-1operator,don'tfeelbadbecauseyou'reingoodcompany.WhyevenKarlGauss,onetheworld'sgreatestmathematicians,calledthej-operatorthe"shadowofshadows".Herewe'llshinesomelighton
3、thatshadowsoyou'llneverhavetocalltheQuadratureSignalPsychicHotlineforhelp.Quadraturesignalprocessingisusedinmanyfieldsofscienceandengineering,andquadraturesignalsarenecessarytodescribetheprocessingandimplementationthattakesplaceinmoderndigitalcommunica
4、tionssystems.Inthistutorialwe'llreviewthefundamentalsofcomplexnumbersandgetcomfortablewithhowthey'reusedtorepresentquadraturesignals.Nextweexaminethenotionofnegativefrequencyasitrelatestoquadraturesignalalgebraicnotation,andlearntospeakthelanguageofqua
5、dratureprocessing.Inaddition,we'llusethree-dimensionaltimeandfrequency-domainplotstogivesomephysicalmeaningtoquadraturesignals.Thistutorialconcludeswithabrieflookathowaquadraturesignalcanbegeneratedbymeansofquadrature-sampling.WhyCareAboutQuadratureSig
6、nals?Quadraturesignalformats,alsocalledcomplexsignals,areusedinmanydigitalsignalprocessingapplicationssuchas:-digitalcommunicationssystems,-radarsystems,-timedifferenceofarrivalprocessinginradiodirectionfindingschemes-coherentpulsemeasurementsystems,-a
7、ntennabeamformingapplications,-singlesidebandmodulators,-etc.Theseapplicationsfallinthegeneralcategoryknownasquadratureprocessing,andtheyprovideadditionalprocessingpowerthroughthecoherentmeasurementofthephaseofsinusoidalsignals.Aquadraturesignalisatwo-
8、dimensionalsignalwhosevalueatsomeinstantintimecanbespecifiedbyasinglecomplexnumberhavingtwoparts;whatwecalltherealpartandtheimaginarypart.(Thewordsrealandimaginary,althoughtraditional,areunfortunatebecausetheirofmeaningsinoureverydayspe
