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1、QuadratureSignals:Complex,ButNotComplicatedbyRichardLyonsIntroductionQuadraturesignalsarebasedonthenotionofcomplexnumbersandperhapsnoothertopiccausesmoreheartachefornewcomerstoDSPthanthesenumbersandtheirstrangeterminologyofj-operator,complex,imaginary,real,andorthogonal
2、.Ifyou'realittleunsureofthephysicalmeaningofcomplexnumbersandthej=-1operator,don'tfeelbadbecauseyou'reingoodcompany.WhyevenKarlGauss,onetheworld'sgreatestmathematicians,calledthej-operatorthe"shadowofshadows".Herewe'llshinesomelightonthatshadowsoyou'llneverhavetocallthe
3、QuadratureSignalPsychicHotlineforhelp.Quadraturesignalprocessingisusedinmanyfieldsofscienceandengineering,andquadraturesignalsarenecessarytodescribetheprocessingandimplementationthattakesplaceinmoderndigitalcommunicationssystems.Inthistutorialwe'llreviewthefundamentalso
4、fcomplexnumbersandgetcomfortablewithhowthey'reusedtorepresentquadraturesignals.Nextweexaminethenotionofnegativefrequencyasitrelatestoquadraturesignalalgebraicnotation,andlearntospeakthelanguageofquadratureprocessing.Inaddition,we'llusethree-dimensionaltimeandfrequency-d
5、omainplotstogivesomephysicalmeaningtoquadraturesignals.Thistutorialconcludeswithabrieflookathowaquadraturesignalcanbegeneratedbymeansofquadrature-sampling.WhyCareAboutQuadratureSignals?Quadraturesignalformats,alsocalledcomplexsignals,areusedinmanydigitalsignalprocessing
6、applicationssuchas:-digitalcommunicationssystems,-radarsystems,-timedifferenceofarrivalprocessinginradiodirectionfindingschemes-coherentpulsemeasurementsystems,-antennabeamformingapplications,-singlesidebandmodulators,-etc.Theseapplicationsfallinthegeneralcategoryknowna
7、squadratureprocessing,andtheyprovideadditionalprocessingpowerthroughthecoherentmeasurementofthephaseofsinusoidalsignals.Aquadraturesignalisatwo-dimensionalsignalwhosevalueatsomeinstantintimecanbespecifiedbyasinglecomplexnumberhavingtwoparts;whatwecalltherealpartandtheim
8、aginarypart.(Thewordsrealandimaginary,althoughtraditional,areunfortunatebecausetheirofmeaningsinoureverydayspe
