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Unit9DigitalSignalProcessingUnit9DigitalSignalProcessingPassageABasicConceptsofDSPPassageBDigitalSignalProcessorsPassageCComparisonofDSPandASPUnit9DigitalSignalProcessingPassageABasicConceptsofDSPWedon’tspeakinadigitalsignal.Adigitalsignalisalanguageof1sand0sthatcanbeprocessedbymathematics.Wespeakinreal-world,analogsignals.Analogsignalsarerealworldsignalsthatweexperienceeveryday-sound,light,temperature,andpressure.Adigitalsignalisanumericalrepresentationoftheanalogsignal.Itmaybeeasierandmorecosteffectivetoprocessthesesignalsinthedigitalworld.Intherealworld,wecanconvertthesesignalsintodigitalsignalsthroughtheanalog-to-digitalconverter,processthesignals,andifneeded,bringthesignalsbackouttotheanalogworldthroughthedigital-to-analogconverter.Unit9DigitalSignalProcessing1.Theessentialsofanalog-to-digitalanddigital-to-analogconversionThefirstessentialstepinanalog-to-digital(A/D)conversion(asshowninFigure9.1)istosampleananalogsignal.Thisstepisperformedbyasampleandholdcircuit,whichsamplesatregularintervalscalledsamplingintervals.Thelengthofthesamplingintervalisthesameasthesamplingperiod,andthereciprocalofthesamplingperiodisthesamplingfrequencyfs.AccordingtotheNyquisttheorem,asignalwithamaximumfrequencyofWHz(calledaband-limitedsignal)mustbesampledatleast2Wsamplespersecondtoensureaccuraterecording.Whenthisminimumisnotrespected,distortioncalledaliasingoccurs.Aliasingcauseshighfrequencysignalstoappearaslowerfrequencysignals.Tobesurealiasingwillnotoccur,samplingisalwaysprecededbylowpassfiltering.Thelowpassfilter,calledtheanti-aliasingfilter,removesallfrequenciesabovehalftheselectedsamplingrate.Unit9DigitalSignalProcessingFigure9.1Analog-to-DigitalConversionsUnit9DigitalSignalProcessingAfterabriefacquisitiontime,duringwhichasampleisacquired,thesampleandholdcircuitholdsthesamplesteadyfortheremainderofthesamplinginterval.ThisholdtimeisneededtoallowtimeforanA/Dconvertertogenerateadigitalcodethatbestcorrespondstotheanalogsample.Unit9DigitalSignalProcessingTheA/Dconverterchoosesaquantizationlevelforeachanalogsample.AnN-bitconverterchoosesamong2Npossiblequantizationlevels.Thelargerthenumberoflevels,thesmallerthequantizationerrors,calculatedasthedifferencebetweenthequantizedlevelandthetruesamplelevel.MostquantizationerrorsarelimitedinsizetohalfaquantizationstepQ.ThequantizationstepsizeiscalculatedasQ=R/2N,whereRisthefullscalerangeoftheanalogsignalandNisthenumberofbitsusedbytheconverter.Thestrengthofthesignalcomparedtothatofthequantizationerrorsismeasuredbydynamicrangeandsignal-to-noiseratio.Unit9DigitalSignalProcessingAdigitalsignalisrepresentedbyasetofverticallineswithcirclesatthetoptomarkthequantizationlevelsselectedforeachsample.ThebitrateforanA/DconverteristheNfs,wherefsisthesamplingrate.Finally,eachdigitalsampleisassignedadigitalcode,whichcompletestheA/Dprocess.Theresultisadigitalbitstream.Itisthiscollectionofdigitalcodesthatisprocessedindigitalsignalprocessing.Unit9DigitalSignalProcessingTosummarize,A/Dcomprisesanti-aliasing,sampling,quantizationanddigitization.Oncedigitalsignalprocessingiscomplete,digital-to-analog(D/A)conversion(asshowninFigure9.2)mustoccur.Thisprocessbeginsbyconvertingeachdigitalcodeintoananalogvoltagethatisproportionalinsizetothenumberrepresentedbythecode.Thisvoltageisheldsteadythroughzeroorderholduntilthenextcodeisavailable,onesamplingintervallater.Thiscreatesastaircase-likesignalthatcontainsfrequenciesaboveWHz.Thesesignalsareremovedwithasmoothinglowpassfilter,thelaststepinD/Aconversion.Unit9DigitalSignalProcessingFigure9.2Digital-to-AnalogConversionsUnit9DigitalSignalProcessingTheimagesofeachfrequencyfpresentinasampledsignalappear,throughsampling,attheinfinitenumberoffrequencieskfs±fHz.WhenthesamplingrateislowerthantherequiredNyquistrate,thatisfs2W,imagesofhighfrequencysignalserroneouslyappearinthebaseband(orNyquistrange)duetoaliasing.Whilethisundersamplingisnormallyavoided,itcanbeexploited.Forexample,signalswhosefrequenciesarerestrictedtoanarrowbandofhighfrequenciescanbesampledataratesimilartotwicethewidthofthebandinsteadoftwicethemaximumfrequency.Alloftheimportantsignalcharacteristicscanbededucedfromthecopyofthespectrumthatappearsinthebasebandthroughsampling.Dependingontherelationshipbetweenthesignalfrequenciesandthesamplingrate,spectralinversionmaycausetheshapeofthespectruminthebasebandtobeinvertedfromthetruespectrumofthesignal.［1］Unit9DigitalSignalProcessing2.TechnologiesfordigitalsignalprocessingIfauniversalmicroprocessorsolutionexistedwithwhicheverydesigncouldberealized,theelectronicsindustrywouldn’tbeaverycompetitiveplace.［2］However,typicallyinmostelectronicdesigns,morethanoneprocessortechnologycanbeusedtoimplementtherequiredfunctions.Thetrickis,ofcourse,tochoosetheonethatbestdeliverstheperformance,size,powerconsumption,features,softwareandtoolstogetthejobdonefast-withoutbreakingthebudget.Afteralmosttwodecadesofdevelopment,digitalsignalprocessorscontinuetotaketheplaceofcompetitiveprocessors.Digitalsignalprocessorsare,afterall,atthecenterofsignalprocessing.Unit9DigitalSignalProcessingAdigitals