标签: convolution

ThischapterpresentstwoimportantDSPtechniques,theoverlap-addmethod,andFFTconvolution.Theoverlap-addmethodisusedtobreaklongsignalsintosmallersegmentsforeasierprocessing.FFTconvolutionusestheoverlap-addmethodtogetherwiththeFastFourierTransform,allowingsignalstobeconvolvedbymultiplyingtheirfrequencyspectra.Forfilterkernelslongerthanabout64points,FFTconvolutionisfasterthanstandardconvolution,whileproducingexactlythesameresult.CHAPTERFFTConvolution18ThischapterpresentstwoimportantDSPtechniques,theoverlap-addmethod,andFFTconvolution.Theoverlap-addmethodisusedtobreaklongsignalsintosmallersegmentsforeasierprocessing.FFTconvolutionusestheoverlap-addmethodtogetherwiththeFastFourierTransform,allowingsignalstobeconvolvedbymultiplyingtheirfrequencyspectra.Forfilterkernelslongerthanabout64points,FFTconvolutionisfasterthanstandardconvolution,whileproducingexactlythesameresult.TheOverlap-AddMethodTherearemanyDSPapplicationswherealongsignalmustbefilteredinsegments.Forinstance,highfidelitydigitalaudiorequiresadatarateof……

ThemovingaverageisthemostcommonfilterinDSP,mainlybecauseitistheeasiestdigitalfiltertounderstandanduse.Inspiteofitssimplicity,themovingaveragefilterisoptimalforacommontask:reducingrandomnoisewhileretainingasharpstepresponse.Thismakesitthepremierfilterfortimedomainencodedsignals.However,themovingaverageistheworstfilterforfrequencydomainencodedsignals,withlittleabilitytoseparateonebandoffrequenciesfromanother.RelativesofthemovingaveragefilterincludetheGaussian,Blackman,andmultiplepassmovingaverage.Thesehaveslightlybetterperformanceinthefrequencydomain,attheexpenseofincreasedcomputationtime.CHAPTERMovingAverageFilters15ThemovingaverageisthemostcommonfilterinDSP,mainlybecauseitistheeasiestdigitalfiltertounderstandanduse.Inspiteofitssimplicity,themovingaveragefilterisoptimalforacommontask:reducingrandomnoisewhileretainingasharpstepresponse.Thismakesitthepremierfilterfortimedomainencodedsignals.However,themovingaverageistheworstfilterforfrequencydomainencodedsignals,withlittleabilitytoseparateonebandoffrequenciesfromanother.RelativesofthemovingaveragefilterincludetheGaussian,Blackman,andmultiple-passmovingaverage.Thesehaveslightlybetterperformanceinthefrequencydomain,attheexpenseofincreasedcomputationtime.Im……

ContinuoussignalprocessingisaparallelfieldtoDSP,andmostofthetechniquesarenearlyidentical.Forexample,bothDSPandcontinuoussignalprocessingarebasedonlinearity,decomposition,convolutionandFourieranalysis.Sincecontinuoussignalscannotbedirectlyrepresentedindigitalcomputers,don'texpecttofindcomputerprogramsinthischapter.Continuoussignalprocessingisbasedonmathematics;signalsarerepresentedasequations,andsystemschangeoneequationintoanother.JustasthedigitalcomputeristheprimarytoolusedinDSP,calculusistheprimarytoolusedincontinuoussignalprocessing.Thesetechniqueshavebeenusedforcenturies,longbeforecomputersweredeveloped.CHAPTERContinuousSignalProcessing13ContinuoussignalprocessingisaparallelfieldtoDSP,andmostofthetechniquesarenearlyidentical.Forexample,bothDSPandcontinuoussignalprocessingarebasedonlinearity,decomposition,convolutionandFourieranalysis.Sincecontinuoussignalscannotbedirectlyrepresentedindigitalcomputers,don'texpecttofindcomputerprogramsinthischapter.Continuoussignalprocessingisbasedonmathematics;signalsarerepresentedasequations,andsystemschangeoneequationintoanother.JustasthedigitalcomputeristheprimarytoolusedinDSP,calculusistheprimarytoolusedincontinuoussignalprocessing.Thesetechniqueshavebeenusedforcenturies,longbeforecomputersweredeveloped.The……

TheDiscreteFourierTransform(DFT)isoneofthemostimportanttoolsinDigitalSignalProcessing.Thischapterdiscussesthreecommonwaysitisused.First,theDFTcancalculateasignal'sfrequencyspectrum.Thisisadirectexaminationofinformationencodedinthefrequency,phase,andamplitudeofthecomponentsinusoids.Forexample,humanspeechandhearingusesignalswiththistypeofencoding.Second,theDFTcanfindasystem'sfrequencyresponsefromthesystem'simpulseresponse,andviceversa.Thisallowssystemstobeanalyzedinthefrequencydomain,justasconvolutionallowssystemstobeanalyzedinthetimedomain.Third,theDFTcanbeusedasanintermediatestepinmoreelaboratesignalprocessingtechniques.TheclassicexampleofthisisFFTconvolution,analgorithmforconvolvingsignalsthatishundredsoftimesfasterthanconventionalmethods.SpectralAnalysisCHAPTERApplicationsoftheDFT9TheDiscreteFourierTransform(DFT)isoneofthemostimportanttoolsinDigitalSignalProcessing.Thischapterdiscussesthreecommonwaysitisused.First,theDFTcancalculateasignal'sfrequencyspectrum.Thisisadirectexaminationofinformationencodedinthefrequency,phase,andamplitudeofthecomponentsinusoids.Forexample,humanspeechandhearingusesignalswiththistypeofencoding.Second,theDFTcanfindasystem'sfrequencyresponsefromthesystem'simpulseresponse,andviceversa.Thisallowssystemstobeanalyzedinthefrequencydomain,justasconvolutionallowssystemstobeanalyzedinthetimedomain.Third,theDFTcanbeusedasanintermediatestepinmoreelaboratesignalp……

Convolutionisamathematicalwayofcombiningtwosignalstoformathirdsignal.ItisthesinglemostimportanttechniqueinDigitalSignalProcessing.Usingthestrategyofimpulsedecomposition,systemsaredescribedbyasignalcalledtheimpulseresponse.Convolutionisimportantbecauseitrelatesthethreesignalsofinterest:theinputsignal,theoutputsignal,andtheimpulseresponse.Thischapterpresentsconvolutionfromtwodifferentviewpoints,calledtheinputsidealgorithmandtheoutputsidealgorithm.ConvolutionprovidesthemathematicalframeworkforDSP;thereisnothingmoreimportantinthisbook.CHAPTERConvolution6Convolutionisamathematicalwayofcombiningtwosignalstoformathirdsignal.ItisthesinglemostimportanttechniqueinDigitalSignalProcessing.Usingthestrategyofimpulsedecomposition,systemsaredescribedbyasignalcalledtheimpulseresponse.Convolutionisimportantbecauseitrelatesthethreesignalsofinterest:theinputsignal,theoutputsignal,andtheimpulseresponse.Thischapterpresentsconvolutionfromtwodifferentviewpoints,calledtheinputsidealgorithmandtheoutputsidealgorithm.ConvolutionprovidesthemathematicalframeworkforDSP;thereisnothingmoreimportantinthisbook.TheDeltaFunctionandImpulseResponseThepreviouschapterdescribesh……

LinearimageprocessingisbasedonthesametwotechniquesasconventionalDSP:convolutionandFourieranalysis.Convolutionisthemoreimportantofthesetwo,sinceimageshavetheirinformationencodedinthespatialdomainratherthanthefrequencydomain.Linearfilteringcanimproveimagesinmanyways:sharpeningtheedgesofobjects,reducingrandomnoise,correctingforunequalillumination,deconvolutiontocorrectforblurandmotion,etc.Theseproceduresarecarriedoutbyconvolvingtheoriginalimagewithanappropriatefilterkernel,producingthefilteredimage.Aseriousproblemwithimageconvolutionistheenormousnumberofcalculationsthatneedtobeperformed,oftenresultinginunacceptablylongexecutiontimes.Thischapterpresentsstrategiesfordesigningfilterkernelsforvariousimageprocessingtasks.Twoimportanttechniquesforreducingtheexecutiontimearealsodescribed:convolutionbyseparabilityandFFTconvolution.CHAPTERLinearImageProcessing24LinearimageprocessingisbasedonthesametwotechniquesasconventionalDSP:convolutionandFourieranalysis.Convolutionisthemoreimportantofthesetwo,sinceimageshavetheirinformationencodedinthespatialdomainratherthanthefrequencydomain.Linearfilteringcanimproveimagesinmanyways:sharpeningtheedgesofobjects,reducingrandomnoise,correctingforunequalillumination,deconvolutiontocorrectforblurandmotion,etc.Theseproceduresarecarriedoutbyconvolvingtheoriginalimagewithanappropriatefilterkernel,producingthefilteredimage.Aseriousproblemwithimageconvolutionistheenormousnumberofcalculationsthatneedtobeperformed,oftenresultinginunacceptably……

Abstract:Acommonviewholdsthatdigitalcircuitsjustworknaturally,butanalogcircuitsarehardtoimplement.Thereistruthtothatoldbelief—analoginterfaceisanexpertsubjectthatrequirestraining.Itis,moreover,alwaysbettertoavoidanissuethantotrytosolveitlater.Thisispreciselywhyweshouldtakeadvantageofsomebasicconceptsthatexperiencedanalogengineersperformasareflex.Thisapplicationnoteprovidessomebasicremindersandconceptsaboutamplifiersandfiltersforyoutoconsiderduringadesign.Maxim>Designsupport>Appnotes>A/DandD/AConversion/SamplingCircuits>APP4993Maxim>Designsupport>Appnotes>AmplifierandComparatorCircuits>APP4993Maxim>Designsupport>Appnotes>AnalogSwitchesandMultiplexers>APP4993Keywords:digitalpotentiometer,lowpassfilter,filter,low-passfilter,lowpassfilte,antialiasing,sampleddatasystem,folded,Nyquist,dataconverters,spectrum,harmonics,FFT,ADC,convolution,DAC,opamps,RC,LC,ButterworthMar08,2011APPLICATIONNOTE4993ReducetheChancesofHumanError:Part2,SuperAmpsandFiltersforAnalogInterfaceBy:BillLaumeister,StrategicApplicationsEngineerAb……

摘要：一种常见的观点认为，数字电路的工作只是自然，但模拟电路是很难实现的。有真相，旧的信仰模拟接口是一个专家的课题，需要培训。，而且，它总是更好，以避免一个问题，而不是试图解决以后。这正是为什么我们应该采取的一些基本概念，有经验的模拟设计工程师作为反射执行的优势。本应用笔记提供了一些基本的提醒有关放大器和滤波器为您和概念设计过程中考虑。Maxim>Designsupport>Appnotes>A/DandD/AConversion/SamplingCircuits>APP4993Maxim>Designsupport>Appnotes>AmplifierandComparatorCircuits>APP4993Maxim>Designsupport>Appnotes>AnalogSwitchesandMultiplexers>APP4993Keywords:digitalpotentiometer,lowpassfilter,filter,low-passfilter,lowpassfilte,antialiasing,sampleddatasystem,folded,Nyquist,dataconverters,spectrum,harmonics,FFT,ADC,convolution,DAC,opamps,RC,LC,ButterworthMar08,2011APPLICATIONNOTE4993ReducetheChancesofHumanError:Part2,SuperAmpsandFiltersforAnalogInterfaceBy:BillLaumeister,StrategicApplicationsEngineerAb……