第1題Whichofthefollowingsystemsisacausalsystem?Ay(n)=x(n+2)By(n)=cos(n+1)x(n)Cy(n)=x(2n)Dy(n)=x(-n)第2題Thecorrectstatementamongthefollowingis()AThespectrumofacontinuousnon-periodicsignalisanon-periodiccontinuousfunctionBThespectrumofacontinuousperiodicsignalisanon-periodiccontinuousfunctionCThespectrumofadiscretenon-periodicsignalisanon-periodiccontinuousfunctionDThespectrumofadiscreteperiodicsignalisanon-periodiccontinuousfunction第3題Giventhesignalofxa(t)asshowninthefigure,itsFouriertransformismostlikely()ABCD第4題ThelinearpropertyoftheZtransformstatesthattheZtransformofthesumoftwosequencesisequaltothesumoftheirindividualZtransforms.()第5題IftheZtransformsoftwosequencesarethesame,thenthetwosequencesarealsothesame.()第6題TheinversetransformoftheZtransformisalwaysunique.()第7題Ifthesequenceiscausal,thentheconvergencedomainofitsZtransformcontainsatleasttheoutsideoftheunitcircle.()第8題TheconvergencedomainoftheZtransformalwayscontainstheunitcircle.()第9題TheZtransformisageneralizationofthediscrete-timeFouriertransform().()第10題Thesystemmustbeacausalsystem.()第11題Assumethatisaconstant,thenthesystemisalinearsystem.()第12題TheFouriertransformofasequencemustbeaperiodicfunction.()第13題Thepolesofthesystemfunctionofacausalandstablesystemmaybeoutsidetheunitcircle.()第14題Iftheoutputofacausalsystemattimendependsonlyontheinputsequenceattimenandbefore,andisindependentoftheinputsequenceaftertimen,thenthesystemissaidtohavecausalproperties,oriscalledacausalsystem.()第15題Whentheinputsequenceisdifferent,theunitsamplingimpulseresponseofthelinearshift-invariantsystemisalsodifferent.()第16題isacausalandunstablesystem.()第17題isalinearsystem.()第18題Asystemthatisbothadditiveandhomogeneousiscalledalinearsystem.()第19題Thesignalissampledatequalintervals,withasamplingperiodof,thenthefoldingfrequencyis200Hz.()第20題TheZtransformofasamplingsequenceontheunitcircleisequaltotheDTFTofthesamplingsequence.()第21題Given,thenistheinversetransformof.()第22題Theofthesequenceis1.()第23題Ifalineartime-invariantsystemiscausal,thenthenecessaryandsufficientconditionthattheunitsamplingresponsesequenceofthesystemshouldmeetand.()第24題Sinusoidalsequencesareallperiodicsequences.()第25題Astablediscrete-timesystemhasallitspoleslocatedoutsidetheunitcircleintheZplane.()第26題Themathematicalmodelofthelineartime-invariantsystemisthelinearconstantcoefficientdifferenceequation.()第27題Acertainsystemis,thenthesystemisalinearsystem.()第28題Giventhatthehighestfrequencyofasignalspectrumis100Hz,andtheminimumsamplingfrequencythatcanrestoretheoriginalsignalis200Hz.()第29題Themathematicalmodelofadiscrete-timesystemisadifferenceequation.()第30題Thesequencerepresentedbyisnotnecessarilyperiodic.()第1題WhatisFFTaformofDFT?()

AApproximatealgorithmBEfficientalgorithmCExactalgorithmbutmorecomplicatedDCompletelydifferentalgorithm第2題FromwhichdomaintowhichdomaindoesDFTtransformthesignal?()

AA.

TimedomaintofrequencydomainBFrequencydomaintotimedomainCComplexdomaintorealdomainDDiscretedomaintocontinuousdomain第3題Amongthefollowingphenomena,()doesnotbelongtothetruncationeffect.

ASpectrumleakage

BTimedomainaliasingCInter-spectralinterferenceDGibbseffect第4題WhichofthefollowingdescriptionsbestfitsthediscreteFouriertransformDFT?()AThetimedomainisadiscretesequence,andthefrequencydomainisalsoadiscretesequenceBThetimedomainisadiscretefinitesequence,andthefrequencydomainisalsoadiscrete

finitesequenceCThetimedomainisadiscreteinfinitesequence,andthefrequencydomainisacontinuousperiodicsignalDThetimedomainisadiscreteperiodicsequence,andthefrequencydomainisalsoadiscreteperiodicsequence第5題Indigitalsignalprocessing,fastFouriertransform()isoftenusedtocalculatecircularconvolutionbecauseitismuchmoreefficientthandirectlycalculatingcircularconvolution.()第6題Whenperformingcircularconvolution,ifthetwosequencesareofdifferentlengths,theymustfirstbepaddedwithzerostothesamelength.()第7題Ifthelinearconvolutionresultsoftwosequencesareuniquewithinacertainperiod,thentheircircularconvolutionisequaltothelinearconvolutionwithinthatperiod.()第8題Thelengthoftheresultofcircularconvolutionisalwaysequaltothelengthofthelongerofthetwosequences.()第9題Spectrumleakagedoesnotbelongtotruncationeffect.()第10題TherelationshipbetweentheconvolutionsumandthecircularconvolutionsumcanbeusedtoconvenientlycalculatethelinearconvolutionusingDFT.()第11題ChangethenumberofDFTpointstomakethespectrumlinesdenserandincreasethenumberoffrequencydomainsamplingpoints.Someoftheoriginallymissedspectramaybedetected.()第12題DecimationinfrequencyanddecimationintimearetwoequivalentFFToperations.()第13題Theoutputofthefrequencyextractionmethodisinnaturalorder,andtheinputisrearrangedaccordingtotheinversionrule.()第14題Thecomputationalcomplexityoftheoverlapretentionmethodandtheoverlapadditionmethodissimilar.()第15題DFTimpliesperiodicity.()第16題Periodicconvolutionistheperiodicextensionoflinearconvolution.()第17題istheequidistantsamplingvalueofontheunitcircle.()第18題DFThasfrequencyselectivecharacteristics.()第19題ThediscreteFouriertransformX()ofafinitelengthsequencex()istheZtransformofx()atanequidistantsamplingpointontheunitcircleoftheZplane.()第20題DFTistheFouriertransformofadiscretesequence.()第21題PeriodicsequencescannotundergoZtransform.()第22題DFTcanbeseenasaperiodofDFS.()第23題Thefirstperiodofaperiodicsequenceiscalledthe"mainvalueinterval".()第24題WhichofthefollowingstatementsaboutthepropertiesofdiscreteFouriertransform()iscorrect?()ADFTisalineartransformBDFThasimplicitperiodicityCDFTcanbeusedtoaccuratelyanalyzethespectrumofcontinuoussignalsDDFTcanberegardedasthesamplingofthesequenceztransformontheunitcircle正確答案：DAB第25題Whichofthefollowingdescriptionsabouttherelationshipbetweencircularconvolutionandlinearconvolutioniscorrect:()AWithoutzeropadding,thelengthofthecircularconvolutionisequaltothelengthoftheshortersequenceBIfthelengthsofthetwosequencesareequal,thentheircircularconvolutionisthesameasthelinearconvolutionCCircularconvolutionisanapproximationoflinearconvolutiononinfinitelengthsequencesDBypaddingzerosattheendofthesequence,circularconvolutioncanbemadeclosetolinearconvolution.正確答案：AD第26題Thepropertiesofcircularconvolutioninclude:()AItsatisfiesthecommutativeandassociativelawsBItslengthisequaltothesumofthelengthsofthetwosequencesminusoneCItcanbeefficientlycalculatedusingDFTandIDFT(inverseDFT)DItisequivalenttolinearconvolutionwhenthelengthislargeenough正確答案：AC第27題RegardingtheperiodicityofdiscreteFouriertransform(),whichofthefollowingstatementiscorrect?()ADFTisperiodicinthetimedomainBDFTisperiodicinthefrequencydomain,withaperiodofN(Nisthesignallength)CTheperiodicityoftheDFTmeansthatX(k)andX(k+N)arethesameDTheperiodicityofDFTisadirectresultofitsdefinition正確答案：DBC第28題InwhichofthefollowingfieldsdoesdiscreteFouriertransform()haveimportantapplications?()ASignalfilteringBSpectrumanalysisCCommunicationsystemDImageprocessing正確答案：DABC第29題Ifadiscrete-timesignalx()isreal-valuedandadiscreteFouriertransform()isperformed,then:()ATheamplitudespectrumofthetransformationresultX(k)issymmetricalBThephasespectrumofthetransformationresultX(k)issymmetricalCX(k)meetsconjugatesymmetry,thatis,X(Nk)=X*(k)DX(0)andX(N/2)(ifNiseven)arerealvalues正確答案：DAC第30題TherelationshipbetweendiscreteFouriertransform()andfastFouriertransform()is:()AFFTisanefficientimplementationalgorithmofDFTBFFTandDFTaremathematicallyequivalentCFFTcanonlybeusedforsignalswhoselengthisapowerof2DThecomputationalcomplexityofFFTisO(N^2),whereNisthelengthofthesignal正確答案：DABChapter4Exercises第1題ThetimecomplexityoftheFFTalgorithmis().

AO(n2)

BO(nlogn)

CO(n3)

DO(logn)第2題Operatea256-pointradix-2FFTdecimatedintimewith______butterfliesateachlevel.()A1024B1024×1024C512×10D1024×10第3題Theoperationflowgraphsymbolshowninthefigureisthebutterflyoperationflowgraphsymbolofthe_______radix-2FFTalgorithm.()ADecimationinfrequencyBDecimationintimeCBothAandBDNeitherAnorB第4題ThemainfunctionoffastFouriertransform(FFT)is().AImprovetheoperationspeedBReducetheoperationcomplexityCPerformspectrumanalysisonthesignalDAlloftheabove第5題ThenumberofcomplexmultiplicationsrequiredforanN-pointFFTis(N/2)log2N.()第6題Inthedecimation-in-timeFFToperationflowchartofN=32,5levelsofbutterflyoperationprocessarerequiredfromx()toX().()第7題ThenumberofcomplexmultiplicationsrequiredtodirectlycalculatetheN-pointDFTisproportionaltoN2.()第8題Thebase2FFTrequiresthenumberofpointsinthesequencetobe2L(whereLisaninteger).()第9題FFTcanbasicallybedividedintotwocategories:decimationintimeanddecimationinfrequency.()第10題FFTisafastalgorithmforDFT.()第11題FFTisanewtransform.()第12題Thebasicoperationunitoftheradix-2FFTalgorithmistheconvolutionoperation.()第13題Operationa256-pointradix-2FFTdecimatedintimewith64butterfliesateachstage.()第14題Tofindthe1024-pointradix-2FFTofthesequencex(),512×10complexmultiplicationsarerequired.()第15題TheoperationcomplexityofN-pointFFTisapproximatelytimescomplexmultiplicationandtimescomplexaddition.()第16題Inthedecimation-in-timeFFToperationflowchartofN=8,3levelsofbutterflyoperationprocessarerequiredfromx()toX().()第17題ThenumberofcalculationsfortheN-pointradix-2FFTofthesequencex()decimatedintimeisthesameasthenumberofcalculationsfortheradix-2FFTdecimatedinfrequency.()第18題TheadvantagesoffastFouriertransforminengineeringpracticeare().ASaveoperationtimeBReducehardwarecostsCImprovesignalprocessingqualityDFacilitatereal-timeprocessing正確答案：ABCD第19題WhattypesofsignalchangescanFFTbeusedtoanalyze?()A.FrequencychangeofthesignalB.AmplitudechangeoftheAPhasechangeofthesignalBTimechangeofthesignal正確答案：A第20題WhenperformingFFTcalculations,themeasuresthatcanbetakentoimprovecalculationaccuracyare().AIncreasethenumberofsamplingpointsBUseahigherprecisiondatatypeC.OptimizethealgorithmimplementationCReducethesignalamplitude正確答案：AB第21題WhichofthefollowingstatementsabouttherelationshipbetweenFFTanddiscreteFouriertransform()arecorrect.()AFFTisafastalgorithmforDFT.BTheresultsofFFTandDFTareexactlythesame.CFFTismoreefficientthanDFT.DFFTisonlyapplicabletosignalsofaspecificlength,whileDFTisapplicabletosignalsofanylength.正確答案：DABC第22題AfterperformingFFTprocessingonasignal,wecangetthesignal’s().AAmplitudespectrumBPhasespectrumCPowerspectrumDTimespectrum正確答案：ABC第23題TheimplementationmethodsoffastFouriertransformare().A.DecimationinTimeADecimationinFrequencyC.MixeddecimationmethodBRecursivealgorithm正確答案：AB第24題TheapplicationsofFFTincommunicationsystemsinclude().AModulationanddemodulationBChannelestimationCSignalfilteringDSignalencryption正確答案：ABC第25題WhichofthefollowingfactorswillaffecttheaccuracyofFFTresults?()ASamplingfrequencyBNumberofsamplingpointsCSignalnoiseDSignalamplitude正確答案：ABC第26題WhichofthefollowingtypesofsignalscanbeprocessedbyfastFouriertransform?()AContinuoussignalBDiscretesignalCPeriodicsignalDNon-periodicsignal正確答案：BCD第27題WhenusingfastFouriertransformforsignalprocessing,theproblemsyoumayencounterinclude().ASpectrumleakageBFenceeffectCOperationaccuracyDDatastorage正確答案：ABCD第28題RegardingthebutterflyoperationofFFT,whichofthefollowingstatementsarecorrect.()AItisthecoreoperationoftheFFTalgorithm.BIthasthecharacteristicsofparalleloperation.CItreducestheamountofoperation.DItisonlyapplicabletosequencesofaspecificlength.正確答案：ABC第29題IntheFFTalgorithm,thefactorsthataffecttheoperationefficiencyare().ASequencelengthBDatatype(realorcomplexnumber)CAlgorithmimplementationDComputerperformance正確答案：ABCD第30題ThefunctionsofInversefastFouriertransform()are().AConvertfrequencydomainsignalstotimedomainsignalsBInverseoperationofFFTCUsedforsignalreconstructionDImprovesignalresolution正確答案：ABCChapter5Exercises第1題WhichofthefollowingstatementaboutdesigningIIRfiltersusingtheimpulseresponseinvariancemethodisincorrect?().AThereisalinearrelationshipbetweendigitalfrequencyandanalogfrequencyBAbletomapalinearphaseanalogfiltertoalinearphasedigitalfilterCFrequencyaliasingeffectispronetooccurDCanbeusedtodesignhigh-passandband-stopfilters第2題ThecorrectstatementaboutdesigningIIRfilterusingbilineartransformationmethodis().AThereisalinearrelationshipbetweendigitalfrequencyandanalogfrequencyBAlwaysmapastableanalogfiltertoastabledigitalfilterCThetransformationusedisamulti-valuedmappingfromthesplanetothezplaneDNotsuitablefordesigninghigh-passandband-stopfilters第3題Assumethatthecutofffrequencyoftheideallow-passdigitalfilterisωc=π2

Thisfilterisobtainedbyconvertingtheideallow-passfilterusingtheimpulseresponseinvariancemethodatT=0.1ms.ThenthecutofffrequencyoftheanalogfilterisΩc=().A50πrad/sB500πrad/sC5000πrad/s

D50000πrad/s第4題AssumingthatananalogfilterHa()isahigh-passfilter,andmappedtoadigitalfilterH()throughs=z+1z?1

,thentheresultingdigitalfilterisa()filter.IfH()isalow-passfilter,thenH(-z)isa()filter.ALowpassB

PassiveCHighpassDActive第5題Thebilineartransformationmethodisanonlineartransformation,sousingittodesignIIRfilterscannotovercomethefrequencyresponsealiasingeffect.()第6題Theimpulseresponseinvariancemethodcannotbeusedtodesignhigh-passdigitalfilters.()第7題Thefrequencycoordinatetransformationofthebilineartransformationmethodisalinearrelationship.()第8題TheIIRfilterdesignedusingtheimpulseresponseinvariancemethodwillnotproducedistortion.()第9題Thepolesofacertainanalogfiltersystemfunctionarelocatedinthelefthalfplaneofthesplane.Whenitismappedtoadigitalfilterusingtheimpulseresponseinvariancemethod,thepolesoftheresultingdigitalfiltersystemfunctionarelocatedwithintheunitcircleofthezplane.()第10題Thebilineartransformationisamappingfromthesplanetothezplane.()第11題DesignanIIRdigitalhigh-passfilterwiththehelpoftheanalogfilter'sH().Ifnospecialrequirementsareemphasized,theimpulseresponseinvariancemethodshouldbeused.()第12題TheButterworthfilterhasamaximumflatamplitudecharacteristicwithinthepassbandanddecreasesmonotonically.()第13題Thedisadvantageofthepulseresponseinvariancemethodisthatitwillproducefrequencyaliasingphenomenon,andtheadvantageisthatωandΩareinalinearrelationship.()第14題IIRfiltersmustbelinearphase.()第15題InthebasicstructuresofIIRfilters,theparalleloperationhastheleastoperationerrorsandthehighestoperationspeed.()第16題InthebasicstructureofIIRfilter,thecascadeoperationhasmoreoperationerrors.()第17題InthebasicstructureofIIRdigitalfilter,thedirectoperationhasmoreoperationerrors.()第18題Theinfiniteimpulseresponse()filterhasafeedbackloopinitsstructure,soitisarecursivestructure.()第19題Digitalfrequencyisthenormalizationofanalogfrequencytosamplingfrequencyanditsvalueisdiscrete.()第20題Thefrequencyresponseofthedigitalfilterwhenrepresentsthehighfrequencyresponse.()第21題Thefrequencyresponseofthedigitalfilterwhenrepresentsthelowfrequencyresponse.()第22題Thebilineartransformationmethodisanonlineartransformation,sousingittodesignanIIRfiltercannotovercomethefrequencyaliasingeffect.()第23題Thefrequencydistortionproducedbythebilineartransformationmethodcannotbeovercome.()第24題Thebilineartransformationmethodisapplicabletoalltypesoffilterdesigns(low-pass,high-pass,band-pass,band-stop).()第25題UsethebilineartransformationmethodtodesignanIIRfilter.Theconversionofanalogangularfrequencytodigitalangularfrequencyisalinearconversion.()第26題Whenusingthebilineartransformationmethodtodesigndigitalfilters,pre-distortioncannoteliminatethenonlineardistortionofallfrequencypointsgeneratedduringthetransformation.()第27題Theimpulseresponseinvariancemethodisapplicabletoalltypesoffilterdesigns(low-pass,high-pass,band-pass,band-stop).()第28題Theimpulseresponseinvariancemethoddoesnotnecessarilymaptheminimumphaseanalogfiltertoaminimumphasedigitalfilter.()第29題Thebasicstructuresofinfiniteunitimpulseresponse()filtersaredirecttypeI,directtypeIIandparalleltype.()第30題WhenusinganalogfilterstodesignIIRdigitalfilters,theanalogprototypefiltersmainlyincludeButterworthfiltersandChebyshevfilters.()Chapter6Exercises第1題

HowmanytypesoflinearphaseFIRfiltersarethere?A1B2C3D4第2題ThesystemfunctionofaFIRfilteris,thenthesystembelongsto()AEven-symmetriclinearphasefilterwithoddNBOdd-symmetriclinearphasefilterwithoddNCEven-symmetriclinearphasefilterwithevenNDOdd-symmetriclinearphasefilterwithevenN第3題Whenonlythesameamplitude-frequencycharacteristicsarerequired,theorderoftheIIRfiltermustbelowerthantheFIRorder.()第4題OnlyFIRfilterscanachievelinearphase,whileIIRfilterscannotachievelinearphase.()第5題WhendesigningFIRdigitalfiltersusingthewindowfunctionmethod,increasingthelengthofthewindowfunctioncanreducethewidthofthetransitionband,andchangingthetypeofwindowfunctioncanchangethestopbandattenuation.()第6題ThedifferencebetweendesigningFIRdigitalfiltersusingthewindowfunctionmethodanddesigningFIRdigitalfiltersusingthefrequencysamplingmethodisthattheformerisperformedinthetimedomainandthelatterisperformedinthefrequencydomain.()第7題WhendesigningFIRdigitalfiltersusingthefrequencysamplingmethod,thebasicideaistosamplethespectrumoftheidealdigitalfiltertoobtainthediscretevaluesoftheactualdesignedfilterspectrum.()第8題FIRfiltersmusthavelinearphase,whileIIRfiltersmostlyhavenonlinearphase-frequencycharacteristics.()第9題ThebasicstructureofFIRfilterhasthesamebasicoperationunittypeasthebasicstructureofIIRfilter.()第10題ThesystemfunctionofacertainFIRdigitalfilteris,thenthissystemisnotalinearphasesystem.()第11題FIRfiltersmustbestable.()第12題SimilartoFIRfilters,IIRfilterscanalsoeasilyachievelinearphase.()第13題WhendesigningFIRfilterusingwindowmethod,themainreasonaffectingthequalityoffilteramplitude-frequencycharacteristicsisthatthemainlobemakesthedigitalfilterhavetransitionband,andthesidelobemakesthedigitalfilterhavefluctuation,reducingstopbandattenuation.()第14題Thezerodistributioncharacteristic