数字信号处理(第四版)第三章PPT课件.ppt

Chapter03-1-Discretre-TimeSignalsinFrequencyDomain,Dr.JiminLiangSchoolofLifeSciencesandTechnologyXidianUniversityjimleung,1,2,Discrete-TimeSignalsinFrequencyDomain,Reviewofcontinuous-timeFouriertransform(CTFT)Discrete-timeFouriertransform(DTFT)DTFTtheoremsDTFTcomputationusingMATLAB,Outline,3,Discrete-TimeSignalsinFrequencyDomain,TimedomainrepresentationofaDTsignalxn=sum_k(a_ndeltan-k)Whatisthefrequencydomainrepresentation?Xejwn,w:normalizedfrequencyinradians,Objectiveofthislecture,4,Discrete-TimeSignalsinFrequencyDomain,DefinitionOmega:radians/secPolarform(1)Magnitudespectrum:|X_a|(2)Phasespectrum:argX_a,3.1ReviewofCTFT,5,Dirichletconditions(1)finitediscontinuities,finitenumberofmaximaandminimainanyfiniteinterval(2)absolutelyintegrableThisisasufficientcondition.,Discrete-TimeSignalsinFrequencyDomain,3.1ReviewofCTFT,6,SignalenergyandenergydensityspectrumEnergydefinitionintimedomain(1)Parsevalstheorem(2)Energydensityspectrum,Discrete-TimeSignalsinFrequencyDomain,3.1ReviewofCTFT,7,Band-limitedcontinuous-timesignals(1)Full-bandvs.band-limited(2)Bandwith:applicationdependent,Discrete-TimeSignalsinFrequencyDomain,3.1ReviewofCTFT,8,DefinitionAnalysisequation:(1)Example3.5(2)Example3.6(Mag=?)(3)Periodicity=2piSynthesisequation:,Discrete-TimeSignalsinFrequencyDomain,3.2Discrete-timeFouriertransform(DTFT),9,BasicpropertiesofDTFTDifferentformsofexpression,Discrete-TimeSignalsinFrequencyDomain,3.2Discrete-timeFouriertransform(DTFT),10,SymmetryrelationsTable3.1,3.2Example3.7,Discrete-TimeSignalsinFrequencyDomain,3.2Discrete-timeFouriertransform(DTFT),11,ConvergenceconditionDefinition:partialsum(1)Absolutelysummable(uniformconvergence)X_kconvergencestoXforallthevaluesoffrequency.Ifasequenceisabsolutelysummable,itsDTFTexists.,Discrete-TimeSignalsinFrequencyDomain,3.2Discrete-timeFouriertransform(DTFT),12,ConvergenceconditionAbsolutelysummableisasufficientcondition.Example2.9,Discrete-TimeSignalsinFrequencyDomain,3.2Discrete-timeFouriertransform(DTFT),13,Convergencecondition(2)Mean-squaresummable:X_kdoesnotconvergencetoXforallthevaluesoffrequency,butconvergencesinthemean-squaresense.,Discrete-TimeSignalsinFrequencyDomain,3.2Discrete-timeFouriertransform(DTFT),14,Example3.8IndependentofK,thereareripplesaroundw_c.Kincreases,thenumberofripplesincreases,buttheheightoflargestrippleremainsthesame.K-inf,error-0Gibbsphenomenon,Discrete-TimeSignalsinFrequencyDomain,3.2Discrete-timeFouriertransform(DTFT),15,Convergencecondition(3)Diracdeltafunction:forsequencesthatareneitherabsolutelysummablenorsquare-summable.Example3.9,Discrete-TimeSignalsinFrequencyDomain,3.2Discrete-timeFouriertransform(DTFT),16,Discrete-TimeSignalsinFrequencyDomain,LinearityTime-reversalTime-shifting:时域平移-频域相移Example3.10,3.3DTFTtheorems,17,Discrete-TimeSignalsinFrequencyDomain,Frequency-shifting:时域相移-频移Example3.12Differentiation-in-frequency,3.3DTFTtheorems,18,Discrete-TimeSignalsinFrequencyDomain,Convolution:时域卷积-频域相乘Proof:,3.3DTFTtheorems,19,Discrete-TimeSignalsinFrequencyDomain,Modulation:时域相乘-频域卷积Parsevalstheorem3.4Energydensityspectrum,3.3DTFTtheorems,20,Discrete-TimeSignalsinFrequencyDomain,MATLABfunctions:freqz,abs,angle,real,imag,unwrapThefunctionfreqzcanbeusedtocomputethevaluesoftheDTFTofasequence,describedasarationalfunctionintheformofataprescribedsetofdiscretefrequencypoints,3.6DTFTcomputationusingMATLAB,21,Discrete-TimeSignalsinFrequencyDomain,Fig_3_4.m,Fig_3_8.m,3.6DTFTcomputationusingMATLAB,22,Discrete-TimeSignalsinFrequencyDomain,Fig_