数字信号处理课程资料

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1、PrinciplesofCommunicationsI(Fall,2002)Signal&LinearSystemAnalysisSignal&LinearSystemAnalysisµSignalModelandClassificationsòDeterministicvs.RandomDeterministicsignals:completelyspecifiedfunctionoftime.Predictable,nouncertaintye.g.x(t)=Acosω0t,−∞

2、antsRandomsignals(stochasticsignals):takeonrandomvaluesatanygiventimeinstantandcharacterizedbypdf(probabilitydensityfunction)“Notcompletelypredictable”,“withuncertainty”e.g.x(n)=dicevalueshownwhentossedattimeindexnModel:A(large,maybe∞)setofwaveformseachassociatedwitha

3、prob-abilitymeasuree.g.pdfcharacterizingtheout-of-bandradionoiseNCTUEE1PrinciplesofCommunicationsI(Fall,2002)Signal&LinearSystemAnalysisòPeriodicvs.AperiodicPeriodicsignal:Asignalx(t)isperiodiciff∃aconstantT0,suchthatx(t+T0)=x(t),∀tThesmallestsuchT0iscalled“fundamenta

4、lperiod”or“simplyperiod”.Aperiodicsignal:cannotfindafiniteT0suchthatx(t+T0)=x(t),∀tòPhasorsignal&SpectraAspecialperiodicfunction~x(t)=Aej(ω0t+θ)=Aejθ⋅ejω0t~jθx(t)≡rotatingphasor;Ae≡phasor;A,θ≡realnumbersWhythiscomplexsignal?1.Keypartofmodulationtheory2.Constructionsig

5、nalforalmostanysignal3.Easymathematicalanalysisforsignal4.PhasecarriestimedelayinformationMoreonPhasorSignal:1.InformationiscontainedinAandθ(givenafixedf0(orω0)).2.Therelatedrealsinusoidalfunction:~1~1~x(t)=Acos(ω0t+θ)=Re{x(t)}orx(t)=Acos(ω0t+θ)=x(t)+x*(t)223.Invector

6、formgraphically:NCTUEE2PrinciplesofCommunicationsI(Fall,2002)Signal&LinearSystemAnalysis4.Frequency-domainrepresentationSingle-sided(SS)amp.&phasorvs.double-sided(DS):Linespectra:E.g.findSSandDSspectraofx(t)=Asin(ω0t+θ)Ans:putintocosineformfirstòSingularityFunctions:o

7、pposedtoregularfunctionsUnitimpulsefunctionδ(t):1.Definedby∞0+0+0+∫−∞x(t)δ(t)dt=∫0x(t)δ(t)dt=x(0)∫0δ(t)dt=x(0);∫0δ(t)dt=1−−−2.Itdefinesaprecisesamplepointofx(t)attimet(ort0ifδ(t−t0))∞x(t)=x(t)δ(t−t)dt0∫0−∞3.Basicfunctionforlinearlyconstructingatimesignal∞x(t)=∫x(τ)δ(t

8、−τ)dτ−∞4.Properties:(Z&T,pp.25-26(don’tbotherproperties5and6))1δ(at)=δ(t);δ(t)=δ(−t):evenfunction

9、a

10、NCTUEE3PrinciplesofCommu