通信原理chapter 2

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1、StateKeyLab.onISN,XidianUniversityYongchaoWangPrinciplesofCommunicationsChapterII:SignalsYongchaoWangEmail:ychwang@mail.xidian.edu.cnXidianUniversityStateKeyLab.onISNOctober25,20111/16StateKeyLab.onISN,XidianUniversityYongchaoWangOutlineClassificationofSignal

2、sCharacteristicsofDeterministicSignalsRandomProcessSignalTransferthroughLinearSystemsBriefSummaryandHomework2/16StateKeyLab.onISN,XidianUniversityYongchaoWangClassificationofSignalss(t)DeterministicSignalsandRandomSignals•Deterministicsignals:thevaluesatanyti

3、mearedeterministicandpredictable.s(t)=sinωt.•Randomsignals:thevaluesatanytimearerandom.s(t)=sinωt+ϕ,ϕ∈U(0,2π).EnergySignalsandPowerSignalsRZT/2212Energy:E=s(t)dt;Power:P=lims(t)dt.T→∞T−T/2•Energysignals:energyisequaltoafinitepositivevalue,butaveragepoweris0.•

4、Powersignals:averagepowerisequaltoafinitepositivevalue,butenergyisinfinite.Question:Howaboutcommunicationsignals?3/16StateKeyLab.onISN,XidianUniversityYongchaoWangFrequencyDomainCharacteristicsFrequencySpectrum•s(t)FourierR+∞−j2πft−−−−−→S(jf)=s(t)edt.−∞Energy/

5、PowerSpectralDensityAccordingtotheParserval’stheorem,theenergyoffrequencydomainsignalsisequaltoitscorrespondingtemporalversion,i.e.,Z∞Z∞E=s2(t)dt=

6、S(f)

7、2df.−∞−∞•Energysignals:E(f)=

8、S(f)

9、2.12•Powersignals:P(f)=lim

10、ST(f)

11、.T→∞T4/16StateKeyLab.onISN,XidianUniver

12、sityYongchaoWangCharacteristicsinTimeDomainAutocorrelationFunctionR∞•Energysignal:R(τ)=s(t)s(t+τ)dt,−∞<τ∞.−∞•Powersignal:Z1T/2R(τ)=lims(t)s(t+τ)dt,−∞<τ∞.T→∞T−T/2CrosscorrelationFunctionR∞•Energysignal:R12(τ)=−∞s1(t)s2(t+τ)dt,−∞<τ∞.•Powersignal:ZT/21R12(τ)=li

13、ms1(t)s2(t+τ)dt,−∞<τ∞.T→∞T−T/2Auto-/cross-correlationfunctionsareevenfunction,i.e.,R(τ)=R(−τ)andR12(τ)=R21(−τ).5/16StateKeyLab.onISN,XidianUniversityYongchaoWangCharacteristicsofRandomSignalsRandomvariable.1-dim•Distributionfunction:F(x)=P(X≤x).dF(x)•Probabi

14、litydensityfunction:f(x)=.dx•Frequentlyusedrandomvariables(1/(b1−b2),b1≤x≤b2,•Uniformvariable:f(x)=0,else•Normal(Gaussian)variable:1(x−a)2f(x)=√exp[−],2πσ2σ2whereaisthemathematicalexpectationand