说明介绍噪声.pptx

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说明介绍噪声.pptx

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NoiseEE202DepartmentofElectronicsandElectricalEngineeringXi’anJiaotong–LiverpoolUniversity

GaussianRandomProcessGaussian(normal)randomprocess:Ataparticulartimet,thesignalamplitudeisGaussiandistributed.AGaussianprocesscanbecompletelyspecifiedbythemeanandautocorrelation.

GaussianDistributionTheR.V.XiscalledGaussian(normal)ifitspdfis: ?--meanofX, --varianceofX.AGaussiandistributioniscompletelyspecifiedbyitsmeanandvariance.WewriteaGaussianR.V.Xas:GaussianDistributionisveryimportantincommunications.x=?fX(x)x

GaussianDistribution:Q-functionWedefineausefulQ-functionas If ,then (Practice:BuildQ-functioninMATLABusingapredefinedfunctionerfc)PropertiesofQ-function:Q(-x)=1-Q(x)(Proof:yourhomework)Q(0)=0.5Whenx1,

AWGNThePSDisflat Thenoisebandwidthisinfinite.ThisimpliesthattheautocorrelationisFormostapplications T=temperatureoftheresistorinKelvin(290K) K=Boltzmann’sconstant1.38x10-23joule/KfN0/20SX(f)tN0/20RX(?)

ApplicationtoNoiseNoiseisacriticalcomponentintheanalysisoftheperformanceofcommunicationsystems.GenerallynoisecanbemodeledasazeromeanGaussianWSSrandomprocess.Ifthenoiseiswhite,thenallfrequencycomponentsappearwithequalpower(whiteisusedinwhitelightforasimilarreason)WeusuallyconsideradditivewhiteGaussiannoise(AWGN)incommunications.

BandlimitedWhiteNoiseInbasebandcommunication,wepassouringsignalsthroughalow-passfilter.Theresultantnoiseissaidtobebandlimited:ThepowerofthebandlimitednoiseisN0B.N0/20SX(f)FilterBandwidthBHzWhitenoiseBandlimitedWhitenoiseN0/20SX(f)B-B

Example1.2Therootmeansquare(rms)voltagemeasuredattheoutputofanamplifierduetointernalnoiseis100?V.Ifweassumethatthefrequencyspectrumofthenoiseisflatfrom0to10MHzandzeroabove10MHz,find:(a)Thespectraldensityfunctionforthenoise;(b)Theautocorrelat