高斯噪声和白噪声.ppt

&WhiteNoise引言:噪声分析的两类方法:Thetwokindsofmethodsfornoiseanalysis随机噪声:服从统计规律,用随机函数描述Randomnoises:obeystatisticallaw,describedwithrandomfunctions单(多)脉冲噪声:瞬态分析法Single(multiplex)pulsenoises:instantaneousanalysis、高斯噪声(依噪声幅度分布特性判定)GaussianNoise:ordingtothemagnitudedistributionfeature定义:,whosemagnitudeobeysGaussianDistributionaredefinedastheGaussianNoises2、中心极限定理(李雅普诺夫定理):大量N个统计独立的、具有有限的数学期望和方差的随机变量之和z=∑x的分布律在N→∞的极限情况下趋于高斯分布律。Thecentrallimittheorem(LiapunovTheorem)Thedistributionofthesumz-2xofagreatnumbernofstatisticindependentrandomvariables,withlimitmathematicalexpectationsandvarianceswillapproachtotheGaussiandistributionundertheconditionofthatA→>∞3、高斯分布律:TheGaussianDistributionLaw(1)一维概率密度函数:The1-Dprobabilitydensityfunction是由均值m和均方差a2唯一确定的函数。The1-DPDFisuniquelydeterminedbymeanvaluemvariance<1>概率密度:Theprobabilitydensityfunctionx一2()2>分布函数:Thedistributionfunction()F(x)=P(X<x)-2-∞<3>当m=0时,whenthemiszero,thePDFisPCA)()4>高斯变量X的n阶中心矩与n阶原点矩Then-ordercentermoment&n-orderoriginmomentofGaussianvariables中心矩:Thecentermoment(-1)2丌-∞原点矩:Theoriginmoment2x0-∞ON为奇数(-2)N为偶数(2)高斯分布的N维联合概率密度TheN-DjointprobabilitydensityfunctionoftheGaussianDistribution∑∑M4(x,-≤x>)(x-≤x>)(1267)(2x)2MwhereMisthematrixofthejoint2ordercentermoment(联合二阶中心矩)oftheRv,1isitsdeterminant(行列式,Misthesurplusfactor(余因子)oftheelementlik4k=kx=<(x2-<x2>)(xk<xk>)>()whenthex,sareincorrelateeachother,wehavea-oandMl-,Eq()willchangeintofollowingformexp(2丌)21IoP(x1)p(x2)….D(x)():TheNGaussianvariableswillbestatisticaleachother,iftheyareuncorrelatedeachother物理含义:如果N个高斯随机变量之间是互不相关的,则它们之间也是统计独立的。4、满足高斯分布的充分条件:ThesufficientnecessaryconditionforRVtoobeyGaussiandistribution(1)客观背景:Theobjectivebackground事实上,噪声函数的瞬时值可视为大量的相互独立的被加项之和,且任意一个被加项与其它被加项相比,在方差或功率上都相差无几。Infact,anoisefunctioncanberegardedasthesumofgreatnumberofstatisticallyindependentsummands(被加数),paredwiththeothers(2)满足高斯分布的条件Theconditionshouldbefulfilledfort