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1、实验一白噪声序列的产生1.实验目的:通过实验学会在计算机上比较经济地产生统计上理想的各种不同分布的白噪声序列。2.实验内容:(1)利用乘同余法产生(0,1)均匀分布的白噪声序列;(2)利用统计近似抽样法产生标准正态分布的白噪声序列。3.实验步骤:(1)熟悉白噪声序列及其产生的相关原理;(2)设计实验方案,编制实验程序;①乘同余法产生(0,1)均匀分布的白噪声序列先用如下递推同余式产生正整数序列{xi},xi≡A∙ximodM,i=1,2,···(式2.5.21),其中,M为2的方幂,即M=2k,k>2
2、的整数;且A不能太小,初值x0取正奇数;再令ξi≡xiM,i=1,2,···(式2.5.22),则序列{ξi}即为伪随机序列。②利用统计近似抽样法产生N(0,1)的随机数设{ξi}是(0,1)均匀分布的随机数序列,则有μξ=12,σξ2=112,根据中心极限定理,当N→∞时,x=i=1Nξi-NμξNσξ2=i=1Nξi-N2N/12~N(0,1),如果η~N(μη,ση2)是所要产生的正态分布随机变量,经标准化后η-μηση2~N(0,1),比较以上两式,可得出η=μη+σηi=1Nξi-N2N/1
3、2,其中ξi为(0,1)均匀分布的随机数,η为N(μη,ση2)正态分布的随机数。经试验当N=12时,η的统计性质比较理想,故可将上式简化为η=μη+ση(i=112ξi-6)(式2.5.45)故实验可针对式2.5.21、式2.5.22、式2.5.45进行编程。(3)上机调试,记录结果,分析结果。乘同余法中取A=179,M=235,x0=11;统计近似抽样法中μη=0,ση2=1。4.实验结果:100个U(0,1)均匀分布的随机数(利用乘同余法)0.05420.7180.35710.84350.710
4、60.51710.91360.9820.19730.55530.52590.77430.31150.39870.12840.60630.75860.36370.98710.53120.78330.10260.68930.0925190.21960.36470.390.55330.31160.28150.81380.03920.78380.38440.66380.02390.30650.81430.81720.28190.8580.75940.27860.46540.58520.93580.87050.
5、30420.74440.51160.81180.45840.25130.58070.31110.04830.98080.9520.69490.64230.57160.40290.38550.97150.31060.12160.99640.89070.60590.76750.36350.43840.46130.37550.06890.47060.5690.2220.33910.24090.85290.73390.70240.11620.67540.37660.72440.8020.89150.40420
6、.67470.55750.57660.35420.76320.78590.21630.39310.61370.6732统计性质比较(乘同余法,数据长度5000)均值方差均方差理论值0.50.083330.33333统计值0.49820.08290.2879乘同余法产生的服从(0,1)随机数的相关函数100个N(0,1)正态分布的随机数(利用统计近似抽样法)19-0.11970.19551.4351-1.38950.5705-0.01091.8899-0.88730.11110.05281.2875-1
7、.8210.89470.89470.44951.4565-1.9531.15480.45371.7135-1.58790.70690.21161.7229-1.22840.52940.87651.3971-0.88250.77110.88731.076-0.96521.02850.82780.6013-0.76351.09761.17730.6399-0.67121.46650.73960.5472-0.15121.50.38440.9432-0.05911.4914-0.19730.8360.422
8、60.9633-0.31590.63780.63731.43-0.53951.17021.08550.9662-0.5781.45721.31170.9499-0.4551.84610.79021.038-0.44821.4560.43820.7957-0.22861.62370.44040.43710.08521.64730.8280.23270.25331.86141.2193-0.33870.33311.19831.2527-0.62960.620