實(shí)驗(yàn)2.1 隨機(jī)過程的模擬與特征估計(jì)

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1、實(shí)驗(yàn)2.1隨機(jī)過程的模擬與特征估計(jì)實(shí)驗(yàn)結(jié)果及分析：實(shí)驗(yàn)2.1（1）估計(jì)x(n)=0.8*x(n-1)+1+4.*randn(N,1)隨機(jī)序列的自相關(guān)函數(shù)和功率譜MATLAB仿真程序%估計(jì)x(n)=0.8*x(n-1)+1+4.*randn(N,1)隨機(jī)序列的自相關(guān)函數(shù)和功率譜%x(n)=0.8*x(n-1)+1+4.*randn(N,1)隨機(jī)序列的產(chǎn)生a=0.8;N=500;w=1+2.*randn(N,1);x(1)=w(1);forn=2:Nx(n)=a*x(n-1)+w(n);endsubplot(3,2,1);plot(x);title('隨機(jī)序列x(n)=0.8*x(n-

2、1)+1+4.*randn(N,1)');gridon%估計(jì)自相關(guān)函數(shù)R=xcorr(x,'coeff');subplot(3,2,2);axis([050001]);plot(R);title('自相關(guān)函數(shù)');gridon%估計(jì)功率譜%周期圖功率譜估計(jì)subplot(3,2,3);periodogram(x,[],512,1000);axis([0500-500]);title('周期圖功率譜估計(jì)')%加漢寧窗window=hann(500);subplot(3,2,4);periodogram(x,window,512,1000);axis([0500-5010]);titl

3、e('漢寧周期功率譜估計(jì)')%相關(guān)函數(shù)法R=xcorr(x)/15000;Pw=fft(R);subplot(3,2,5);f=(0:length(Pw)-1)*1000/length(Pw);plot(f,10*log10(abs(Pw)));axis([0500-5010]);title('BT功率譜估計(jì)')gridonsubplot(3,2,6);pwelch(x,128,64,[],1000);axis([0500-5010]);title('韋爾奇功率譜估計(jì)');gridon；實(shí)驗(yàn)2.1（2）x=sin(2*pi*0.05*n)+2*cos(2*pi*0.12*n)+ra

4、ndn(N,1)隨機(jī)序列的自相關(guān)函數(shù)和功率譜N=256時(shí)的結(jié)果：N=1024時(shí)的結(jié)果：MATLAB仿真程序N=256:%估計(jì)x=sin(2*pi*0.05*n)+2*cos(2*pi*0.12*n)+randn(N,1)隨機(jī)序列的自相關(guān)函數(shù)和功率譜%x=sin(2*pi*0.05*n)+2*cos(2*pi*0.12*n)+randn(N,1)隨機(jī)序列的產(chǎn)生N=256;%N=256或1024w=randn(N,1);forn=1:Nx(n)=sin(2*pi*0.05*n)+2*cos(2*pi*0.12*n)+w(n);endsubplot(3,2,1);plot(x);axis

5、([0260-88]);title('隨機(jī)序列x(N)=sin(2*pi*0.05*n)+2*cos(2*pi*0.12*n)+randn(N,1)/N=256');gridon%估計(jì)自相關(guān)函數(shù)R=xcorr(x,'coeff');subplot(3,2,2);plot(R);axis([0500-11]);title('自相關(guān)函數(shù)/N=256');gridon%估計(jì)功率譜%周期圖功率譜估計(jì)subplot(3,2,3);periodogram(x,[],512,1000);axis([0500-500]);title('周期圖功率譜估計(jì)/N=256')%加漢寧窗window=han

6、n(256);subplot(3,2,4);periodogram(x,window,256,1000);axis([0500-5010]);title('漢寧周期功率譜估計(jì)')%相關(guān)函數(shù)法R=xcorr(x)/15000;Pw=fft(R);subplot(3,2,5);f=(0:length(Pw)-1)*1000/length(Pw);plot(f,10*log10(abs(Pw)));axis([0500-5010]);title('BT功率譜估計(jì)/N=256')gridonsubplot(3,2,6);pwelch(x,128,64,[],1000);axis([0500

7、-5010]);title('韋爾奇功率譜估計(jì)/N=256');gridon;N=1024:%估計(jì)x=sin(2*pi*0.05*n)+2*cos(2*pi*0.12*n)+randn(N,1)隨機(jī)序列的自相關(guān)函數(shù)和功率譜%x=sin(2*pi*0.05*n)+2*cos(2*pi*0.12*n)+randn(N,1)隨機(jī)序列的產(chǎn)生N=1024;%N=256或1024w=randn(N,1);forn=1:Nx(n)=sin(2*pi*0.05*n)+2*cos(2*