实验2.1 随机过程的模拟与特征估计.doc

实验2.1 随机过程的模拟与特征估计实验结果及分析：实验2.1 （1）估计x(n)=0.8*x(n-1)+1+4.*randn(N,1)随机序列的自相关函数和功率谱MATLAB仿真程序%估计x(n)=0.8*x(n-1)+1+4.*randn(N,1)随机序列的自相关函数和功率谱%x(n)=0.8*x(n-1)+1+4.*randn(N,1)随机序列的产生a=0.8;N=500;w=1+2.*randn(N,1);x(1)=w(1); for n=2:Nx(n)=a*x(n-1)+w(n); endsubplot(3,2,1);plot(x);title(随机序列x(n)=0.8*x(n-1)+1+4.*randn(N,1);grid on%估计自相关函数R=xcorr(x,coeff);subplot(3,2,2);axis(0 500 0 1);plot(R);title(自相关函数);grid on%估计功率谱%周期图功率谱估计subplot(3,2,3);periodogram(x,512,1000);axis(0 500 -50 0);title(周期图功率谱估计)%加汉宁窗window=hann(500);subplot(3,2,4);periodogram(x,window,512,1000);axis(0 500 -50 10);title(汉宁周期功率谱估计)%相关函数法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(0 500 -50 10);title(BT功率谱估计)grid onsubplot(3,2,6);pwelch(x,128,64,1000);axis(0 500 -50 10);title(韦尔奇功率谱估计);grid on；实验2.1 （2）x=sin(2*pi*0.05*n)+2*cos(2*pi*0.12*n)+randn(N,1)随机序列的自相关函数和功率谱N=256时的结果：N=1024时的结果：MATLAB仿真程序N=256:%估计x=sin(2*pi*0.05*n)+2*cos(2*pi*0.12*n)+randn(N,1)随机序列的自相关函数和功率谱%x=sin(2*pi*0.05*n)+2*cos(2*pi*0.12*n)+randn(N,1)随机序列的产生N=256; %N=256或1024w=randn(N,1); for n=1:N x(n)=sin(2*pi*0.05*n)+2*cos(2*pi*0.12*n)+w(n); endsubplot(3,2,1);plot(x);axis(0 260 -8 8);title(随机序列x(N)=sin(2*pi*0.05*n)+2*cos(2*pi*0.12*n)+randn(N,1)/N=256);grid on%估计自相关函数R=xcorr(x,coeff);subplot(3,2,2);plot(R);axis(0 500 -1 1);title(自相关函数/N=256);grid on%估计功率谱%周期图功率谱估计subplot(3,2,3);periodogram(x,512,1000);axis(0 500 -50 0);title(周期图功率谱估计/N=256)%加汉宁窗window=hann(256);subplot(3,2,4);periodogram(x,window,256,1000);axis(0 500 -50 10);title(汉宁周期功率谱估计)%相关函数法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(0 500 -50 10);title(BT功率谱估计/N=256)grid onsubplot(3,2,6);pwelch(x,128,64,1000);axis(0 500 -50 10);title(韦尔奇功率谱估计/N=256);grid on;N=1024:%估计x=sin(2*pi*0.05*n)+2*cos(2*pi*0.12*n)+randn(N,1)随机序列的自相关函数和功率谱%x=sin(2*pi*0.05*n)+2*cos(2*pi*0.12*n)+randn(N,1)随机序列的产生N=1024; %N=256或1024w=randn(N,1); for n=1:N x(n)=sin(2*pi*0.05*n)+2*cos(2*pi*0.12*n)+w(n); endsubplot(3,2,1);plot(x);axis(0 1030 -8 8);title(随机序列x(N)=sin(2*pi*0.05*n)+2*cos(2*pi*0.12*n)+randn(N,1)/N=1024);grid on%估计自相关函数R=xcorr(x,coeff);subplot(3,2,2);plot(R);axis(0 2000 -1 1);title(自相关函数/N=1024);grid on%估计功率谱%周期图功率谱估计subplot(3,2,3);periodogram(x,1024,1000);axis(0 500 -50 0);title(周期图功率谱估计/N=1024)%加汉宁窗window=hann(1024);subplot(3,2,4);periodogram(x,window,1024,1000);axis(0 500 -50 10);title(汉宁周期功率谱估计)%相关函数法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);a