实验题目 实验二 随机信号通过线性系统仿真和窄带随机信号仿真
    一、实验目的：
    1. 讨论随机信号通过线性系统之后的自相关函数和功率谱密度。
    2. 窄带随机信号的产生与窄带高斯信号包络和相位的概率分布。
    熟悉常用的信号处理仿真平台：MATLAB
    二、实验内容：
    image.png
    h = fir1(71,[0.25 0.55]);
    [h1,w1]=freqz(h,1,512) ;subplot(211);
    plot(w1/pi,20log10(abs(h1))); grid on;
    axis([0,1,-100,0]);
    subplot(212);
    plot(w1/pi,unwrap(angle(h1))    180*pi);
    grid on;
    image.png
    N=500;xt=random(‘norm’,0,1,1,N);
    ht=fir1(101,[0.2,0.6]);
    HW=fft(ht,2N);
    Rxx=xcorr(xt,’biased’);
    Sxx= abs(fft(xt,2    N).^2)/(2N);
    HW2=abs(HW).^2;
    Syy=Sxx.    HW2;
    Ryy=fftshift(ifft(Syy));
    w=(1:N)/N;
    t=(-N:N-1)/N*(N/20000);
    subplot(4,1,1);plot(w,abs(Sxx(1:N)));
    title(“输入信号功率谱密度”)
    subplot(4,1 ,2);plot(w,abs(HW2(1:N)));
    title(“功率传递函数”)
    subplot(4,1,3);plot(w,abs(Syy(1:N)));
    title(“功率谱密度”)
    subplot(4,1, 4);plot(t,Ryy);
    title(“自相关函数”)
    image.png


    N=10000;
    f0=10000;
    deltf=500;
    fs=22000;
    M=200;
    X=Narrowbandsignal(N,f0,deltf,fs,M);
    [Ac,As]= Lowfsignal( X,f0,fs);
    plot(X)
    f0= 10000;
    deltf=500;
    fs=22000;
    M=200;
    X=Narrowbandsignal(N,f0,deltf,fs,M);
    [Ac,As]= Lowfsignal( X,f0,fs);
    plot(Ac)
    figure(2)
    plot(As)
    N=10000;
    f0= 10000;
    deltf=500;
    fs=22000;
    M=200;
    X=Narrowbandsignal(N,f0,deltf,fs,M);
    [Ac,As]= Lowfsignal( X,f0,fs);
    Rx=xcorr(X,’biased’);
    Rac=xcorr(Ac,’biased’);
    Ras=xcorr(As,’biased’);
    Racw=abs(fft(Rac));
    Rasw=abs(fft(Ras));
    Rxw=abs(fft(Rx));
    N1=2N-1;
    f=fs/N1:fs/N1:fs/2;
    subplot(3,1,1)
    plot(f,10    log10(Rxw(1:(N1-1)/2)+eps));
    subplot(3,1,2);
    plot(f,10log10(Racw(1:(N1-1)/2)+eps));
    subplot(3,1,3);
    plot(f,10    log10(Rasw(1:(N1-1)/2)+eps));
    image.png



    N=20000;
    f0=10000;
    deltf=500;
    fs=22000;
    M=50;
    X=Narrowbandsignal(N,f0,deltf,fs,M);
    X=X/sqrt(var(X));
    [At,Ph,A2]=EnvelopPhase(X,f0,fs);
    LA=0:0.05:4.5;
    histogram(At,LA);
    LP=-pi/2:0.05:pi/2;
    figure;
    histogram(Ph,LP);
    LA2=0:0.2:16;
    figure;
    histogram(A2,LA2);

    image.png
    N=10000;
    f0=10000;
    deltf=400;
    fs=22000;
    M=50;
    b1=2;
    b2=4;
    b3=8;
    sit1=pi/6;
    sit2=pi/4;
    sit3=pi/3;
    X=Narrowbandsignal(N,f0,deltf,fs,M);
    X=X/sqrt(var(X));
    t=0:1/fs:((N-1)/fs);
    X1= X+b1cos(2pif0t+sit1);
    X2=X+b2cos(2pif0t+sit2);
    X3=X+b3cos(2pif0t+sit3);
    [At1 Ph1 A21]=EnvelopPhase(X1,f0,fs);
    [At2 Ph2 A22]=EnvelopPhase(X2,f0,fs);
    [At3 Ph3 A23]=EnvelopPhase(X3,f0,fs);
    LA=0:0.4:12;
    GA1=hist(At1,LA);
    GA2=hist(At2,LA);
    GA3=hist(At3,LA);
    plot(LA,GA1,’-‘,LA,GA2,’-‘,LA,GA3,’-‘);
    figure;LP=-pi/2:0.05:pi/2;
    GP1=hist((Ph1-sit1),LP);
    GP2=hist((Ph2-sit2),LP);
    GP3=hist((Ph3-sit3),LP);
    plot(LP,GP1,’-‘,LP,GP2,’-‘,LP,GP3,’-‘);
    figure
    LA2=0:1:120;
    GA21=hist(A21,LA2);
    GA22=hist(A22,LA2);
    GA23=hist(A23,LA2);
    plot(LA2,GA21,’—‘,
    LA2,GA22,’-‘,LA2,GA23,’-‘);


    使用到的函数

    function X=Narrowbandsignal(N,f0,deltf,fs,M)
    N1=N-M;xt=random(‘norm’,0,1,[1,N1]);
    f1=f02/fs;
    df1=deltf/fs;
    ht=fir1(M,[f1-df1 f1+df1]);

    X=conv(xt,ht);
    return


    function [Ac,As]= Lowfsignal(X,f0,fs)
    HX=imag(hilbert(X));
    [M,N]=size(X);
    t=0:1/fs:((N-1)/fs);
    Ac=X.    cos(2pif0t)
    +HX.    sin(2pif0t);
    As=HX.    cos(2pif0t)
    -X.    sin(2pif0t);
    return



    function [At,Ph,A2]=EnvelopPhase(X,f0,fs)
    HX=imag(hilbert(X));
    [M,N]=size(X);
    for i=1:1:M
    t(i,:)=(0:N-1)/fs;
    end
    Ac=X.    cos(2pif0t)
    +HX.    sin(1pif0t);
    As=HX.    cos(2pif0t)
    -X.    sin(2pif0*t);
    At=(Ac.^2+As.^2).^0.5;
    Ph=atan(As./Ac);
    A2=At.^2;
    return
    三、实验总结：
    利用matlab讨论随机信号通过线性系统之后的自相关函数和功率谱密度，窄带随机信号的产
    生与窄带高斯信号包络和相位的概率分布，加深了对这部分内容的了解，深入了解了怎么分析一个信号的功率及其其他性质，为以后分析信号工程奠定了坚实基础。