现代数字信号处理（何子述）第四章matlab仿真习题

4-17仿真代码：function[EPP1]=lms2(mu)%产生系统输入白噪声v1(n)sigma_v1_2=0.27;%方差为0.27b(1)=-0.8458;b(2)=0.9458;a(1)=-(b(1)+b(2));a(2)=b(1)*b(2);datlen=500;%迭代次数为500，即样本数目为500P=zeros(2,datlen);E=zeros(1,datlen);fori=1:datlenrand('state',sum(100*clock));s=sqrt(sigma_v1_2)*randn(datlen,1);%产生系统输入白噪声x=filter(1,[1,a],s);%得到信号x(n)%-产生输入滤波器的未知信号u(n)和期望响应信号d(n)sigma_v2_2=0.1;u=x+sqrt(sigma_v2_2)*randn(datlen,1);d=filter(1,[1,-b(1)],s);%LMS迭代算法w0=[1;0];%初始化权向量w=w0;M=length(w0);%FIR滤波器抽头的个数N=length(u);%mu=0.015;P1=zeros(M,datlen);forn=M:Nui=u(n:-1:n-M+1);y(n)=w'*ui;e(n)=d(n)-y(n)';w=w+(mu).*conj(e(n)).*ui;P1(:,n)=w;endP=P+P1;E=E+e.^2;endend[E1P1P11]=lms2(0.015);[E2P2P12]=lms2(0.025);[E3P3P13]=lms2(0.05);g=500;figure(1);plot(conj(E1)'/g);holdon;plot(conj(E2)'/g);holdon;plot(conj(E3)'/g);xlabel('迭代次数');ylabel('MSE');title('学习曲线');figure(2);plot(conj(P1)'/g);holdon;plot(conj(P11)');xlabel('迭代次数');ylabel('权值');title('步长为0.015');figure(3);plot(conj(P2)'/g);holdon;plot(conj(P12)');xlabel('迭代次数');ylabel('权值');title('步长为0.025');figure(4);plot(conj(P3)'/g);holdon;plot(conj(P13)');xlabel('迭代次数');ylabel('权值');title('步长为0.05');仿真结果：得到的学习曲线如下：步长为0.015时权向量收敛曲线：步长为0.025时权向量收敛曲线：步长为0.05时权向量收敛曲线：4-18仿真代码：%（1）产生N=512点的样本序列data_len=512;%样本序列的长度trials=100;%随机试验的次数A=zeros(data_len,2);EA=zeros(data_len,1);B=zeros(data_len,2);EB=zeros(data_len,1);form=1:trialsa1=-0.975;a2=0.95;sigma_v_2=0.0731;v=sqrt(sigma_v_2)*randn(data_len,1,trials);%产生v(n)u0=[00];num=1;den=[1a1a2];Zi=filtic(num,den,u0);%滤波器的初始条件u=filter(num,den,v,Zi);%产生样本序列u(n)%（2）用LMS滤波器来估计w1和w2mu1=0.05;mu2=0.005;w1=zeros(2,data_len);w2=zeros(2,data_len);e1=zeros(data_len,1);e2=zeros(data_len,1);d1=zeros(data_len,1);d2=zeros(data_len,1);%LMS迭代过程forn=3:data_len-1w1(:,n+1)=w1(:,n)+mu1*u(n-1:-1:n-2,:,m)*conj(e1(n));w2(:,n+1)=w2(:,n)+mu2*u(n-1:-1:n-2,:,m)*conj(e2(n));d1(n+1)=w1(:,n+1)'*u(n:-1:n-1,:,m);d2(n+1)=w2(:,n+1)'*u(n:-1:n-1,:,m);e1(n+1)=u(n+1,:,m)-d1(n+1);e2(n+1)=u(n+1,:,m)-d2(n+1);endA=A+conj(w1)';EA=EA+e1.^2;B=B+conj(w2)';EB=EB+e2.^2;end%剩余均方误差和失调参数wopt=zeros(2,trials);Jmin=zeros(1,trials);sum_eig=zeros(trials,1);form=1:trials;rm=xcorr(u(:,:,m),'biased');R=[rm(512),rm(513);rm(511),rm(512)];p=[rm(511);rm(510)];wopt(:,m)=R\p;[v,d]=eig(R);Jmin(m)=rm(512)-p'*wopt(:,m);sum_eig(m)=d(1,1)+d(2,2);endsJmin=sum(Jmin)/trials;e1_100trials_ave=sum(e1)/trials;e2_100trials_ave=sum(e2)/trials;Jex1=e1_100trials_ave-sJmin;Jex2=e2_100trials_ave-sJmin;sum_eig_100trials=sum(sum_eig)/100;Jexfin=mu1*sJmin*(sum_eig_100trials/(2-mu1*sum_eig_100trials));Jexfin2=mu2*sJmin*(sum_eig_100trials/(2-mu2*sum_eig_100trials));M1=Jexfin/sJminM2=Jexfin2/sJminfigure(1);plot(A/trials);holdon;plot(conj(w1)');xlabel('迭代次数');ylabel('权向量');title('步长为0.05权向量收敛曲线');figure(2);plot(B/trials);holdon;plot(conj(w2)');xlabel('迭代次数');ylabel('权向量');title('步长为0.005权向量收敛曲线');figure(3);plot(EA/trials,'*');holdon;plot(EB/trials,'-');xlabel('迭代次数');ylabel('均方误差');title('步长分别为0.05和0.005学习曲线');仿真结果：剩余均方误差和失调参数结果分别为：M1=0.0502M2=0.00484-19仿真代码：clearall%产生观测信号和期望信号trials=100;%随机试验的次数data_len=1000;%样本数目n=1:data_len;A1=zeros(data_len,2);EA1=zeros(data_len,1);fori=1:trialssigma_v_2=0.5;phi=2*pi*rand(1,1);%随机相位signal=sin(pi/2*n'+phi);%信号s(n)u=signal+sqrt(sigma_v_2)*randn(data_len,1);%观测信号u(n)d=2*cos(pi/2*n'+phi);%期望响应信号d(n)%LMS迭代算法mu=0.015;M=2;w=zeros(M,data_len);e=zeros(data_len,1);y=zeros(data_len,1);form=2:data_len-1w(:,m+1)=w(:,m)+mu*u(m:-1:m-1)*conj(e(m));y(m+1)=w(:,m+1)'*u(m+1:-1:m);e(m+1)=d(m+1)-y(m+1);endA1=A1+conj(w)';EA1=EA1+e.^2;endfigure(1);plot(e);xlabel('迭代次数');ylabel('均方误差');title('单次实验学习曲线');figure(2);plot(EA1/trials);xlabel('迭代次数');ylabel('均方误差');title('100次独立试验学习曲线');figure(3);plot(A1/trials);holdon;plot(conj(w)');xlabel('迭代次数');ylabel('权向量');title('权向量收敛曲线');仿真结果：