现代数字信号处理及应用仿真题答案

1、仿真作业姓名：李亮学号：S1301010834.17程序clc;clear;for i=1:500sigma_v1=0.27;b(1)=-0.8458;b(2)=0.9458;a(1)=-(b(1)+b(2);a(2)=b(1)*b(2);datlen=500;rand('state',sum(100*clock);s=sqrt(sigma_v1)*randn(datlen,1);x=filter(1,1,a,s);%sigma_v2=0.1;u=x+sqrt(sigma_v2)*randn(datlen,1);d=filter(1,1,-b(1),s);%w0=1;0;w=w

2、0;M=length(w0);N=length(u);mu=0.005; for n=M:N ui=u(n:-1:n-M+1); y(n)=w'*ui; e(n)=d(n)-y(n); w=w+mu.*conj(e(n).*ui; w1(n)=w(1); w2(n)=w(2); ee(:,i)=mean(e.2,2);endendep=mean(ee');plot（ep）;xlabel('迭代次数');ylabel('MSE');title('学习曲线');plot(w1);hold;plot(w2);仿真结果： 步长0.015仿

3、真结果 步长0.025仿真结果步长0.005仿真结果4.18 程序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);for m = 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 = 0 0;num = 1;den = 1 a

4、1 a2;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for n =3 :data_len - 1 w1

5、( :, 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) - d

6、2(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);for m=1:trials;rm=xcorr(u(:,:,m),'biased'); R=rm(512),rm(513);rm(511),rm(512); p=rm(511);rm(510);wopt(:,m)=Rp; v,d=eig(R);Jmin(m)=

7、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

8、=mu2*sJmin*(sum_eig_100trials/(2-mu2*sum_eig_100trials);M1=Jexfin/sJminM2=Jexfin2/sJminfigure(1);plot(A/trials);hold on;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);hold on;plot(conj(w2)');xlabel('迭代次数');ylabel(

9、'权向量');title('步长为0.005权向量收敛曲线');figure(3);plot(EA/trials,'*');hold on;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');仿真结果失调参数 M1= 0.0545 M2= 0.00524.19程序clear all%产生观测信号和期望信号trials = 100; %随机试验的次数data_len = 1000;

10、 %样本数目n =1 : data_len;A1 = zeros(data_len, 2);EA1 = zeros(data_len, 1);for i = 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 = 0.01

11、5;M = 2;w = zeros(M,data_len);e = zeros(data_len,1);y = zeros(data_len,1);for m = 2: data_len-1 w(:, 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

12、('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);hold on;plot(conj(w)');xlabel('迭代次数');ylabel('权向量');title('权向量收敛曲线');仿真结果：5.1

13、0 (1)(2)(3) 特征值分解eig(R2)=diag0.4704,93.6270Eig(R3)=diag0.3148,0.9362,139.8951特征值扩展：X(R2)=199.0370X(R3)=444.4107（4）程序clear allclc;L=10000;sigma_v1=0.93627;A1 = zeros(L, 2);EA1 = zeros(L, 1);for i=1:100 v=sqrt(sigma_v1)*randn(L,1); a1=-0.99; u(1)=v(1); for k=2:L u(k)=-a1*u(k-1)+v(k); end % u=u(500:end

14、); M=2; w(1,:)=zeros(1,M); e(1)=u(1); mu=0.001; uu=zeros(1,M); w(2,:)=w(1,:)+mu*e(1)*uu; uu=u(1) uu(1:M-1); dd=(w(2,:)*uu')' e(2)=u(2)-dd; for k=3:L w(k,:)=w(k-1,:)+mu*e(k-1)*uu; uu=u(k-1) uu(1:M-1); dd=(w(k,:)*uu')' e(k)=u(k)-dd; end A1 = A1 + conj(w); EA1 = EA1 +(e.2)'endfigure

15、(1);plot(EA1/100);xlabel('迭代次数');ylabel('均方误差');title('迭代500次，步长0.001'); figure(2);plot(A1/100);hold on;plot(conj(w);xlabel('迭代次数');ylabel('权向量');title('权向量收敛曲线');5.11clear allclear;clc;for i=1:1500N=1000;M=5;L=2;h=0.389 1 0.389;sigma=1e-3; vn=sqrt(sig

16、ma)*randn(2*M+N,1); H=zeros(2*M+1,2*M+L+1); for k=1:2*M+1 H(k,k:1:k+L)=h; end s=randsrc(2*M+L+N,1); S=zeros(2*M+L+1,N); V=zeros(2*M+1,N); for k=1:N S(:,k)=s(2*M+L+k:-1:k); V(:,k)=vn(2*M+k:-1:k); end U=H*S+V; dn=S(M+L+1,:); if (i<=500) mu=0.01; elseif (i>500&&i<=1000) mu=0.025; else

17、mu=0.05; end a=size(U); M=a(1); N=a(2); err=zeros(N,1); w=zeros(M,N); w(M-1)/2+1,1)=1; err(1)=dn(1)-w(:,1)'*U(:,1); for k=1:N-1 w(:,k+1)=w(:,k)+mu*U(:,k)*conj(err(k); err(k+1)=dn(k+1)-w(:,k+1)'*U(:,k+1); end if (i<=500) ee1(:,i)=mean(abs(err).2,2); elseif (i>500&&i<=1000) ee2(:,i)=mean(abs(err).2,2); else ee3(:,i)=mean(abs