现代数字信号处理及应用仿真题答案

仿真作业

姓名：李亮

学号：S130101083

4.17程序

clc;

clear;

for i=1:500

sigma_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=w0;

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);

end

end

ep=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仿真结果

0.10.20.30.4

0.50.60.7迭代次数

M S E

学习曲线

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: trials

a1 = -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 a1 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w2

mu1 = 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( :, 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);

end

A = 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)=R\p;

[v,d]=eig(R);

Jmin(m)=rm(512)-p'*wopt(:,m);

sum_eig(m)=d(1,1)+d(2,2);

end

sJmin=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/sJmin

M2=Jexfin2/sJmin

figure(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('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= 0.0052

4.19

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; %样本数目

n =1 : data_len;

A1 = zeros(data_len, 2);

EA1 = zeros(data_len, 1);

for i = 1: trials

sigma_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);

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);

end

A1 = A1 + conj(w)';

EA1 = EA1 +e.^2;

end

figure(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);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：

5.10

(1)

247.04846.5783 46.578347.0487

R

??=????

(2)

347.048746.578346.1125 46.578347.048746.5783 46.112546.578647.0487

R

??

??=??

????

(3) 特征值分解

eig(R2)=diag{0.4704,93.6270}

Eig(R3)=diag{0.3148,0.9362,139.8951}

特征值扩展：

X(R2)=199.0370

X(R3)=444.4107

（4）程序

clear all

clc;

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);

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)';

end

figure(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');

5.11

clear all

clear;

clc;

for i=1:1500

N=1000;

M=5;

L=2;

h=[0.389 1 0.389];

sigma=1e-3;

vn=sqrt(sigma)*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

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(err).^2,2);

end

end

ep1=mean(ee1');

ep2=mean(ee2');

ep3=mean(ee3');

figure(1);

plot(ep1);

hold on;

plot(ep2);

hold on;

plot(ep3)

xlabel('μü′ú′?êy');ylabel('?ù·??ó2?');