基于RLS算法和LMS的自适应滤波器的MATLAB程序

% RLS算法

randn('seed', 0)

rand('seed', 0)

NoOfData = 8000 % Set no of data points used for training

Order = 32 % 自适应滤波权数

Lambda = 0.98 % 遗忘瞎友因子

Delta = 0.001 % 相关矩阵R的初始化

x = randn(NoOfData, 1) %高斯随机系列

h = rand(Order, 1) % 系统随机抽样

d = filter(h, 1, x) % 期望输出

% RLS算法的初始化

P = Delta * eye ( Order, Order ) %相关矩阵

w = zeros ( Order, 1 ) %滤波系数矢量的初始化

% RLS Adaptation

for n = Order : NoOfData

u = x(n:-1:n-Order+1) %延时函数

pi_ = u' * P %互相关函数

k = Lambda + pi_ * u

K = pi_'/k%增益矢量

e(n) = d(n) - w' * u %误差函数

w = w + K * e(n) %递归公式

PPrime = K * pi_

P = ( P - PPrime ) / Lambda %误差相关矩阵

w_err(n) = norm(h - w) %真实估计散哪误差

end

% 作图表示结果

figure

plot(20*log10(abs(e))) %| e |的误差曲线

title('学习曲线')

xlabel('迭代次数')

ylabel('输出误差估计')

figure

semilogy(w_err) %作实际估计误差图

title('矢量估计误差')

xlabel('迭代次数')

ylabel('误差权矢量')

%lms 算法

clear all

close all

hold off%系统信道权数

sysorder = 5 %抽头数

N=1000%总采样次数

inp = randn(N,1)%产生高斯随机系列

n = randn(N,1)

[b,a] = butter(2,0.25)

Gz = tf(b,a,-1)%逆变换函数

h= [0.09760.28730.33600.22100.0964]%信道特性向量

y = lsim(Gz,inp)%加入噪声

n = n * std(y)/(10*std(n))%噪声信号

d = y + n%期望输出信号

totallength=size(d,1)%步长

N=60 %60节点作为训练序列

%算法的开始

w = zeros ( sysorder , 1 ) %初始化

for n = sysorder : N

u = inp(n:-1:n-sysorder+1) % u的矩阵

y(n)= w' * u%系统输出

e(n) = d(n) - y(n) %误差

if n <20

mu=0.32

else

mu=0.15

end

w = w + mu * u * e(n) %迭代方程

end

%检验结果

for n = N+1 : totallength

u = inp(n:-1:n-sysorder+1)

y(n) = w' * u

e(n) = d(n) - y(n) %误差

end

hold on

plot(d)

plot(y,'r')

title('系统输出')

xlabel('样本')

ylabel('实际输出')

figure

semilogy((abs(e))) % e的绝对值坐标

title('误差曲线')

xlabel('样本')

ylabel('误差矢量')

figure%作图

plot(h, 'k+')

hold on

plot(w, 'r*')

legend('实际权矢量','估计权矢量')

title('比磨掘槐较实际和估计权矢量')

axis([0 6 0.05 0.35])

%lms算法源程序

clear all

close all

%channel system order

sysorder = 5

% Number of system points

N=2000

inp = randn(N,1)

n = randn(N,1)

[b,a] = butter(2,0.25)

Gz = tf(b,a,-1)

%This function is submitted to make inverse Z-transform (Matlab central file exchange)

%The first sysorder weight value

%h=ldiv(b,a,sysorder)'

% if you use ldiv this will give h :filter weights to be

h= [0.0976

0.2873

0.3360

0.2210

0.0964]

y = lsim(Gz,inp)

%add some noise

n = n * std(y)/(10*std(n))

d = y + n

totallength=size(d,1)

%Take 60 points for training

N=60

%begin of algorithm

w = zeros ( sysorder , 1 )

for n = sysorder : N

u = inp(n:-1:n-sysorder+1)

y(n)= w' * u

e(n) = d(n) - y(n)

% Start with big mu for speeding the convergence then slow down to reach the correct weights

if n <20

mu=0.32

else

mu=0.15

end

w = w + mu * u * e(n)

end

%check of results

for n = N+1 : totallength

u = inp(n:-1:n-sysorder+1)

y(n) = w' * u

e(n) = d(n) - y(n)

end

hold on

plot(d)

plot(y,'r')

title('System output')

xlabel('Samples')

ylabel('True and estimated output')

figure

semilogy((abs(e)))

title('Error curve')

xlabel('Samples')

ylabel('Error value')

figure

plot(h, 'k+')

hold on

plot(w, 'r*')

legend('Actual weights','Estimated weights')

title('Comparison of the actual weights and the estimated weights')

axis([0 6 0.05 0.35])

% RLS 算法

randn('seed', 0)

rand('seed', 0)

NoOfData = 8000 % Set no of data points used for training

Order = 32% Set the adaptive filter order

Lambda = 0.98% Set the forgetting factor

Delta = 0.001% R initialized to Delta*I

x = randn(NoOfData, 1) % Input assumed to be white

h = rand(Order, 1) % System picked randomly

d = filter(h, 1, x) % Generate output (desired signal)

% Initialize RLS

P = Delta * eye ( Order, Order )

w = zeros ( Order, 1 )

% RLS Adaptation

for n = Order : NoOfData

u = x(n:-1:n-Order+1)

pi_ = u' * P

k = Lambda + pi_ * u

K = pi_'/k

e(n) = d(n) - w' * u

w = w + K * e(n)

PPrime = K * pi_

P = ( P - PPrime ) / Lambda

w_err(n) = norm(h - w)

end

% Plot results

figure

plot(20*log10(abs(e)))

title('Learning Curve')

xlabel('Iteration Number')

ylabel('Output Estimation Error in dB')

figure

semilogy(w_err)

title('Weight Estimation Error')

xlabel('Iteration Number')

ylabel('Weight Error in dB')

a=image_mean

a=double(a)

[dep,wide]=size(a)

new_image=ones(size(a))

for i=3:dep-2

for j=3:wide-2

new_image(i,j)=median([a(i-2,j-2) a(i-2,j-1) a(i-2,j) a(i-2,j+1) a(i-2,j+2) a(i-1,j-2) a(i-1,j-1) a(i-1,j) a(i-1,j+1) a(i-1,j+2) a(i,j-2) a(i,j-1) a(i,j) a(i,j+1) a(i,j+2) a(i+1,j-2) a(i+1,j-1) a(i+1,j) a(i+1,j+1) a(i+1,j+2) a(i+2,j-2) a(i+2,j-1) a(i+2,j) a(i+2,j+1) a(i+2,j+2)])

end

end

for i=3:dep-2 %处理每一行的最头上两个和最边上凳稿哗2

new_image(i,1)=new_image(i,3)

new_image(i,2)=new_image(i,3)new_image(i,wide)=new_image(i,wide-2)

new_image(i,wide-1)=new_image(i,wide-2)

end

new_image(1,:)=new_image(3,:)%把第三行的所有元素赋值给第一行枣行

new_image(2,:)=new_image(3,:)

new_image(dep,:)=new_image(dep-2,:)%把倒数第二行的所有元素值赋给最后一行

new_image(dep-1,:)=new_image(dep-2,:)

figure

imshow(uint8(new_image))

第敬友一行是我接着我做的东西的上面来的，表示读入图片，你可以换成I=imread('F:\exam\Matlab\shibie\1.jpg')等，根据情况读入图片就行了。最后一行我是把它进行了强制转换，你也可以试试不转换看能不能显示。

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