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2018-11-18 回答

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') ;