rls.m

该算法是基于rls自适应滤波的算法

clear all 
close all 
clc
% RLS 算法 

Fs = 600 ; % Set no of data points used for training 
N = 4 ; % Set the adaptive filter order 

Lambda = 0.998 ; % Set the forgetting factor 
Delta = 0.0001 ; % R initialized to Delta*I 

f1=10;
f2=50;
det=1/Fs;
t=0:det:1-det;
d=2*cos(2*pi*f1*t);
snr=20;
s_power=var(d);             %var函数: 返回方差值
linear_snr=10^(snr/10);
factor=sqrt(s_power/linear_snr);
%noise=randn(1,length(d))*factor+sin(2*pi*f2*t);
%noise=randn(1,length(d))*factor;
noise=randn(1,length(d))*factor;
x=d+noise;
x=x';

M=Fs;
% Initialize RLS 
P = 1/Delta * eye ( N, N ) ; 
w = zeros ( N,1 ) ; 

y1=zeros(M,N);
% RLS Adaptation 
%引入遗忘因子Lambda<1
for n = N : M ; 
u = x(n:-1:n-N+1) ;%延时函数
K=P*u/(Lambda+u'*P*u);
y(n)=w'*u;
e(n) = d(n) - w' * u ;%误差函数
w = w + K * e(n) ;%递归公式
P=(P-K*u'*P)/Lambda;
%w_err(n) = norm(h - w) ;%真实估计误差
end ;

figure(1);
subplot(3,1,1)
plot(x);xlabel('Hz')
title('原始信号')

subplot(3,1,2)
plot(y)
title('经未知系统后信号');xlabel('Hz')

subplot(3,1,3)
plot(20*log10(abs(e)))
axis([0 Fs/2 -150 5]);
title('经自适应FIR滤波器后信号');xlabel('Hz')