%% Algoritmo funcional LMS
close all; clear all
fs=8000;
T=1/fs;  
t=0:T:0.1;
x=randn(1,length(t));
n=filter([ 0 0 0 0 0 0 0 0 0 0.8 ],1,x);
o=sin(2*pi*300*t);
d=sin(2*pi*300*t)+n;% generate signal plus noise
mu=0.001;
N=16;
w=zeros(1,N);
y=zeros(1,length(t));
e=y;

% adaptive filtering using LMS algorithm
for m=N+1:1:length(t)-1
    sum=0;
    for i=1:1:N
        sum=sum+w(i)*x(m-i);
    end
    y(m)=sum;
    e(m)=d(m)-y(m);
    for i=1:1:N
        w(i)=w(i)+2*mu*e(m)*x(m-i);
        W(:,m)=w';
    end
end
D=2*abs(fft(d))/length(d);D(1)=D(1)/2;
O=2*abs(fft(o))/length(o);O(1)=O(1)/2;
f=[0:1:length(d)/2]*8000/length(d);
E=2*abs(fft(e))/length(e);
E(1)=E(1)/2;

subplot(4,1,1),plot(o,'k');grid; ylabel('Original signal')
subplot(4,1,2),plot(d,'k');grid; ylabel('Corrupt. signal')
subplot(4,1,3),plot(x,'k');grid;ylabel('Ref. noise');
subplot(4,1,4),plot(e,'k');grid; ylabel('Clean signal');
xlabel('Number of samples');
figure
subplot(3,1,1),plot(f,O(1:length(f)),'k');grid; 
ylabel('Original. spectrum')
subplot(3,1,2),plot(f,D(1:length(f)),'k');grid; 
ylabel('Corrupt. spectrum')
subplot(3,1,3),plot(f,E(1:length(f)),'k');grid
ylabel('Enhanced spectrum'); xlabel('Frequency (Hz)');

figure(3)
plot(W')