main2.m

A simple code for understanding lms nlms and wiener filters for beginners

clear all
u = rand(1000,1);
W = [1 2 3]'
d = filter(flipud(W),1,u);
[row,col]=size(u);
r = xcorr(u,2);                         %  Calculate (k)th autocorrelation and accumulate
p = xcorr(d,u,2);                       %  Calculate (k)th cross correlation and accumulate

R = toeplitz(r(2+1:2*(2+1)-1))/(row*col)   %  (L x L) input autocorrelation matrix
p = p(2+1:2*(2+1)-1)/(row*col)  

N=length(u);

winit=[0;0];
mu=0.05;
wo=inv(R)*p;
Jmin=mean(d.^2)-W'*p
w1=[wo(1):1:(wo(1)+2)];
w2=[wo(2):1:(wo(2)+2)];

Jm = jmat(w1,w2,R,p,Jmin);
[w,J]=sd(mu,winit,N,R,p,Jmin);

[MSE,wm]=lms(mu,5,u,d);

figure(2)
contour(w1,w2,Jm',50);xlabel('w1');ylabel('w2');
hold on
plot(w(1,:),w(2,:),'-O');grid
plot(wm(1,:),wm(2,:),'-x');grid
hold off

figure(3)
plot(J);grid on;xlabel('No. of Itterations');ylabel('MSE');title('Steepest Descent');
figure(4)
plot(MSE);grid on;xlabel('No. of Itterations');ylabel('MSE');title('LMS');