LMS_code.m

clear,clc,close all;
%%
b =[1 -0.99];
a =(1);
e=zeros(10000,1);
mu=[0.01 0.05 0.1];
w = zeros(10000,1);
figure
 for k = 1:3
	for i2=1:100
		v = sqrt(0.02)*randn(12000,1);
		v = v(1001:end);
		u = filter(a,b,v);
		u = u(1001:end);
		for i=1:9999
			e(i)=u(i+1)-w(i).*u(i);
			w(i+1)=w(i)+mu(k).*u(i).*e(i);
		end
		opt_wieght(k,:)= w;
		e_total(:,i2)=e.^2;
		W_total(:,i2)=w;
	end
	av(k,:) = mean(transpose(W_total));    
	av2 =mean(transpose(e_total));

	i=(1:600);
	plot(i,av2(1:600),'LineWidth', 1.5);
	hold on
 end
 legend("Mu=0.01", "Mu=0.05" ,"Mu=0.1");
 hold off;
 figure(2)
 plot(-1.*av(1,1:1000),'k','LineWidth', 1.5)
 hold on
 plot(-1.*opt_wieght(1,1:1000),'b--','LineWidth', 1.5)
 legend("ensample-averaged over 100 runs", "single realization" );