ex3_1.m

PSD using BT/AR/ method,get the auto-correlation funtion

function ex3_1(uu,a1,a2,v_var,l1,l2)
N1=1000;N2=512;k=100;
sum=zeros(1,N2);
w0=zeros(1,2);
jn2=0;
for nn=1:k
v=zeros(1,N1);
v=sqrt(v_var)*randn(1,N1);
u1=zeros(1,N1);
for n=3:N1
      u1(n)=-a1*u1(n-1)-a2*u1(n-2)+v(n);
end
u=zeros(1,N2);
u=u1(N1-N2+1:N1);% select the stable data
w1=zeros(1,N2);
w2=zeros(1,N2);
e=zeros(1,N2);
e(1)=u(1);
e(2)=u(2);
w1(3)=uu*u(1)*u(2);
for m=3:N2
e(m)=u(m)-conj(w1(m))*u(m-1)-conj(w2(m))*u(m-2);
w1(m+1)=w1(m)+uu*conj(e(m))*u(m-1);
w2(m+1)=w2(m)+uu*conj(e(m))*u(m-2);
end
sum=sum+abs(e).^2;
jn2=jn2+abs(e(N2))^2;
w0=w0+[w1(N2),w2(N2)];
end
sum=sum./k;
w0=w0./k
jn2=jn2/k;
ex_jn2=jn2-v_var
M=uu*(l1+l2)/(2-uu*(l1+l2))
ex_jinfi=M*v_var
est_M=ex_jn2/v_var
x=1:N2;
plot(x,sum);
grid on;
title('learning curve');
xlabel('n');
ylabel('估计均方误差');
end