% mademo.m
% fitting a time series into a ma model using spectral factorization
% S(z) = B(z)B(1/z*) = R(0) + sum_k=1  R(k)(z^k + z^-k)
% 1. Estimate R(k) from time series, then 
% 2. find the roots of S(z) that should be z and 1/z* pairs
% 3. assume B(z) has all zeros within unit circle, find zeros of B(z)
% 4. form B(z) from its roots
%

clear all
b=[1 0.5]
M=length(b);
L=1000;
u=randn(L,1);  u=u-mean(u); % input, zero mean
y=filter(b,1,u);  y=y(M-1:L);     %
rlen=min(L, 10*M);
ry=autocorr(y,rlen);
figure(1),clf,stem([0:rlen-1],ry),
title('autocorrelation lags of y')
Mhat=input('MA model order = ');
bhat=mafun(y,Mhat)