function [a,err] = mcov(x,p)
%MCOV	All-pole signal modeling using the modified covariance method.
%----
%USAGE	[a,err] = mcov(x,p) 
%
%	An all-pole of order p is found for the input sequence x using
%	the modified covariance method.  The model is of the form
%		H(z) = b(0)/A(z) 
%	The coefficients of A(z) are returned in the vector
%		a=[1, a(1), ... a(p)]
%	and the modeling error is returned in err.
%
%  See also:  FCOV, COVM, and BURG
%
%---------------------------------------------------------------
% copyright 1996, by M.H. Hayes.  For use with the book 
% "Statistical Digital Signal Processing and Modeling"
% (John Wiley & Sons, 1996).
%---------------------------------------------------------------
%

x   = x(:);
N   = length(x);
if p>=length(x), error('Model order too large'), end
X   = toeplitz(x(p+1:N),flipud(x(1:p+1)));
R   = X'*X;
R1  = R(2:p+1,2:p+1);
R2  = flipud(fliplr(R(1:p,1:p)));
b1  = R(2:p+1,1);
b2  = flipud(R(1:p,p+1));
a   = [1 ; -(R1+R2)\(b1+b2)];
err = R(1,:)*a+fliplr(R(p+1,:))*a;
end;



