function [a,epsilon]=rtoa(r)
%RTOA	Levinson-Durbin recursion.
%----
%USAGE:	[a,epsilon]=rtoa(r)
%
%	Solves the Toeplitz normal equations
%		R a = epsilon [1 0 ... 0]'
% 	where R=toeplitz(r) is a Toeplitz matrix that contains
%	the autocorrelation sequence r(k).  The ouputs are the
%	coefficients of the all-pole model a(k) and the constant
%	epsilon.
%
%  see also ATOG, ATOR, GTOA, GTOR, RTOG
%
%---------------------------------------------------------------
% copyright 1996, by M.H. Hayes.  For use with the book 
% "Statistical Digital Signal Processing and Modeling"
% (John Wiley & Sons, 1996).
%---------------------------------------------------------------

r=r(:);
p=length(r)-1;
a=1;
epsilon=r(1);
for j=2:p+1;
	gamma=-r(2:j)'*flipud(a)/epsilon;
	a=[a;0] + gamma*[0;conj(flipud(a))];
	epsilon=epsilon*(1 - abs(gamma)^2);
	end