gtor.m

solution for the Statistical modelling for digital signal processing by hayes

function r=gtor(gamma,epsilon)

%GTOR	Inverse Levinson-Durbin recursion.

%----

%USAGE: r=gtor(gamma,epsilon)

%

%	Finds the autocorrelation sequence r(k) from the 

%	reflection coefficients gamma.  If the optional input

%	epsilon is omitted,

%		r=gtor(gamma)

%	then the autocorrelation sequence is normalized so 

%	that r(0)=1.

%

%  see also ATOG, ATOR, GTOA, RTOA, RTOG

%

%---------------------------------------------------------------

% copyright 1996, by M.H. Hayes.  For use with the book 

% "Statistical Digital Signal Processing and Modeling"

% (John Wiley & Sons, 1996).

%---------------------------------------------------------------



   p=length(gamma);

   aa=gamma(1);

   r=[1 -gamma(1)];

   for j=2:p;

      aa=[aa;0]+gamma(j)*[conj(flipud(aa));1];

      r=[r -fliplr(r)*aa];

      end;

   if nargin == 2,

   r = r*epsilon/prod(1-abs(gamma).^2);

   end;