function [a,e,V,FPE]=arlsfb(x,p)
% All-Pole (AR) modeling using No-Windowing
% forward-backward linear least-squares
% Model parameters [1 a1...ap V]
% V=input signal variance.
% FPE=Akaike's final prediction error criterion
%
% Programmed by: Dimitris Manolakis, 16/3/94
% same as lsfblp.m, which uses "fast" covariance computation.
%
%-----------------------------------------------------------
% Copyright 2000, by Dimitris G. Manolakis, Vinay K. Ingle,
% and Stephen M. Kogon.  For use with the book
% "Statistical and Adaptive Signal Processing"
% McGraw-Hill Higher Education.
%-----------------------------------------------------------


Lx=length(x);
R=zeros(p,p);
d=zeros(p,1);
R1=zeros(p+1,p+1);

for n=p+1:Lx
   s=x(n-p:n);
   R1=R1+s*s';
end

R1=fliplr(flipud(R1))+R1;


R=R1(2:p+1,2:p+1);
d=-R1(2:p+1,1);

c=R\d;

a=[1 c(1:p)']';

e=filter(a,1,x);

for n=1:p e(n)=0; end;

V=(e'*e)/(Lx-p);
FPE=V*(1+p/Lx)/(1-p/Lx);