function a=lsf_to_a(f);
% Syntax: a=lsf_to_a(f);
%
% Computes prediction coefficients from Line Spectral Frequencies (LSF)
% f is the vector of P normalized frequencies (Fe=1), where P is the
% order of the polynomial A(z)=[1 a1 a2 ... aP].
% Vector a has P+1 elements (contains a0=1).
% Vectors f and a are COLUMN

M=length(f);

if (M/2)==floor(M/2),		% M even - P and Q will have odd no. of roots,
				% in addition to f, P will have root at 0,
				% Q at 1/2.
  fq=f(1:2:M-1); fq=[-fq; 0.5; fq];  % Q will have the 1st freq from f
  fp=f(2:2:M);   fp=[-fp; 0  ; fp];  % P will have the 2nd 
else				% M odd - P and Q will have even no. of roots.	
				% P will have additional roots at 0 and 1/2,
				% Q is taking more frequencies from f
  fq=f(1:2:M); fq=[-fq; fq];    % Q will have the 1st freq from f, no other
  fp=f(2:2:M-1);   fp=[-fp; 0; fp; 0.5];  
  				% P will have the 2nd, additional at 0 and 1/2
end

fp=fp*2*pi; fq=fq*2*pi;		% denormalize
rp=exp(i*fp); rq=exp(i*fq);	% roots
%[rp rq]
P=real(poly(rp))'; Q=real(poly(rq))';		% polynomials
%[P Q]
a=(P+Q)/2; 
a=a(1:M+1);		% a must be shortened