function f=a_to_lsf(a);
% Syntax: f=a_to_lsf(a);
%
% Computes Line Spectrum Frenquencies from LPC coefficients. 
% a is the vector of LPC coefficients of dimension M+1. [1 a1 a2 ... aM]
% f is the vector of M normalized frequencies (Fe=1) of significant zeros of 
%  2 following polynomes:
%    P(z)=A(z)-B(z) 
%    Q(z)=A(z)+B(z),   where B(z)=z^-(M+1) A(z^-1)  (flippen and shifted A(z) ).
% Significant means, that the zero at f=0 and f=1/2 are not taken into account.
% a and f are COLUMN vectors

M=length(a)-1;

a=[a; 0];
p=a-a(M+2:-1:1);
q=a+a(M+2:-1:1);

rp=roots(p);
rq=roots(q);

lp=sort(angle(rp)); 
lq=sort(angle(rq)); 
if M/2 == floor(M/2),	% M even - P has zero at f=0, Q has zero at f=1/2:
  lp=lp(M/2+2:M+1);% coupe les lp negatives et zero
  lq=lq(M/2+1:M);  % coupe les lp negatives et pi
else			% M odd - P has zeros at f=0 and f=1/2
  lp=lp((M+1)/2+1:M);% coupe les lp negatives, zero et 1/2
  lq=lq((M+1)/2+1:M+1);  % coupe les lp negatives 
end
  
f=sort ([lp; lq]) / (2*pi);