function C=a_to_cepst(A,NBC);
% COnversion of LPC coefficints to LPC cepstra
%
% Syntax: C=a_to_cepst(A)
%      or C=a_to_cepst(A,NBC)
%
% A is matrix with a vector of P+1 LPC coefficients n each column (including
%    a0=1): [1 a(1) a(2) ... a(P)]'
% NBC is the desired number of LPCC coefficients without c0. (default P)
% C is the matrix with vector of LPCC coefficients (without c0) in each 
%    column: [c(1) c(2) ... c(NBC)]'

[P_1, Nram] = size(A);
P=P_1 - 1;

if nargin==1,
 NBC=P;
end
 
C=zeros(NBC, Nram);
for ii=1:Nram,
  a=A(:,ii);  
  c=zeros(NBC,1);                       % initialization of cps vector
  ahelp=[a; zeros(NBC-length(a)+1,1)];  % "prolongation" of  a
  c(1)=-ahelp(2); 

  for n=2:NBC,
    divis=(1:n-1)/n;
    som=divis*(c(1:(n-1)).*ahelp(n:-1:2));   % "vectorised" sum
    c(n)=-ahelp(n+1)-som; 
  end					% one vector ready
  C(:,ii) = c;
end                                     % all vectors ready