function [B_min,A_min,B_all,A_all] = f_minall (b,a)

%F_MINALL: Factor filter into minimum-phase and allpass parts
%
% Usage: [B_min,A_min,B_all,A_all] = f_minall (b,a)
%        
% Inputs: 
%         b   = vector of length m+1 containing coefficients 
%               of numerator polynomial.
%         a   = vector of length n+1 containing coefficients
%               of denominator polynomial (n >= m).
% Outputs: 
%          B_min = (q+1) by 1 vector containing numerator 
%                  coefficients of minimum-phase part  
%          A_min = (r+1) by 1 vector containing denominator
%                  coefficients of minimum-phase part  
%          B_all = (s+1) by 1 vector containing numerator 
%                  coefficients of allpass part  
%          A_all = (s+1) by 1 vector containing denominator
%                  coefficients of allpass part  
%
% See also:
%           F_PZPLOT

% Initialize

b0 = b(1);
z = roots(b)
m = length(z);
B_all = 1;
A_all = 1;
B_min = f_torow(b);
A_min = f_torow(a);

% Decompose into minimum-phase and allpass parts

for i = 1 : m
   if abs(z(i)) > 1
      Fb = [-z(i) 1];
      Fa = [1 -z(i)];
      [B_min,R] = deconv (B_min,Fa);
      B_min = conv (B_min,Fb);
      B_all = conv (B_all,Fa);
      A_all = conv (A_all,Fb);
   end
end

% Finalize

B_all = B_all/A_all(1);
A_all = A_all/A_all(1);