sos2zp.m

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function [z,p,k] = sos2zp(sos)
%SOS2ZP Second-order sections to zero-pole-gain linear system model conversion
%   [Z,P,K] = SOS2ZP(SOS) returns the zeros Z, poles P and gain K of the
%   system given by SOS in second-order sections form.  SOS is an L by 6 
%   matrix which contains the coefficients of each second-order section
%   in its rows:
%       SOS = [ b01 b11 b21  a01 a11 a21 
%               b02 b12 b22  a02 a12 a22
%               ...
%               b0L b1L b2L  a0L a1L a2L ]
%   The system transfer function is the product of the second-order transfer
%   functions of the sections.  Each row of the SOS matrix describes
%   a 2nd order transfer function as
%       b0k +  b1k z^-1 +  b2k  z^-2
%       ----------------------------
%       a0k +  a1k z^-1 +  a2k  z^-2
%   where k is the row index.
%
%   See also ZP2SOS, SOS2TF, SOS2SS, SS2SOS

%   Author(s): T. Krauss, 1993
%   Copyright (c) 1988-98 by The MathWorks, Inc.
%   $Revision: 1.7 $  $Date: 1997/11/26 20:13:06 $
 
if nargin ~= 1,
    error('Requires one input argument.')
end

L = size(sos,1);
z = []; p = [];
for i=1:L,
    z = [z; roots(sos(i,[1 2 3]))];
    p = [p; roots(sos(i,[4 5 6]))];
end

if nargout == 3,
    k = prod(sos(:,1)./sos(:,4));
end