Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / signal-1.1.3 / sos2zp.m

diff --git a/octave_packages/signal-1.1.3/sos2zp.m b/octave_packages/signal-1.1.3/sos2zp.m
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+%% Copyright (C) 2005 Julius O. Smith III <jos@ccrma.stanford.edu>
+%%
+%% This program is free software; you can redistribute it and/or modify it under
+%% the terms of the GNU General Public License as published by the Free Software
+%% Foundation; either version 3 of the License, or (at your option) any later
+%% version.
+%%
+%% This program is distributed in the hope that it will be useful, but WITHOUT
+%% ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+%% FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
+%% details.
+%%
+%% You should have received a copy of the GNU General Public License along with
+%% this program; if not, see <http://www.gnu.org/licenses/>.
+
+%% -*- texinfo -*-
+%% @deftypefn {Function File} {[@var{z}, @var{p}, @var{g}] =} sos2zp (@var{sos}, @var{Bscale})
+%% Convert series second-order sections to zeros, poles, and gains
+%% (pole residues).
+%%
+%% INPUTS:@*
+%% @itemize
+%%
+%% @item
+%% @var{sos} = matrix of series second-order sections, one per row:@*
+%% @var{sos} = [@var{B1}.' @var{A1}.'; ...; @var{BN}.' @var{AN}.'], where@*
+%% @code{@var{B1}.'==[b0 b1 b2] and @var{A1}.'==[1 a1 a2]} for 
+%% section 1, etc.@*
+%% b0 must be nonzero for each section.
+%% See @code{filter()} for documentation of the
+%% second-order direct-form filter coefficients @var{B}i and @var{A}i.
+%%
+%% @item
+%% @var{Bscale} is an overall gain factor that effectively scales
+%% any one of the input @var{B}i vectors.
+%% @end itemize
+%%
+%% RETURNED:
+%%   @itemize
+%%   @item
+%%   @var{z} = column-vector containing all zeros (roots of B(z))@*
+%%   @item
+%%   @var{p} = column-vector containing all poles (roots of A(z))@*
+%%   @item
+%%   @var{g} = overall gain = @var{B}(Inf)
+%%   @end itemize
+%% 
+%% EXAMPLE:
+%% @example
+%%   [z,p,g] = sos2zp([1 0 1, 1 0 -0.81; 1 0 0, 1 0 0.49])
+%%   => z = [i; -i; 0; 0], p = [0.9, -0.9, 0.7i, -0.7i], g=1
+%% @end example
+%%
+%% @seealso{zp2sos sos2tf tf2sos zp2tf tf2zp}
+%% @end deftypefn
+
+function [z,p,g] = sos2zp (sos, Bscale = 1)
+
+  if (nargin < 1 || nargin > 2)
+    print_usage;
+  endif
+
+  gains = sos(:,1); % All b0 coeffs
+  g = prod(gains)*Bscale; % pole-zero gain
+  if g==0, error('sos2zp: one or more section gains is zero'); end
+  sos(:,1:3) = sos(:,1:3)./ [gains gains gains];
+
+  [N,m] = size(sos);
+  if m~=6, error('sos2zp: sos matrix should be N by 6'); end
+
+  z = zeros(2*N,1);
+  p = zeros(2*N,1);
+  for i=1:N
+    ndx = [2*i-1:2*i];
+    zi = roots(sos(i,1:3));
+    z(ndx) = zi;
+    pi = roots(sos(i,4:6));
+    p(ndx) = pi;
+  end
+end
+
+%!test 
+%! b1t=[1 2 3]; a1t=[1 .2 .3]; 
+%! b2t=[4 5 6]; a2t=[1 .4 .5];
+%! sos=[b1t a1t; b2t a2t];
+%! z = [-1-1.41421356237310i;-1+1.41421356237310i;...
+%!     -0.625-1.05326872164704i;-0.625+1.05326872164704i];
+%! p = [-0.2-0.678232998312527i;-0.2+0.678232998312527i;...
+%!      -0.1-0.538516480713450i;-0.1+0.538516480713450i];
+%! k = 4;
+%! [z2,p2,k2] = sos2zp(sos,1);
+%! assert({cplxpair(z2),cplxpair(p2),k2},{z,p,k},100*eps);