--- /dev/null
+%% 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{sos}, @var{g}] =} zp2sos (@var{z}, @var{p})
+%% Convert filter poles and zeros to second-order sections.
+%%
+%% INPUTS:@*
+%% @itemize
+%% @item
+%% @var{z} = column-vector containing the filter zeros@*
+%% @item
+%% @var{p} = column-vector containing the filter poles@*
+%% @item
+%% @var{g} = overall filter gain factor
+%% @end itemize
+%%
+%% RETURNED:
+%% @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, i=1:N.
+%%
+%% @item
+%% @var{Bscale} is an overall gain factor that effectively scales
+%% any one of the @var{B}i vectors.
+%% @end itemize
+%%
+%% EXAMPLE:
+%% @example
+%% [z,p,g] = tf2zp([1 0 0 0 0 1],[1 0 0 0 0 .9]);
+%% [sos,g] = zp2sos(z,p,g)
+%%
+%% sos =
+%% 1.0000 0.6180 1.0000 1.0000 0.6051 0.9587
+%% 1.0000 -1.6180 1.0000 1.0000 -1.5843 0.9587
+%% 1.0000 1.0000 0 1.0000 0.9791 0
+%%
+%% g =
+%% 1
+%% @end example
+%%
+%% @seealso{sos2pz sos2tf tf2sos zp2tf tf2zp}
+%% @end deftypefn
+
+function [sos,g] = zp2sos(z,p,g)
+
+ if nargin<3, g=1; end
+ if nargin<2, p=[]; end
+
+ [zc,zr] = cplxreal(z);
+ [pc,pr] = cplxreal(p);
+
+ % zc,zr,pc,pr
+
+ nzc=length(zc);
+ npc=length(pc);
+
+ nzr=length(zr);
+ npr=length(pr);
+
+ % Pair up real zeros:
+ if nzr
+ if mod(nzr,2)==1, zr=[zr;0]; nzr=nzr+1; end
+ nzrsec = nzr/2;
+ zrms = -zr(1:2:nzr-1)-zr(2:2:nzr);
+ zrp = zr(1:2:nzr-1).*zr(2:2:nzr);
+ else
+ nzrsec = 0;
+ end
+
+ % Pair up real poles:
+ if npr
+ if mod(npr,2)==1, pr=[pr;0]; npr=npr+1; end
+ nprsec = npr/2;
+ prms = -pr(1:2:npr-1)-pr(2:2:npr);
+ prp = pr(1:2:npr-1).*pr(2:2:npr);
+ else
+ nprsec = 0;
+ end
+
+ nsecs = max(nzc+nzrsec,npc+nprsec);
+
+ % Convert complex zeros and poles to real 2nd-order section form:
+ zcm2r = -2*real(zc);
+ zca2 = abs(zc).^2;
+ pcm2r = -2*real(pc);
+ pca2 = abs(pc).^2;
+
+ sos = zeros(nsecs,6);
+ sos(:,1) = ones(nsecs,1); % all 2nd-order polynomials are monic
+ sos(:,4) = ones(nsecs,1);
+
+ nzrl=nzc+nzrsec; % index of last real zero section
+ nprl=npc+nprsec; % index of last real pole section
+
+ for i=1:nsecs
+
+ if i<=nzc % lay down a complex zero pair:
+ sos(i,2:3) = [zcm2r(i) zca2(i)];
+ elseif i<=nzrl % lay down a pair of real zeros:
+ sos(i,2:3) = [zrms(i-nzc) zrp(i-nzc)];
+ end
+
+ if i<=npc % lay down a complex pole pair:
+ sos(i,5:6) = [pcm2r(i) pca2(i)];
+ elseif i<=nprl % lay down a pair of real poles:
+ sos(i,5:6) = [prms(i-npc) prp(i-npc)];
+ end
+ end
+end
+
+%!test
+%! B=[1 0 0 0 0 1]; A=[1 0 0 0 0 .9];
+%! [z,p,g] = tf2zp(B,A);
+%! [sos,g] = zp2sos(z,p,g);
+%! [Bh,Ah] = sos2tf(sos,g);
+%! assert({Bh,Ah},{B,A},100*eps);
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff