/usr/share/octave/packages/signal-1.3.2/zp2sos.m is in octave-signal 1.3.2-1+b1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 | ## 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})
## @deftypefnx {Function File} {[@var{sos}, @var{g}] =} zp2sos (@var{z}, @var{p})
## @deftypefnx {Function File} {[@var{sos}, @var{g}] =} zp2sos (@var{z}, @var{p}, @var{k})
## @deftypefnx {Function File} {@var{sos} =} zp2sos (@dots{})
## 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{k} = overall filter gain factor
## If not given the gain is assumed to be 1.
## @end itemize
##
## RETURNED:
## @itemize
## @item
## @var{sos} = matrix of series second-order sections, one per row:
## @example
## @var{sos} = [@var{B1}.' @var{A1}.'; ...; @var{BN}.' @var{AN}.']
## @end example
## where
## @code{@var{B1}.' = [b0 b1 b2] and @var{A1}.' = [1 a1 a2]} for
## section 1, etc. The b0 entry 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{g} is the overall gain factor that effectively scales
## any one of the @var{B}i vectors.
## @end itemize
##
## If called with only one output argument, the overall filter gain is
## applied to the first second-order section in the matrix @var{sos}.
##
## EXAMPLE:
## @example
## [z, p, k] = tf2zp ([1 0 0 0 0 1], [1 0 0 0 0 .9]);
## [sos, g] = zp2sos (z, p, k)
##
## 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,k)
if nargin<3, k=1; endif
if nargin<2, p=[]; endif
[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; endif
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;
endif
## Pair up real poles:
if npr
if mod(npr,2)==1, pr=[pr;0]; npr=npr+1; endif
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;
endif
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)];
endif
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)];
endif
endfor
## If no output argument for the overall gain, combine it into the
## first section.
if (nargout < 2)
sos(1,1:3) *= k;
else
g = k;
endif
endfunction
%!test
%! B=[1 0 0 0 0 1]; A=[1 0 0 0 0 .9];
%! [z,p,k] = tf2zp(B,A);
%! [sos,g] = zp2sos(z,p,k);
%! [Bh,Ah] = sos2tf(sos,g);
%! assert({Bh,Ah},{B,A},100*eps);
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