/usr/share/octave/packages/signal-1.3.0/sos2zp.m is in octave-signal 1.3.0-1.
This file is owned by root:root, with mode 0o644.
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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 | ## 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{k}] =} sos2zp (@var{sos})
## @deftypefnx {Function File} {[@var{z}, @var{p}, @var{k}] =} sos2zp (@var{sos}, @var{g})
## 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:
## @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.
##
## @item
## @var{g} is an overall gain factor that effectively scales
## any one of the input @var{B}i vectors.
## If not given the gain is assumed to be 1.
## @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{k} = overall gain = @var{B}(Inf)
## @end itemize
##
## EXAMPLE:
## @example
## [z, p, k] = sos2zp ([1 0 1, 1 0 -0.81; 1 0 0, 1 0 0.49])
## @result{} z = [i; -i; 0; 0]
## @result{} p = [0.9, -0.9, 0.7i, -0.7i]
## @result{} k = 1
## @end example
##
## @seealso{zp2sos, sos2tf, tf2sos, zp2tf, tf2zp}
## @end deftypefn
function [z,p,k] = sos2zp (sos, g = 1)
if (nargin < 1 || nargin > 2)
print_usage;
endif
gains = sos(:,1); # All b0 coeffs
k = prod(gains)*g; # pole-zero gain
if k==0, error('sos2zp: one or more section gains is zero'); endif
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'); endif
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;
endfor
endfunction
%!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);
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