/usr/share/octave/packages/signal-1.3.0/filtic.m is in octave-signal 1.3.0-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 | ## Copyright (C) 2004 David Billinghurst <David.Billinghurst@riotinto.com>
##
## 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{zf} =} filtic (@var{b}, @var{a}, @var{y})
## @deftypefnx {Function File} {@var{zf} =} filtic (@var{b}, @var{a}, @var{y}, @var{x})
##
## Set initial condition vector for filter function
## The vector zf has the same values that would be obtained
## from function filter given past inputs x and outputs y
##
## The vectors x and y contain the most recent inputs and outputs
## respectively, with the newest values first:
##
## x = [x(-1) x(-2) ... x(-nb)], nb = length(b)-1
## y = [y(-1) y(-2) ... y(-na)], na = length(a)-a
##
## If length(x)<nb then it is zero padded
## If length(y)<na then it is zero padded
##
## zf = filtic(b, a, y)
## Initial conditions for filter with coefficients a and b
## and output vector y, assuming input vector x is zero
##
## zf = filtic(b, a, y, x)
## Initial conditions for filter with coefficients a and b
## input vector x and output vector y
## @end deftypefn
function zf = filtic(b,a,y,x)
if (nargin>4 || nargin<3) || (nargout>1)
print_usage;
endif
if nargin < 4, x = []; endif
nz = max(length(a)-1,length(b)-1);
zf=zeros(nz,1);
## Pad arrays a and b to length nz+1 if required
if length(a)<(nz+1)
a(length(a)+1:nz+1)=0;
endif
if length(b)<(nz+1)
b(length(b)+1:nz+1)=0;
endif
## Pad arrays x and y to length nz if required
if length(x) < nz
x(length(x)+1:nz)=0;
endif
if length(y) < nz
y(length(y)+1:nz)=0;
endif
for i=nz:-1:1
for j=i:nz-1
zf(j) = b(j+1)*x(i) - a(j+1)*y(i)+zf(j+1);
endfor
zf(nz)=b(nz+1)*x(i)-a(nz+1)*y(i);
endfor
endfunction
%!test
%! ## Simple low pass filter
%! b=[0.25 0.25];
%! a=[1.0 -0.5];
%! zf_ref=0.75;
%! zf=filtic(b,a,[1.0],[1.0]);
%! assert(zf,zf_ref,8*eps);
%!
%!test
%! ## Simple high pass filter
%! b=[0.25 -0.25];
%! a=[1.0 0.5];
%! zf_ref = [-0.25];
%! zf=filtic(b,a,[0.0],[1.0]);
%! assert(zf,zf_ref,8*eps);
%!
%!test
%! ## Second order cases
%! [b,a]=butter(2,0.4);
%! N=1000; ## Long enough for filter to settle
%! xx=ones(1,N);
%! [yy,zf_ref] = filter(b,a,xx);
%! x=xx(N:-1:N-1);
%! y=yy(N:-1:N-1);
%! zf = filtic(b,a,y,x);
%! assert(zf,zf_ref,8*eps);
%!
%! xx = cos(2*pi*linspace(0,N-1,N)/8);
%! [yy,zf_ref] = filter(b,a,xx);
%! x=xx(N:-1:N-1);
%! y=yy(N:-1:N-1);
%! zf = filtic(b,a,y,x);
%! assert(zf,zf_ref,8*eps);
%!
%!test
%! ## Third order filter - takes longer to settle
%! N=10000;
%! [b,a]=cheby1(3,10,0.5);
%! xx=ones(1,N);
%! [yy,zf_ref] = filter(b,a,xx);
%! x=xx(N:-1:N-2);
%! y=yy(N:-1:N-2);
%! zf = filtic(b,a,y,x);
%! assert(zf,zf_ref,8*eps);
%!
%!test
%! ## Eight order high pass filter
%! N=10000;
%! [b,a]=butter(8,0.2);
%! xx = cos(2*pi*linspace(0,N-1,N)/8);
%! [yy,zf_ref] = filter(b,a,xx);
%! x=xx(N:-1:N-7);
%! y=yy(N:-1:N-7);
%! zf = filtic(b,a,y,x);
%! assert(zf,zf_ref,8*eps);
%!
%!test
%! ## Case with 3 args
%! [b,a]=butter(2,0.4);
%! N=100;
%! xx=[ones(1,N) zeros(1,2)];
%! [yy,zf_ref] = filter(b,a,xx);
%! y=[yy(N+2) yy(N+1)];
%! zf=filtic(b,a,y);
%! assert(zf,zf_ref,8*eps);
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