/usr/share/octave/packages/signal-1.3.2/filtfilt.m is in octave-signal 1.3.2-5.
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 | ## Copyright (C) 1999 Paul Kienzle <pkienzle@users.sf.net>
## Copyright (C) 2007 Francesco Potortì <pot@gnu.org>
## Copyright (C) 2008 Luca Citi <lciti@essex.ac.uk>
##
## 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{y} =} filtfilt (@var{b}, @var{a}, @var{x})
##
## Forward and reverse filter the signal. This corrects for phase
## distortion introduced by a one-pass filter, though it does square the
## magnitude response in the process. That's the theory at least. In
## practice the phase correction is not perfect, and magnitude response
## is distorted, particularly in the stop band.
##
## Example
## @example
## @group
## [b, a]=butter(3, 0.1); # 5 Hz low-pass filter
## t = 0:0.01:1.0; # 1 second sample
## x=sin(2*pi*t*2.3)+0.25*randn(size(t)); # 2.3 Hz sinusoid+noise
## y = filtfilt(b,a,x); z = filter(b,a,x); # apply filter
## plot(t,x,';data;',t,y,';filtfilt;',t,z,';filter;')
## @end group
## @end example
## @end deftypefn
## FIXME: My version seems to have similar quality to matlab,
## but both are pretty bad. They do remove gross lag errors, though.
function y = filtfilt(b, a, x)
if (nargin != 3)
print_usage;
endif
rotate = (size(x,1)==1);
if rotate, # a row vector
x = x(:); # make it a column vector
endif
lx = size(x,1);
a = a(:).';
b = b(:).';
lb = length(b);
la = length(a);
n = max(lb, la);
lrefl = 3 * (n - 1);
if la < n, a(n) = 0; endif
if lb < n, b(n) = 0; endif
## Compute a the initial state taking inspiration from
## Likhterov & Kopeika, 2003. "Hardware-efficient technique for
## minimizing startup transients in Direct Form II digital filters"
kdc = sum(b) / sum(a);
if (abs(kdc) < inf) # neither NaN nor +/- Inf
si = fliplr(cumsum(fliplr(b - kdc * a)));
else
si = zeros(size(a)); # fall back to zero initialization
endif
si(1) = [];
for (c = 1:size(x,2)) # filter all columns, one by one
v = [2*x(1,c)-x((lrefl+1):-1:2,c); x(:,c);
2*x(end,c)-x((end-1):-1:end-lrefl,c)]; # a column vector
## Do forward and reverse filtering
v = filter(b,a,v,si*v(1)); # forward filter
v = flipud(filter(b,a,flipud(v),si*v(end))); # reverse filter
y(:,c) = v((lrefl+1):(lx+lrefl));
endfor
if (rotate) # x was a row vector
y = rot90(y); # rotate it back
endif
endfunction
%!error filtfilt ();
%!error filtfilt (1, 2, 3, 4);
%!test
%! randn('state',0);
%! r = randn(1,200);
%! [b,a] = butter(10, [.2, .25]);
%! yfb = filtfilt(b, a, r);
%! assert (size(r), size(yfb));
%! assert (mean(abs(yfb)) < 1e3);
%! assert (mean(abs(yfb)) < mean(abs(r)));
%! ybf = fliplr(filtfilt(b, a, fliplr(r)));
%! assert (mean(abs(ybf)) < 1e3);
%! assert (mean(abs(ybf)) < mean(abs(r)));
%!test
%! randn('state',0);
%! r = randn(1,1000);
%! s = 10 * sin(pi * 4e-2 * (1:length(r)));
%! [b,a] = cheby1(2, .5, [4e-4 8e-2]);
%! y = filtfilt(b, a, r+s);
%! assert (size(r), size(y));
%! assert (mean(abs(y)) < 1e3);
%! assert (corr(s(250:750), y(250:750)) > .95)
%! [b,a] = butter(2, [4e-4 8e-2]);
%! yb = filtfilt(b, a, r+s);
%! assert (mean(abs(yb)) < 1e3);
%! assert (corr(y, yb) > .99)
%!test
%! randn('state',0);
%! r = randn(1,1000);
%! s = 10 * sin(pi * 4e-2 * (1:length(r)));
%! [b,a] = butter(2, [4e-4 8e-2]);
%! y = filtfilt(b, a, [r.' s.']);
%! yr = filtfilt(b, a, r);
%! ys = filtfilt(b, a, s);
%! assert (y, [yr.' ys.']);
%! y2 = filtfilt(b.', a.', [r.' s.']);
%! assert (y, y2);
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