--- /dev/null
+## 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/>.
+
+## usage: y = filtfilt(b, a, 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
+## [b, a]=butter(3, 0.1); % 10 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;')
+
+
+## TODO: (pkienzle) 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;
+ end
+ 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; end
+ if lb < n, b(n) = 0; end
+
+ ## 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
+ end
+ 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);
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff