--- /dev/null
+## Copyright (C) 1999 Paul Kienzle <pkienzle@users.sf.net>
+## Copyright (C) 2003 Doug Stewart <dastew@sympatico.ca>
+## Copyright (C) 2011 Alexander Klein <alexander.klein@math.uni-giessen.de>
+##
+## 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/>.
+
+## Generate a butterworth filter.
+## Default is a discrete space (Z) filter.
+##
+## [b,a] = butter(n, Wc)
+## low pass filter with cutoff pi*Wc radians
+##
+## [b,a] = butter(n, Wc, 'high')
+## high pass filter with cutoff pi*Wc radians
+##
+## [b,a] = butter(n, [Wl, Wh])
+## band pass filter with edges pi*Wl and pi*Wh radians
+##
+## [b,a] = butter(n, [Wl, Wh], 'stop')
+## band reject filter with edges pi*Wl and pi*Wh radians
+##
+## [z,p,g] = butter(...)
+## return filter as zero-pole-gain rather than coefficients of the
+## numerator and denominator polynomials.
+##
+## [...] = butter(...,'s')
+## return a Laplace space filter, W can be larger than 1.
+##
+## [a,b,c,d] = butter(...)
+## return state-space matrices
+##
+## References:
+##
+## Proakis & Manolakis (1992). Digital Signal Processing. New York:
+## Macmillan Publishing Company.
+
+function [a, b, c, d] = butter (n, W, varargin)
+
+ if (nargin>4 || nargin<2) || (nargout>4 || nargout<2)
+ print_usage;
+ end
+
+ ## interpret the input parameters
+ if (!(length(n)==1 && n == round(n) && n > 0))
+ error ("butter: filter order n must be a positive integer");
+ end
+
+ stop = 0;
+ digital = 1;
+ for i=1:length(varargin)
+ switch varargin{i}
+ case 's', digital = 0;
+ case 'z', digital = 1;
+ case { 'high', 'stop' }, stop = 1;
+ case { 'low', 'pass' }, stop = 0;
+ otherwise, error ("butter: expected [high|stop] or [s|z]");
+ endswitch
+ endfor
+
+
+ [r, c]=size(W);
+ if (!(length(W)<=2 && (r==1 || c==1)))
+ error ("butter: frequency must be given as w0 or [w0, w1]");
+ elseif (!(length(W)==1 || length(W) == 2))
+ error ("butter: only one filter band allowed");
+ elseif (length(W)==2 && !(W(1) < W(2)))
+ error ("butter: first band edge must be smaller than second");
+ endif
+
+ if ( digital && !all(W >= 0 & W <= 1))
+ error ("butter: critical frequencies must be in (0 1)");
+ elseif ( !digital && !all(W >= 0 ))
+ error ("butter: critical frequencies must be in (0 inf)");
+ endif
+
+ ## Prewarp to the band edges to s plane
+ if digital
+ T = 2; # sampling frequency of 2 Hz
+ W = 2/T*tan(pi*W/T);
+ endif
+
+ ## Generate splane poles for the prototype butterworth filter
+ ## source: Kuc
+ C = 1; # default cutoff frequency
+ pole = C*exp(1i*pi*(2*[1:n] + n - 1)/(2*n));
+ if mod(n,2) == 1, pole((n+1)/2) = -1; end # pure real value at exp(i*pi)
+ zero = [];
+ gain = C^n;
+
+ ## splane frequency transform
+ [zero, pole, gain] = sftrans(zero, pole, gain, W, stop);
+
+ ## Use bilinear transform to convert poles to the z plane
+ if digital
+ [zero, pole, gain] = bilinear(zero, pole, gain, T);
+ endif
+
+ ## convert to the correct output form
+ if nargout==2,
+ a = real(gain*poly(zero));
+ b = real(poly(pole));
+ elseif nargout==3,
+ a = zero;
+ b = pole;
+ c = gain;
+ else
+ ## output ss results
+ [a, b, c, d] = zp2ss (zero, pole, gain);
+ endif
+
+endfunction
+
+%!shared sf, sf2, off_db
+%! off_db = 0.5;
+%! ##Sampling frequency must be that high to make the low pass filters pass.
+%! sf = 6000; sf2 = sf/2;
+%! data=[sinetone(5,sf,10,1),sinetone(10,sf,10,1),sinetone(50,sf,10,1),sinetone(200,sf,10,1),sinetone(400,sf,10,1)];
+
+%!test
+%! ##Test low pass order 1 with 3dB @ 50Hz
+%! data=[sinetone(5,sf,10,1),sinetone(10,sf,10,1),sinetone(50,sf,10,1),sinetone(200,sf,10,1),sinetone(400,sf,10,1)];
+%! [b, a] = butter ( 1, 50 / sf2 );
+%! filtered = filter ( b, a, data );
+%! damp_db = 20 * log10 ( max ( filtered ( end - sf : end, : ) ) );
+%! assert ( [ damp_db( 4 ) - damp_db( 5 ), damp_db( 1 : 3 ) ], [ 6 0 0 -3 ], off_db )
+
+%!test
+%! ##Test low pass order 4 with 3dB @ 50Hz
+%! data=[sinetone(5,sf,10,1),sinetone(10,sf,10,1),sinetone(50,sf,10,1),sinetone(200,sf,10,1),sinetone(400,sf,10,1)];
+%! [b, a] = butter ( 4, 50 / sf2 );
+%! filtered = filter ( b, a, data );
+%! damp_db = 20 * log10 ( max ( filtered ( end - sf : end, : ) ) );
+%! assert ( [ damp_db( 4 ) - damp_db( 5 ), damp_db( 1 : 3 ) ], [ 24 0 0 -3 ], off_db )
+
+%!test
+%! ##Test high pass order 1 with 3dB @ 50Hz
+%! data=[sinetone(5,sf,10,1),sinetone(10,sf,10,1),sinetone(50,sf,10,1),sinetone(200,sf,10,1),sinetone(400,sf,10,1)];
+%! [b, a] = butter ( 1, 50 / sf2, "high" );
+%! filtered = filter ( b, a, data );
+%! damp_db = 20 * log10 ( max ( filtered ( end - sf : end, : ) ) );
+%! assert ( [ damp_db( 2 ) - damp_db( 1 ), damp_db( 3 : end ) ], [ 6 -3 0 0 ], off_db )
+
+%!test
+%! ##Test high pass order 4 with 3dB @ 50Hz
+%! data=[sinetone(5,sf,10,1),sinetone(10,sf,10,1),sinetone(50,sf,10,1),sinetone(200,sf,10,1),sinetone(400,sf,10,1)];
+%! [b, a] = butter ( 4, 50 / sf2, "high" );
+%! filtered = filter ( b, a, data );
+%! damp_db = 20 * log10 ( max ( filtered ( end - sf : end, : ) ) );
+%! assert ( [ damp_db( 2 ) - damp_db( 1 ), damp_db( 3 : end ) ], [ 24 -3 0 0 ], off_db )
+
+%!demo
+%! sf = 800; sf2 = sf/2;
+%! data=[[1;zeros(sf-1,1)],sinetone(25,sf,1,1),sinetone(50,sf,1,1),sinetone(100,sf,1,1)];
+%! [b,a]=butter ( 1, 50 / sf2 );
+%! filtered = filter(b,a,data);
+%!
+%! clf
+%! subplot ( columns ( filtered ), 1, 1)
+%! plot(filtered(:,1),";Impulse response;")
+%! subplot ( columns ( filtered ), 1, 2 )
+%! plot(filtered(:,2),";25Hz response;")
+%! subplot ( columns ( filtered ), 1, 3 )
+%! plot(filtered(:,3),";50Hz response;")
+%! subplot ( columns ( filtered ), 1, 4 )
+%! plot(filtered(:,4),";100Hz response;")
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff